Imaging aims to create a correspondence between the distribution of light in an object plane, in which the objects of interest are placed, and in an image plane, where a sensor measures intensity. An imaging device is characterized by resolution, which determines how sharp is the correspondence between the two conjugate planes, and depth of field, which fixes the longitudinal distance range in which the object can move, while its image is still well focused on the sensor. Unfortunately, a natural tradeoff between resolution and depth of field entails that focusing a high-resolution image is much harder than focusing a low-resolution one. Moreover, standard imaging devices are not able to recover information on the out-of-focus planes after the acquisition. The goal of plenoptic imaging is to overcome this limitation, by retrieving combined information on both the spatial distribution and the direction of light in the scene of interest, which opens the possibility to refocus planes of the scene in a much wider range than the natural depth of field of the system, and also to change the point of view on the scene. Though plenoptic imaging is one of the most promising techniques for 3D imaging, in all the devices based on intensity measurements its advantages come at the expense of spatial resolution, which can no longer reach its diffraction limit. In this paper, we review the possibility to avoid loss of resolution by integrating second-order intensity correlation measurements in a simple single-lens imaging setup. The described device, based on the correlation plenoptic imaging (CPI) technique, enables one to perform either standard or plenoptic imaging, while keeping the resolution at the diffraction limit. We show that the proposed setup outperforms both standard imaging and first-order plenoptic imaging in terms of resolution and depth of field.

Unravelling the mysteries of the complex neural network dynamics of the brain is of utmost importance to science as it might lead to a deeper understanding of perception, cognition and consciousness. Numerous techniques are being used for brain imaging including intracellular electrophysiology, calcium imaging and microelectrode arrays imaging. However, all these technologies are facing severe limitations in the spatio-temporal resolutions and are thus unable to resolve fast real-time single neuron activity over a larger area of the brain. I will discuss our recent efforts in developing a new technique for neuroscience that offer wide-field brain imaging with unprecedented spatio-temporal resolution. It is based on magnetic field sensing of the neuron activity using magneto-optically sensitive Nitrogen-Vacancy color centers in a diamond crystal combined with light microscopy.

Photonic Molecule, also called Photonic Dimer, is a quantum bound state of two photons. A photonic bound state has a specific entanglement of a Lorentzian anti-correlation in frequency space and two photons are in proximity due to its binding nature.Such signatures of a photonic molecule illuminates a potential tool that increases the two-photon microscopy efficiency to orders of magnitude higher. Here we numerically and analytically demonstrate the two-photon excitation efficiency between photonic molecules, long uncorrelated light pulses and ultrashort light pulses. The high excitation efficiency of a photonic molecule enables a saturation of fluorophores, such that the linear dependence of two-photon excitation crosssection does not necessarily hold. Also, we exhibits two possible methods to obtain the photonic molecules, as a fundamental possibility for a continuous photonic molecule source.

In the lore of quantum metrology, one often hears (or reads) the following no-go theorem: If you put a vacuum into one input port of a balanced Mach-Zehnder interferometer, then no matter what you put into the other input port, and no matter what your detection scheme, the sensitivity can never be better than the shot-noise limit (SNL). Often the proof of this theorem is cited to be in C. Caves, Phys. Rev. D 23, 1693 (1981), but upon further inspection, no such claim is made there. Quantum-Fisher-information-based arguments suggestive of this no-go theorem appear elsewhere in the literature, but are not stated in their full generality. Here we thoroughly explore this no-go theorem and give a rigorous statement: the no-go theorem holds whenever the unknown phase shift is split between both of the arms of the interferometer, but remarkably does not hold when only one arm has the unknown phase shift. In the latter scenario, we provide an explicit measurement strategy that beats the SNL. We also point out that these two scenarios are physically different and correspond to different types of sensing applications.

We study the problem of quantum temporal imaging in the case where the time lens is implemented by a sum frequency generation nonlinear process. We consider the general case where the time lens is characterized by a finite aperture and a not-perfect phase-matching in a regime close to 100% conversion efficiency. In particular we tackle this problem in term of the eigenmodes of the entire transformation of the field in the temporal imaging system. We show that in the case of modeling the phase-matching function by a double Gaussian the eigenmodes are given by chirped Gauss-Hermite functions. The effective number of involved eigenmodes is estimated as the ratio of the temporal aperture of the lens to the walk-off time of the signal and the idler waves in the nonlinear crystal. Our theoretical treatment allows us to identify the criteria for designing imaging schemes with close to unity efficiencies

Low-loss nano- and micro-photonic platforms provide strong optical confinement and as a result enhance the effective material nonlinearity by several orders of magnitude, making them appealing candidates for quantum nonlinear photonics. One such platform is based on high-Q crystalline whispering-gallery-mode (WGM) microresonators, which can provide for highly efficient three-wave mixing, where even a single photon has a strong effect. We present experimental progress on the fabrication of small microresonators (R⪅100 μm) with Q-factors ≥ 10⁶ that are capable of supporting such strong coupling. We also demonstrate direct imaging of the spatial profiles of the WGMs, which is useful for identifying the phase-matched resonances of three-wave-mixing processes. Additionally, we present theoretical modeling of the cavity dynamics which suggests that single-photon-driven nonlinear processes are feasible in these crystalline microresonators. This crystalline WGM microresonator platform, therefore, can enable deterministic generation of non-classical light, including entangling gates for quantum information processing.

We study transparent ceramics made of erbium doped yttria, as a candidate material for quantum storage of photons in the telecom wavelength. Samples with different heat processing conditions are compared. Two different species of Er³⁺ ions with drastically different dephasing properties are identified. In general, samples processed at lower temperature show narrower inhomogeneous and homogeneous linewidths. We also demonstrate both type I and type II waveguide in the material using a femtosecond laser, with propagation loss of 0.22 dB/mm.

Future quantum photonic networks require coherent optical memories, preferably operating at room temperature, for synchronizing quantum sources and gates of probabilistic nature. Until now, however, room-temperature atomic memories have suffered from an intrinsic read-out noise. Here we demonstrate a fast ladder memory (FLAME) mapping the optical field onto the superposition between electronic orbitals of rubidium vapor. Employing a ladder level-system of orbital transitions with nearly degenerate frequencies simultaneously enables high bandwidth, low noise, and long memory lifetime. We store and retrieve 1.7-ns-long pulses, containing 0.5 photons on average, and observe short-time external efficiency of 25%, memory lifetime (1/e) of 86 ns, and below 10⁻⁴ added noise photons. Consequently, coupling this memory to a probabilistic source would enhance the on-demand photon generation probability by a factor of 12, the highest number yet reported for a noise-free, room-temperature memory. This paves the way towards the controlled production of large quantum states of light from probabilistic photon sources.

Atomic ensembles in the form of rare-earth-doped crystals offer significant potential for implementing a quantum memory due to their long coherence lifetimes, enhanced light-matter interaction, and the potential for integration. We use a double Lambda configuration based on hyperfine levels in praseodymium doped yttrium orthosilicate. In this scheme, a probabilistically generated collective excitation of the internal atomic states in the form of a spin-wave is signaled by emission of a Stokes-shifted herald photon via spontaneous Raman scattering. After a storage delay, a read field addresses the appropriate transition, mapping the spin wave back to a photon, resulting in the emission of an anti-Stokes shifted retrieved photon. Momentum conservation, as dictated by phase-matching conditions, ensure that the herald and retrieved photons are emitted in a well-defined spatial modes relative to the co-propagating write and read optical fields. Inhomogeneous broadening of the absorption profile precludes straightforward implementation of the above scheme, and we resort to spectral hole-burning techniques to prepare a sub-ensemble of atoms with a narrow range of optical transition energy in the ground state. Using a second identical crystal, we also implement an optical spectral filter that suppresses the powerful write and read beams, and spontaneous-emission noise, while transmitting the herald and retrieved photons. We report on the second-order optical correlations between the herald and retrieved photons that are the signature of generation and retrieval of a stored spin-wave excitation. Demonstration of such a quantum memory is an enabling step towards distributing entanglement for a quantum repeater scheme.

New color centers are being discovered in diamond every year. For the most part these are guided by the desire to replace the silicon-vacancy (SiV) by emitters with higher quantum efficiency and longer storage times. I will discuss color centers produced by some of the most recently implanted elements into diamond including Ge, Sn, Pb, Mg. I will also discuss the rationale for elements to be implanted soon. Finally I will also discuss new options for the future, including designer color centers made possible by novel diamond growth techniques.

Silicon photonics promises scalable manufacturing of integrated photonic devices through utilization of established CMOS processing techniques and facilities. Unfortunately, the silicon photonics platform lacks a viable light source, which has historically been overcome through heterogeneous integration techniques. To further improve economic viability, the platform must transition to direct epitaxy on Si to bypass the scaling limits imposed by the small sizes and high cost of III-V substrates in heterogeneous integration. InAs quantum dots have demonstrated themselves as the most promising candidate for achieving high performance light emitters epitaxially grown on Si. Using molecular beam epitaxy, we have grown quantum dot lasers composed of InAs dot-in-a-well active layers on industry-standard, on-axis (001) Si substrates. In this report, we utilized p-doping of the quantum dot active region to increase gain for improved dynamic performance and reliability. These devices have been subjected to accelerated aging conditions at 60°C and a bias multiple of twice threshold current density. After 2,750 hours of continuous aging, an extrapolated lifetime of more than 100,000 hours has been calculated.

Long-distance quantum communication relies on the ability to efficiently generate and prepare single photons at telecom wavelengths. MBE grown single photon emitters in the telecom E-band produce indistinguishable photons in a range of configurations including photons emitted from different quantum dots that are in separate photonics structures. During growth, circular InAs quantum dots spontaneously form on InP surfaces during cooling of a planar InAs layer that is grown at an elevated temperature. Despite manipulation of the dot shape, brightness suffers at c-band wavelengths, which is evaluated using atomic resolution electron microscopy and attributed to extended defects forming in and around the larger dots.

There is ongoing research into information-theoretically secure digital signature schemes. Mathematically based approaches typically require additional resources such as anonymous broadcast and/or a trusted authority to achieve information-theoretical security. The principles of quantum mechanics can be applied to the problem to create the approach known as quantum digital signatures, which does not have these limitations. This presentation will provide an overview of the development of experimental quantum digital signatures. The evolution of experimental test-beds will be charted from small scale demonstrators to long distance implementations with commercial prototypes, along with overviews of the theoretical background of each stage.

We study Lambda-type electromagnetically induced transparency (EIT) in cryogenically-cooled, europium and praseodymium doped yttrium orthosilicate (Eu:YSO and Pr:YSO). We use spectral hole burning techniques to vary the optical inhomogeneous width of the sub-ensemble of atoms participating in the EIT. The effect of inhomogeneous broadening has been studied in the context of Doppler broadened gases, but less so in solids where motional effects are absent and the coherence is not limited by the transit of atoms through the optical field. Rare earth doped crystals, like many solid-state systems, exhibit spectral hole burning in which a narrowband laser field optically pumps atoms to states in the ground manifold that are dark with respect to the applied field, opening up a transparency window that persists after the pumping laser is shuttered. More complex sequences of fields at multiple frequencies can create arbitrary spectral profiles, within bounds set by the particular energy level structure of the atoms. For both Eu:YSO and Pr:YSO, there are three hyperfine ground states and three hyperfine excited states (at zero magnetic field) and all nine transitions are dipole-allowed with varying transition strengths. We use spectral hole-burning techniques to prepare a sub-ensemble of atoms in a particular frequency class and a particular ground spin state, while also pumping atoms out of another ground state to create a Lambda system. We observe the same functional dependence of the EIT width on the optical inhomogeneous width and independently calibrated control field Rabi frequency in both systems.

Quantum illumination is an attractive scheme for target detection utilizing quantum entanglement to improve error probability of discrimination for target presence or absence even in a lossy and noisy environment. In the quantum illumination with two-mode squeezed vacuum states, one of the entangled beams, a signal beam is transmitted towards a lossy optical medium. And the other beam, a reference beam is directly sent to receiver with a lossless channel. So, the entangled light beams are affected by the asymmetric optical loss. In this work we calculate the correlation variance of quadrature phase amplitudes of two-mode squeezed light under the asymmetric optical-loss conditions and discuss its non-classical correlation based on Duan’s and Simon’s inseparability criterion. The asymmetric optical loss sensitively increases the correlation variance and violates the inseparability criterion. In this work we consider asymmetric two-mode squeezed light as an initial state where the signal beam has larger quadrature phase amplitudes than the reference beam. After exposition to the asymmetric optical loss only the quadrature phase amplitudes of the signal beam is attenuated and become comparable to those of the reference beam. As a result it is expected that the asymmetric two-mode squeezed light has an ability to compensate the effect of the asymmetric optical loss and can maintain the inseparability criterion in the sense of Duan and Simon.

Accurate estimation of unknown quantum states using limited number of samples is very important but difficult task using fixed measurement basis states since the best local unbiased estimator (LUE) for estimating the parameter depends, in general, on the unknown parameter itself. In order to solve this problem, Nagaoka advocated an adaptive quantum state estimation (AQSE) procedure. Later, Fujiwara proved the strong consistency and asymptotic efficiency for AQSE. AQSE has been demonstrated by us for the linear polarizations of photons, and recently for a single polarization qubit. However, in order to apply AQSE to actual measurement including application to life science, we need to improve the speed of the system which is limited by the response time of the mechanical rotation stage used in the previous experiment [Phys. Rev. Lett. 109, 130404 (2012)]. To solve this problem, we realized high-speed AQSE experiment using liquid crystal retarder (LCR). We demonstrate the adaptive quantum state estimation using a LCR instead of a half wave plate on a mechanical rotator in previous research. We realized a substantial speed-up of estimation time, keeping the accuracy of estimation at the same level. In fact, it took 0.40 second per photon in the previous study, whereas 0.073 second per photon in the present. Specifically, the time to determine the polarization measurement basis was greatly decreased, from 0.34 second per photon in the previous study to 0.010 second per photon in the present.

Entanglement swapping is a core ingredient of a quantum repeater and requires that quantum correlations be established between independent photons. Entanglement swapping also implies that a quantum state has been teleported between two parties. Here we outline recent work in entanglement swapping with spatial modes of light. We show quantum correlations between photons that have never interacted, and demonstrate this in both a two-dimensional and high-dimensional subspace using orbital angular momentum. Finally, we outline a ghost imaging experiment across a virtual link, where object and image are linked through photons with no initial position correlations.

Homomorphic encryption is a cryptographic primitive that enables information processing on encrypted data. Such primitives are useful in a delegated computing setting in which a client delegates processing to a server, but does not trust the server fully with her information. Here, I discuss a way of performing quantum homomorphic encryption. A homomorphic encryption protocol comprises of four algorithms: random key generation, encryption, evaluation, and decryption. Our technique requires that a pair of commuting operators be used to implement the encryption and evaluation. The client randomly selects the former, while the server implements the latter. Then post-evaluation, if the client decrypts using the inverse of the encryption, he retrieves the input state with the desired computation implemented. The code space has to be chosen carefully so that non-trivial evaluations can be performed on the logical qubits. Since the encryption key is not known to the server, the randomness introduced by key generation hides some information about the encoded data despite it being put into the hands of the server. This framework is powerful because it gives a general description for implementing quantum homomorphic encryption. For example, families of commuting groups of operators are known to exist via the Schur-Weyl duality. However, it is limited by a no-go theorem that states that an exponential overhead is needed if arbitrary computation and perfect security are desired. Nonetheless, our protocols are still interesting as an application for near-term quantum computers, especially when the computational tasks require only low-depth circuits.

In quantum communications, vortex photons can encode higher-dimensional quantum states and build highdimensional communication networks (HDCNs). The interfaces that connect different wavelengths are significant in HDCNs. We construct a coherent orbital angular momentum (OAM) frequency bridge via difference frequency conversion in a nonlinear bulk crystal. Using a single resonant cavity, maximum quantum conversion efficiencies from visible to infrared are 36%, 15%, and 7.8% for topological charges of 0,1, and 2, respectively. The average fidelity obtained using quantum state tomography for the down-converted infrared OAM-state of topological charge 1 is 96.51%. We also prove that the OAM is conserved in this process by measuring visible and infrared interference patterns. This coherent OAM frequency-down conversion bridge represents a basis for an interface between two high-dimensional quantum systems operating with different spectra.

Quantum communication which is our ability to transmission quantum information between remote locations is a primitive operation necessary for a future quantum internet. Quantum communication at its heart relies on establishing entangled links between remote locations which can then be used to teleport quantum data. Typically channel losses limit the distance that photons can be sent without some form of quantum repeater networks which segments the channel into smaller pieces. Entanglement distribution, purification and swapping operations then allows one to create high fidelity entangled pairs between the desired remote locations. Several generations of quantum repeaters have been proposed with dramatically increasing performance but the ultimate network performance is limited by channel losses which are typically fundamental in nature. Here we introduce the concept of quantum multiplexing, which allows us to both minimize the number of photons needed in the entanglement distribution processing but also enhance the quality of the entangled pairs generated. In this presentation we discuss the potential performance gains our quantum multiplexing approach gives.

Here we report our recent experimental progresses in optical quantum information processing. In particular, the following topics are included. First, we extend the heralding scheme to multi-mode states and demonstrate heralded creation of qutrit states. Next, we demonstrate storage of single-photon states and synchronized release of them. Then, we demonstrate real-time acquisition of quadrature values of heralded states by making use of an exponentially rising shape of wave-packets. Finally, we demonstrate cluster states in an arbitrarily long chain in the longitudinal direction.

Quantum cryptography provides perfect secrecy if the key exchanged is used for one-time-pad encryption. However, this requires very long keys which are not practical in most scenarios. Further, the key exchange bit-rate for quantum key distribution is very low. Consequently, often quantum key distribution algorithms only exchange (128, 192 or 256 bit) AES keys and then AES is used for data encryption. While Grover's algorithm will force us to only use AES- 256 and does not pose a catastrophic failure to AES, AES does not provide provable security. In this paper, we discuss methods that provide provable security but at the same time the key lengths may be controlled to practical levels. Difficulty of breaking the cipher is directly proportional to the key length and depends on the specific algorithm employed. The key idea is that key lengths can be tweaked such that an acceptable and provable level of security is achieved and therefore the cipher is not reliant on any assumptions for security. The paper will discuss different ways of achieving the above goal.

We consider private communication over bosonic Gaussian channels via the most general adaptive protocols based on local operations and two-way classical communication. These protocols include all the possible strategies allowed by quantum mechanics where two remote parties have local quantum computers but do not share prior quantum entanglement. In this context, Pirandola-Laurenza-Ottaviani-Banchi (PLOB) [Nat. Commun. 8, 15043 (2017)] established weak converse upper bounds for the secret key capacity of these channels. These bounds were computed by combining teleportation stretching, able to simplify any adaptive protocol into a block form, and the channel’s relative entropy of entanglement, so that data-processing properties allow one to write simple single-letter quantities. Here we discuss an extension of these bounds to repeater-assisted quantum communications. Then, using an energy-constrained version of the diamond norm and the Braunstein-Kimble teleportation protocol, we can rigorously show the strong converse property of the bounds discovered by PLOB. Our analysis provides a full mathematical justification of recent claims appeared in the literature.

This paper discusses the most relevant aspects of the practical implementation of a long-range Quantum Key Distribution (QKD) link with trusted nodes, achieving the highest possible secret key rate generation within the security and system level constraints. To this purpose, the implementation of an end-to-end QKD system will be discussed, including implementation aspects from physical transmission of photon states through a standard telecommunications grade optical fiber, to consideration of device imperfections, information reconciliation protocols. In addition, since there are circumstances when a fiber optical link may not be available, we will also discuss a test bench implementation of a Free Space Optics (FSO) QKD link.

Furthermore, in spite of the fact that Discrete Variable QKD (DV-QKD) systems have reached a maturity level that allows their potential full realization and implementation for creation of a secure network backbone for key distribution in nations, in realistic links DV-QKD is really limited by technology and physical constraints associated with construction of reliable high rate single photon (or at least low photon count) sources, and of fast and reliable single photon detectors with very low dark count rates. In these cases, the use of Continuous Variable QKD (CV-QKD) schemes may be advantageous. For this reason the paper also discusses the problem of information reconciliation in CVQKD scenarios, showing that in long distance links the sign of the received Gaussian samples contains the largest fraction of information, leading to the design of an Unequal Error Protection (UEP) reverse reconciliation scheme.

Free-Space Optical (FSO) communication provides very large bandwidth, relatively low cost, low power, low mass of implementation, and improved security when compared to conventional Free-Space Radio-Frequency (FSRF) systems. In this paper, we demonstrate a communication protocol that demonstrates improved security and longer-range FSO communication, compared to existing FSO security techniques, such as N-slit interferometers. The protocol integrates chaotic communications with Quantum Key Distribution (QKD) techniques. A Lorenz chaotic system, which is inherently secure and auto-synchronized, is utilized for secure data communications over a classical channel, while QKD is used to exchange crucial chaotic system parameters over a secure quantum channel. We also provide a concept of operations for a NASA mission combining chaotic communications and QKD operating synergistically in an end-to-end space communications link. The experimental simulation results and analysis are favorable towards our approach.

Many fundamental and applied experiments in quantum optics require transferring nonclassical states of light through large distances. In this context the free-space channels are a very promising alternative to optical fibers as they are mobile and enable to establish communications with moving objects, using satellites for global quantum links. For such channels the atmospheric turbulence is the main disturbing factor. The statistical properties of the fluctuating transmittance through the turbulent atmosphere are given by the probability distribution of transmittance (PDT). We derive the consistent PDTs for the atmospheric quantum channels by step-by-step inclusion of various atmospheric effects such as beam wandering, beam broadening and deformation of the beam into elliptic form, beam deformations into arbitrary forms. We discuss the applicability of PDT models for different propagation distances and optical turbulence strengths in the case when the receiver module has an annular aperture. We analyze the optimal detection and correction strategies which can improve the channel transmission characteristics. The obtained results are important for the design of optical experiments including postselection and adaptive strategies and for the security analysis of quantum communication protocols in freespace.

Weak value measurements have been a real breakthrough in the quantum measurement framework. In particular, quantum measurements may take advantage by anomalous weak values, i.e. values out of the eigenvalues spectrum of the measured observable, both for implementing new measurement techniques and studying Quantum Mechanics foundations. In this report we show three experiments with single photons presenting anomalous weak values: the first one tests the incompatibility between quantum mechanics and noncontextual hidden variables theories, the second one is the first realization of a sequential weak value evaluation of two incompatible observables on the same photon, and the last one shows how sequential weak values can be used to test Leggett-Garg inequalities extended to multiple-measurements scenarios.

We show how squeeze operators appear in paraxial field propagation,i.e., in classical optics. Then, we show how squeezed states may be generated in multiphoton processes that occur in single photon resonant transitions of the atom-field interaction when conditional measurements take place. We study field properties, to show that the field does not only acquire squeezed properties but also can gain or lose more than one photon.

Free-space quantum links have clear practical advantages which are unaccessible with fiber-based optical channels — establishing satellite-mediated quantum links, communications through hardly accessible regions, and communications with moving objects. We consider the effect of the atmospheric turbulence on properties such as quadrature squeezing, entanglement, Bell nonlocality, and nonclassical statistics of photocounts, which are resources for quantum communications. Depending on the characteristics of the given channels, we study the efficiency of different techniques, which enable to preserve these quantum features post-, pre-selection, and adaptive methods. Furthermore, we show that copropagation of nonclassically-correlated modes, which is used in some communication scenarios, has clear advantages in free-space links.

The Heisenberg-Robertson uncertainty relation presents a lower bound on the product of variance of two observables, and provides a trade-off relation of measurement errors of these two observables for any given quantum states. Recently multi-observable uncertainty relations relating on that product of variances are proposed. Here we experimentally demonstrate these multi-observable uncertainty relations are valid in a state-dependent manner and the lower bound is tight for multi-observable being incompatible on the state of the system being measured. We find the behaviour of multiple incompatible observables agrees with the predictions of quantum theory.

Entanglement detection is one of the most fundamental and practical tasks for quantum information processing. The framework of entanglement witnesses provides an experimentally feasible method detecting entangled states. Although It is clear that no entanglement witness per se can detect all entangled states, little is known about how useful a single entanglement witness is. In this work, we show that an entanglement witness can construct another entanglement witness. This means that the same measurement outcomes can be repeatedly applied to constructing different entanglement witnesses.

In this work, by combining the wavelength- and time-division multiplexing technologies, we demonstrate a multiplexing time-bin entangled photon pair source based on a silicon nanowire waveguide and distribute entangled photons into 3(time) × 14(wavelength) channels independently. The indistinguishability of photon pairs in each time channel is confirmed by a fourfold Hong-Ou-Mandal quantum interference.

We report the observation of a counterintuitive phenomenon in multipath correlation interferometry with thermal light. The intensity correlation between the outputs of two unbalanced Mach-Zehnder interfer- ometers (UMZIs) with two classically correlated beams of thermal light at the input exhibits genuine second-order interference with the visibility of 1=3. Surprisingly, the second-order interference does not degrade at all no matter how much the path length difference in each UMZI is increased beyond the coherence length of the thermal light. Moreover, the second-order interference is dependent on the difference of the UMZI phases. These results differ substantially from those of the entangled-photon Franson interferometer, which exhibits two-photon interference dependent on the sum of the UMZI phases and the interference vanishes as the path length difference in each UMZI exceeds the coherence length of the pump laser. Our work offers deeper insight into the interplay between interference and coherence in multiphoton interferometry.

As a security parameter of Y-00 quantum stream cipher, a guessing probability by an eavesdropper for a secret key of legitimate users is discussed. Assuming that Eve employs the direct detection and Gaussian intensity distribution of each intensity level of Y-00 cipher signals are same, an analytic solution of probability of correct guessing of the secret key in a case of the ciphertext-only attack is derived. The solution is applied to experimentally measure the probabilities of our Y-00 quantum stream cipher transceiver. A very low probability of the Y-00 cipher transceiver is experimentally confirmed.

Since the wavefunction of a photon only describes the probability of photon detection in time and space, it is impossible to derive uniquely defined trajectories describing the path taken by the photon between emission and detection. However, it is possible to test whether a particular set of trajectories is consistent with the statistics observed at different times for photons in the same initial state. Recently, I have shown that quantum interference effects between position and momentum can result in a violation of inequalities associated with motion along straight lines. Here, I present a more detailed analysis on the origin of the effect and its relation with other experimentally observable aspects of quantum statistics such as weak measurements and quantum tomography. It is shown that the interference pattern between a quantum state component of well-defined position and a quantum state component of well-defined momentum describes a modified causality relation between the positions detected at different times. The phase of the interference pattern is identified with the classical action of particle motion and the relation between uncertainty and causality is considered. The specific case of single photon wavefunctions is used to explain the possibilities and limitations of control at the ultimate quantum limit.

Consider two bosonic modes which are prepared in one of two possible Gaussian states with the same local energy: either a tensor-product thermal state (with zero correlations) or a separable Gaussian state with maximal correlations (with both classical and quantum correlations, the latter being quantified by quantum discord). For the discrimination of these states, we compare the optimal joint coherent measurement with the best local measurement based on single-mode Gaussian detections. We show how the coherent measurement always strictly outperforms the local detection strategy for both single- and multi-copy discrimination. This means that using local Gaussian measurements (assisted by classical communication) is strictly suboptimal in detecting discord. A better performance may only be achieved by either using non Gaussian measurements (non linear optics) or coherent non-local measurements.