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- Front Matter: Volume 8400
- Quantum Imaging, Sensing, and Measurement
- Quantum Key Distribution and Cryptography
- Quantum Bits and Logic Gates
- Quantum Computing
- Quantum Information Theory I
- Quantum Information Theory II
- Quantum Entanglement
- Poster Session

Front Matter: Volume 8400

Front Matter: Volume 8400

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This PDF file contains the front matter associated with SPIE Proceedings Volume 8400, including the Title Page, Copyright information, Table of Contents, and the Conference Committee listing.

Quantum Imaging, Sensing, and Measurement

Probing correlation in quantum arrays

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We consider the problem of identifying the degree of correlation θ in the depolarization rates of an array of qubits,
such as might be found in a holding register in a quantum information processing architecture. We treat this
as a problem in quantum channel identification and use the quantum Fisher information about θ in the channel
output to compare different candidate probe states. We consider channel probes in general pure N-qubit cat
states and find that partial entanglement is always suboptimal; the best cat probe state is either separable or
maximally entangled, and we lay out for any given depolarizing rate p and correlation θ, the (p, θ)-regions for
which separable and maximally entangled probes each yield the most information. In the case of very large
qubit arrays, we find that the quantum Fisher information obtained about θ using any pure cat probe state is
asymptotically independent of the state and identically equal to the information available about a classical coin's
bias from a single coin toss. Finally, we turn our attention to arrays of N qudits (with common dimension D)
that are depolarizing with some correlation θ. We consider both separable and maximally entangled cat probe
states and find and compare their quantum Fisher informations in both the large N and large D regimes.

Manipulations of cold atoms on a chip: double well potential and 1D Bose gas

Jason Alexander,
Violeta Prieto,
Christopher Rowlett,
et al.

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We report on progress for a couple of experiments on manipulating cold atoms on a chip for quantum sensing. The first
experiments are directed towards developing a compact atom interferometer on an atom chip using a double-well
potential. The interferometer uses

^{87}Rb atoms magnetically confined in an atomic waveguide produced by wires on the surface of a lithographically patterned chip. Finite element modeling of combinations of different current configurations with various external bias fields indicated a means of coherently splitting the atomic cloud through dynamically adjusting the currents and bias fields. In these experiments we investigate real-time transformations between different double-well configurations adiabatically and non-adiabatically, and study their effects on the initially trapped atoms. Coherence properties of the two atomic wavepackets are examined. In another set of experiments we investigate the properties of bosons confined to (quasi) one dimension in our magnetic waveguide. When the atom-atom repulsive interaction becomes much larger than the kinetic energy, bosons confined in one dimension can enter a new state of matter, the Tonks-Girardeau gas, in which they behave like non-interacting fermions. However, the bosons can still occupy the same momentum state and therefore the gas cannot be fully described by either Bose-Einstein or Fermi-Dirac statistics. This transition has been observed in optical lattices but not in magnetic atom chip waveguides. We discuss the conditions for obtaining a Tonks-Girardeau gas with^{87}Rb atoms in our atom chip waveguide as well as a novel signature for observing the transition in our system.
Optical frequency combs for atomic quantum control on atom chips

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A technique to drive stimulated Raman transition between spin and/or momentum states of ultracold

^{87}Rb atoms confined on an atomchip trap is discussed. We present our experimental and theoretical approach to an all-optical manipulation of the atoms using an optical frequency comb emitted by a modelocked ultrafast pulsed laser.
Spectroscopy of a deterministic single-donor device in silicon

M. Fuechsle,
J. A. Miwa,
S. Mahapatra,
et al.

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We present a single electron transistor (SET) based on an individual phosphorus dopant atom in an epitaxial silicon
environment. Using scanning tunneling microscope (STM) hydrogen lithography, the single impurity is deterministically
placed with a spatial accuracy of ±
1 lattice site within a donor-based transport device. Low temperature transport
measurements confirm the presence of the single donor and show that the donor charge state can be precisely controlled
via gate voltages. We observe a charging energy that is remarkably similar to the value expected for isolated P donors in
bulk silicon, which is in sharp contrast to previous experiments on single-dopant transport devices. We show that
atomistic modeling can fully capture the effects of the highly-doped transport electrodes on the electronic states of the
donor, thus highlighting the high level of control over the electrostatic device properties afforded by a deterministic
single donor architecture. Our fabrication method therefore opens the door for the realization of a scalable donor-based
qubit architecture in silicon.

Phonons in a double-well: transverse vibrations in a pair of trapped ions

Patricia J. Lee

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Double-well potentials have extensive applications in many branches of physics and have resulted in devices that are useful for precision sensing as well as quantum information processing. Here, we present a theoretical analysis of the transverse phonon coupling between a pair of trapped ions as described by a double-well system. Typically the phonons in trapped ions are used as an intermediary in quantum information processing, but here we focus on the dynamics of the phonons themselves. The double-well system is a special case of the more generalized Bose-Hubbard Model, with exactly two sites available to store particles. We draw an analogy to another double-well system in solid state physics: a Josephson junction containing a thin insulating barrier between two superconductors. Applications of the Josephson junction include superconducting quantum interference devices (SQUIDs), which have emerged as sensitive magnetometers and also as qubits for quantum computation. Another analogy is the recent demonstrations of matter-wave interference with Bose-Einstein condensates in double-well traps, which have also shown great promise for applications in precise inertial and gravitational field sensing. We will also discuss experimental techniques that can be applied to control and manipulate this double-well system.

Quantum Key Distribution and Cryptography

LDPC error correction in the context of quantum key distribution

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Secret keys can be established through the use of a Quantum channel monitored through classical channel which can be
thought of as being error free. The quantum channel is subject to massive erasures and discards of erroneously measured
bit values and as a result the error correction mechanism to be used must be accordingly modified. This paper addresses
the impact of error correction (known as Reconciliation) on the secrecy of the retained bits and issues concerning the
efficient software implementation of the Low Density Parity Check algorithm in the Quantum Key Distribution
environment. The performance of three algorithmic variants are measured through implementations and the collected
sample data suggest that the implementation details are particularly important

Thwarting the photon number splitting attack with entanglement enhanced BB84 quantum key distribution

Carl F. Sabottke,
Chris D. Richardson,
Petr M. Anisimov,
et al.

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We develop an improvement to the weak laser pulse BB84 scheme for quantum key distribution, which utilizes
entanglement to increase the security of the scheme and enhance its resilience to the photon-number-splitting attack.
This protocol relies on the non-commutation of phase and number to detect an eavesdropper performing quantum nondemolition
measurement on photon number. The potential advantages and disadvantages of this scheme are compared to
the coherent decoy state protocol.

Quantum Bits and Logic Gates

Szilard engine reversibility as quantum gate function

F. Matthew Mihelic

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A quantum gate is a logically and thermodynamically reversible situation that effects a unitary transformation of
qubits of superimposed information, and essentially constitutes a situation for a reversible quantum decision. A
quantum decision is a symmetry break, and the effect of the function of a Szilard engine is a symmetry break. A
quantum gate is a situation in which a reversible quantum decision can be made, and so if a logically and
thermodynamically reversible Szilard engine can be theoretically constructed then it would function as a quantum
gate. While the traditionally theorized Szilard engine is not thermodynamically reversible, if one of the bounding
walls of a Szilard engine were to be constructed out of the physical information by which it functions in such a
manner as to make that information available to both sides of the wall simultaneously, then such a Szilard engine
would be both logically and thermodynamically reversible, and thus capable of function as a quantum gate. A
theoretical model of the special case of a reversible Szilard engine functioning as a quantum gate is presented and
discussed, and since a quantum decision is made when the shutter of a Szilard engine closes, the coherence of linked
reversible Szilard engines should be considered as a state during which all of the shutters of linked Szilard engines
are open simultaneously.

Quantum Computing

Finsler metrics in quantum circuit optimization

Howard E. Brandt

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A brief review is given of possible Finsler metrics de…ned on the SU(2

^{n}) group tangent bundle which may be suitable for quantum circuit optimiza- tion.
Study of improved semantics on quantum elements and programmable architecture

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In this paper we study an improved semantics of some basic elements in quantum computation, which can be
helpful to build quantum compiler and quantum operating system.

A multilayer three-dimensional superconducting nanowire photon detector

A. Matthew Smith

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Here we propose a new design paradigm for a superconducting nanowire single photon detector that uses a
multi-layer architecture that places the electric leads beneath the nanowires. This allows for a very large number
of detector elements, which we will call pixels in analogy to a conventional CCD camera, to be placed in close
proximity. This leads to signicantly better photon number resolution than current single and multi-nanowire
meanders, while maintaining similar detection areas. We discuss the reset time of the pixels and how the
design can be modied to avoid the latching failure seen in extremely short superconducting nanowires. These
advantages give a multi-layer superconducting number-resolving photon detector signicant advantages over the
current design paradigm of long superconducting nanowire meanders. Such advantages are desirable in a wide
array of photonics applications.

Generalized Donkor model with induced dipole-dipole forbidden transitions using Maple

Camilo Jaramillo Correa

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The idea of this work was to generalize the Donkor model (Quantum Information and Computation IX, edited by Eric
Donkor, Andrew R. Pirich, Howard E. Brandt, Proc. of SPIE Vol. 8057) about the application of induced dipole-dipole forbidden transitions to quantum
computation. Using computer algebra we were able to reproduce the original Donkor model. Then we applied some
modifications to this model and obtained the respective solutions. It is expected that this model has applications for
quantum computation.

All optical XOR, CNOT gates with initial insight for quantum computation using linear optics

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The design for an all optical XOR gate is proposed. The basic idea is to split the input beams and let them cancel
or strengthen each other selectively or flip the encoded information based on their polarization properties. The
information is encoded in terms of polarization of the beam. Polarization of a light beam is well understood hence
the design should be feasible to implement. The truth table of the optical circuit is worked out and compared
with the expected truth table. Then it is demonstrated that the design complies with the linear behavior of the
XOR function. In the next section, based on a similar idea, the design of an all optical CNOT gate is proposed.
The truth table for the gate is verified. Then, it is discussed how this approach can be used for Linear Optics
Quantum Computation (LOQC). It is shown that with a Hadamard gate and a rotation gate, the CNOT gate
makes up a universal set of quantum gates based on linear optics. This novel approach requires no additional
power supply, extra input beam or ancilla photon to operate. It also doesn't require the expensive and complex
single photon source and detector. Only narrowband laser sources are required to operate these gates.

Quantum Information Theory I

Quantum system decomposition for the semi-classical quantum Fourier transform

Ben Greco,
Jack Lenahan,
Suzanne Huerth,
et al.

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For classical simulation, the quantum Fourier transform (QFT) requires very large matrix operations. Previous
work has shown that the semi-classical quantum Fourier transform (SCQFT) can use these individual coefficients
to perform the QFT using only single-quantum bit (qubit) unitary gates and measurement operators. However,
the SCQFT requires these individual decomposed qubits of the quantum system as input to the algorithm. We
devise two methods to find separable approximations of quantum systems to serve as inputs to the SCQFT. We
introduce an application of the approach on classical radio frequency signals represented through a quantum
model. The resulting decomposition and QFT are computed on several simulated results, and an example is
given using an experimental signal.

Freedom of choice in tracking an atomic resonance

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The International Second (SI) is defined in terms of a resonant frequency of cesium imagined at 0 K, differing from any
measurable resonant frequency by an offset calculated from a chosen wave function. As proved in prior work, the choice
of wave function cannot be determined by measured data but requires a reach beyond anything measurable or calculable,
thereby bringing incalculablility, along with an element of free choice, into the definition and the realization of the second.
A clock that realizes the second contains a variable-frequency oscillator controlled by a measurement model running
in a computational process, and the chosen wave function is embodied in the measurement model. Embedded in a computational
process, the measurement model, with its dependence on the chosen wave function, acts as an active agent,
responding to incalculable detections by calculating numbers that adjust the oscillator.
Because the choice of realization of a proper clock influences the measured numbers that give evidence of spacetime
curvature, the chosen wave function for cesium clocks affects spacetime curvature, inviting exploration of offsets of
imagined proper clocks from measurable frequencies in interesting situations, such as stellar interiors.

Battle of the sexes game analysis using Yang-Baxter operator as quantum gate

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The Battle of the Sexes game is analyzed from quantum game theory using quantum initial states as possible strategies
for two players. Quantum circuits are presented as schemes of development proposing also the use of Yang-Baxter
operators as quantum gates in the circuits. This formalism is implemented using a Computer Algebra Software (CAS)
due to its complex and long mathematical treatment. Payoff matrices of the players are given as the results for each case
shown. Biology and finances applications are also proposed.

Strictly discordant quantum probes of the qubit depolarizing channel

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Quantum mutual information defined in terms of von Neumann entropy captures and quantifies all correlations,
quantum and classical, between the two parts of a bipartite quantum system. Within this framework entanglement
is the most distinguished type of quantum correlation, and a rich body of theory and experiment establishes
that entanglement is a potent and fungible resource for quantum information processing broadly. Bipartite systems
can exhibit quantum correlations beyond entanglement. Such non-classical states are called discordant in
general and strictly discordant (or dissonant) when the quantum state is separable. We show that strict discord
can increase the amount of information available from probing a quantum channel. We focus in this study on
the qubit depolarizing channel, using quantum Fisher information to measure the information available about
the channel depolarizing probability. We consider channel probes prepared, along with an ancilla, in a separable
two-qubit Bell-diagonal state. We prove for Bell-diagonal probes of the qubit depolarizing channel that, in the
absence of entanglement and controlling for marginal purity and degree of classical correlation, any increase in
strict discord between the probe and ancilla yields an accompanying increase in available statistical information
about the channel depolarizing probability.

A geometric view of quantum cellular automata

Jonathan R. McDonald,
Paul M. Alsing,
Howard A. Blair

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Nielsen, et al.

^{1, 2}proposed a view of quantum computation where determining optimal algorithms is equivalent to extremizing a geodesic length or cost functional. This view of optimization is highly suggestive of an action principle of the space of N-qubits interacting via local operations. The cost or action functional is given by the cost of evolution operators on local qubit operations leading to causal dynamics, as in Blute et. al.^{3}Here we propose a view of information geometry for quantum algorithms where the inherent causal structure determines topology and information distances^{4, 5}set the local geometry. This naturally leads to geometric characterization of hypersurfaces in a quantum cellular automaton. While in standard quantum circuit representations the connections between individual qubits, i.e. the topology, for hypersurfaces will be dynamic, quantum cellular automata have readily identifiable static hypersurface topologies determined via the quantum update rules. We demonstrate construction of quantum cellular automata geometry and discuss the utility of this approach for tracking entanglement and algorithm optimization.
Local availability of mathematics and number scaling: effects on quantum physics

Paul Benioff

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Local availability of mathematics and number scaling provide an approach to a coherent theory of physics and
mathematics. Local availability of mathematics assigns separate mathematical universes, x, to each space time
point, x.. The mathematics available to an observer, Ox, at x is contained in x . Number scaling is based on
extending the choice freedom of vector space bases in gauge theories to choice freedom of underlying number
systems. Scaling arises in the description, in x, of mathematical systems in y . If ay or ψy is a number or a
quantum state in y, then the corresponding number or state in x is ry,xax or ry,xψx. Here ax and ψx are the
same number and state in x as ay and ψy are in y . If y = x+ μdx is a neighbor point of x, then the scaling
factor is r

_{y,x}= exp( A(x) • μdx) where A is the gradient of a scalar field. The effects of scaling and local availability of mathematics on quantum theory show that scaling has two components, external and internal. External scaling is shown above for ay and ψy. Internal scaling occurs in expressions with integrals or derivatives over space time. An example is the replacement of the position expectation value, ∫ψ*(y)yψ(y)dy, by ∫_{x}r_{y},ψ_{x}* x(yx)yxψx(yx)dy_{x}. This is an integral in x . The good agreement between quantum theory and experiment shows that scaling is negligible in a space region,*L*, in which experiments and calculations can be done, and results compared.*L*includes the solar system, but the speed of light limits the size of*L*to a few light years. For observers in*L*and events outside*L*, at cosmological distances, scaling is not limited by theory experiment agreement requirements.Quantum Information Theory II

Quantum algorithms for the Jones polynomial and Khovanov homology

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This paper generalizes the AJL algorithm for quantum computation of the Jones polynomial to continuous ranges
of values on the unit circle for the Jones parameter and shows that the Kauffman-Lomonaco 3-strand algorithm
for the Jones polynomial is a special case of this generalization. We then describe a quantum algorithm for the
Jones polynomial that is related to Khovanov homology.

Possible universal quantum algorithms for generalized Khovanov homology and the Rasmussen's invariant

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Possible quantum algorithms for generalized Khovanov homology and the Rasmussen's invariant are proposed. Such
algorithms are resulting from adaptations of the recently proposed Kauffman's algorithm for the standard Khovanov
homology. The method that was applied consists in to write the relevant quantum invariant as the trace of a certain
unitary operator and then to compute the trace using the Hadamard test. We apply such method to the quantum
computation of the Jones polynomial, HOMFLY polynomial, Chromatic polynomial, Tutte polynomial and Bollobàs-
Riordan polynomial. These polynomials are quantum topological invariants for knots, links, graphs and ribbon graphs
respectively. The Jones polynomial is categorified by the standard Khovanov homology and the others polynomials are
categorified by generalized Khovanov homologies, such as the Khovanov-Rozansky homology and the graph
homologies. The algorithm for the Rasmussen's invariant is obtained using the gauge theory; and the recently
introduced program of homotopyfication is linked with the super-symmetric quantum mechanics. It is claimed that a
new program of analytification could be development from the homotopyfication using the celebrated Atiyah-Singer
theorem and its super-symmetric interpretations. It is hoped that the super-symmetric quantum mechanics provides the
hardware for the implementation of the proposed quantum algorithms.

Applications of the Yang-Baxter-Rowell equation to topological quantum computation

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The main goal of this paper is to apply the Yang-Baxter-Rowell equation in topological quantum
computation, using the symbolic computational software Maple. Initially, using Maple, I reproduced the Dye
classification of the 4x4 unitary solutions of the Yang-Baxter equation. Then, also using Maple, I reproduced
the solutions given by Rebecca Chen to the Yang-Baxter-Rowell equation. Finally, the obtained solutions
were applied to the problem of topological quantum categorification of the chromatic polynomial for graphs.
It was claimed that the Yang-Baxter-Rowell operators, considered as quantum gates, can be incorporated in
quantum circuit models and quantum games, such as the Grover algorithm and the game Battle of the Sexes.
It is expected that a future investigation can provide a more complete classification of the solution to the
Yang-Baxter-Rowell equation and its possible applications on topological quantum computation.

Quantum Entanglement

Nonlocality, entanglement witnesses, and supra-correlations

Paul M. Alsing,
Jonathan R. McDonald

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While entanglement is believed to underlie the power of quantum computation and communication, it is not generally
well understood for multipartite systems. Recently, it has been appreciated that there exists proper no-signaling
probability distributions derivable from operators that do not represent valid quantum states. Such systems exhibit
supra-correlations that are stronger than allowed by quantum mechanics, but less than the algebraically allowed
maximum in Bell-inequalities (in the bipartite case). Some of these probability distributions are derivable from an
entanglement witness W, which is a non-positive Hermitian operator constructed such that its expectation value with a
separable quantum state (positive density matrix) ρ

_{sep}is non-negative (so that Tr[W ρ]< 0 indicates entanglement in quantum state ρ). In the bipartite case, it is known that by a modification of the local no-signaling measurements by spacelike separated parties A and B, the supra-correlations exhibited by any W can be modeled as derivable from a physically realizable quantum state ρ. However, this result does not generalize to the n-partite case for n>2. Supracorrelations can also be exhibited in 2- and 3-qubit systems by explicitly constructing "states" Ο (not necessarily positive quantum states) that exhibit PR correlations for a fixed, but arbitrary number, of measurements available to each party. In this paper we examine the structure of "states" that exhibit supra-correlations. In addition, we examine the affect upon the distribution of the correlations amongst the parties involved when constraints of positivity and purity are imposed. We investigate circumstances in which such "states" do and do not represent valid quantum states.
A multipli-entangled photon source for cluster state generation

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This paper expands upon prior work on an entangled photon source generating six pairs of photons via spontaneous
parametric down-conversion in a single pass configuration. Experimental results measuring entangled photons at 810 nm
are shown and other wavelength regimes will be discussed. The design and fabrication considerations for a group
velocity matched (GVM) superlattice photon source are discussed. An application of this source enables various multiqubit
cluster states to be generated in a compact unidirectional configuration. This configuration simplifies the
interferometric stability for any associated feed-forward methods required in photon-based quantum logic circuitry.

Generation, detection, and applications of quantum hyper-entangled and entangled states

James F. Smith III

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Methods of generating N00N, M&N, linear combinations of M&N states as well as more complicated quantum
entangled and quantum hyper-entangled states will be considered. Quantum hyper-entanglement refers to quantum
entanglement in more than one degree of freedom, e.g. energy-time, polarization, orbital angular momentum, etc.
Internal noise and loss within the entanglement or hyper-entanglement generators and external noise and loss due to
atmospheric effects and detectors are modeled. Analysis related to the devices that generate these entangled or hyperentangled
states will be provided. The following will be derived: closed form expressions for wave function
normalization, wave function, density operator, reduced density operator, phase error bound, the symmetrized
logarithmic derivative, the quantum Fisher information, the quantum Cramer-Rao lower bound, the relevant projection
operators and the related probability of detection expressions. Generation and detection of the entangled or hyperentangled
states will be considered. The entanglement generators will use linear and nonlinear optical devices.
Optimization criteria for the quantum states, generation and detection schemes and designs optimal with respect to the
criteria will be discussed. Applications of the generated states for producing super sensitivity and super resolution will
be discussed. The fundamental role of coincidence measurement for generating entanglement is included. Hyperentanglement
offers N times classical resolution, where N is a quantum number associated with the system.

Nonlocal realism considered for entangled photons

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Experimental measurements of entangled photons have enabled effective probing of foundational principles of physical
law, Quantum Mechanics (QM) in particular. When it was noted that QM is non-local and precludes certain real
properties, change in the description of basic phenomena was required. Bell's Inequality work clarified this conflict with
Local-Realistic descriptions but left open whether locality, realism, or both should be abandoned. More recent
investigations consider models that maintain forms of non-local realism as alternatives to QM. Problems with those are
illustrated here, and support a non-local QM description of entangled photons having non-determinate properties.

Generating and storing nonclassical correlations in a warm Rb vapor cell with buffer gas

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Quantum memory is regarded as one of the essential components in the fields of quantum computing and quantum
communication. Warm atomic vapor cells for quantum memory, as originally described in DLCZ (for Duan, Lukin,
Cirac, and Zoller) protocol, are appealing due to the perceived reduction in experimental complexity and commercial
availability. However, published studies on quantum memory using warm vapor cells were performed under widely
dissimilar experimental conditions and reported ambiguous results. In order for the memory to exhibit non-classical
behavior to a high degree of certainty, the cross-correlation value between the Stokes and anti-Stokes photons needs to
be greater than two. In this work we demonstrate quantum memory with cross-correlation value between the Stokes and
anti-Stokes photons greater than two lasting for 4 μs using warm Rb vapor with buffer gas for nearly co-propagating
write and read beams.

Poster Session

Theory and experimental requirements of imperfect two-qubit linear optical photonic gates

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We propose an experiment in Linear Optical Quantum Computing (LOQC) in the style rst suggested by Knill,
La
amme, and Milburn. This experiment is intended to test the theories proposed in the authors' previous work
on imperfect LOQC gates using number-resolving photon-detectors. We develop a simple physical apparatus
capable of producing controllable delity less than 1 and success rates higher than the current theoretical maximum
(S=2/27) for perfect delity. This experimental setup is within the reach of many experimental groups
and would provide an interesting experiment in photon-based quantum computing.