Showing papers in "Physical Review A in 1998"
TL;DR: In this paper, a universal set of one-and two-quantum-bit gates for quantum computation using the spin states of coupled single-electron quantum dots is proposed, and the desired operations are effected by the gating of the tunneling barrier between neighboring dots.
Abstract: We propose an implementation of a universal set of one- and two-quantum-bit gates for quantum computation using the spin states of coupled single-electron quantum dots. Desired operations are effected by the gating of the tunneling barrier between neighboring dots. Several measures of the gate quality are computed within a recently derived spin master equation incorporating decoherence caused by a prototypical magnetic environment. Dot-array experiments that would provide an initial demonstration of the desired nonequilibrium spin dynamics are proposed.
5,801 citations
TL;DR: It is argued that the statistical basis of the measure of entanglement determines an upper bound to the number of singlets that can be obtained by any purification procedure.
Abstract: We improve previously proposed conditions each measure of entanglement has to satisfy. We present a class of entanglement measures that satisfy these conditions and show that the quantum relative entropy and Bures metric generate two measures of this class. We calculate the measures of entanglement for a number of mixed two spin-1/2 systems using the quantum relative entropy, and provide an efficient numerical method to obtain the measures of entanglement in this case. In addition, we prove a number of properties of our entanglement measure that have important physical implications. We briefly explain the statistical basis of our measure of entanglement in the case of the quantum relative entropy. We then argue that our entanglement measure determines an upper bound to the number of singlets that can be obtained by any purification procedure.
1,253 citations
TL;DR: In this paper, the dynamics of a decohering two-level system driven by a suitable control Hamiltonian is studied, where the control procedure is implemented as a sequence of radio-frequency pulses that repetitively flip the state of the system, a technique that can be termed quantum ''bang-bang'' control after its classical analog.
Abstract: The dynamics of a decohering two-level system driven by a suitable control Hamiltonian is studied. The control procedure is implemented as a sequence of radio-frequency pulses that repetitively flip the state of the system, a technique that can be termed quantum ``bang-bang'' control after its classical analog. Decoherence introduced by the system's interaction with a quantum environment is shown to be washed out completely in the limit of continuous flipping and greatly suppressed provided the interval between the pulses is made comparable to the correlation time of the environment. The model suggests a strategy to fight against decoherence that complements existing quantum error-correction techniques.
1,241 citations
TL;DR: In this paper, the question of how many entangled or separable states there are in the set of all quantum states is considered, and a natural measure in the space of density matrices is proposed to describe $N$-dimensional quantum systems.
Abstract: The question of how many entangled or, respectively, separable states there are in the set of all quantum states is considered. We propose a natural measure in the space of density matrices $\ensuremath{\varrho}$ describing $N$-dimensional quantum systems. We prove that, under this measure, the set of separable states possesses a nonzero volume. Analytical lower and upper bounds of this volume are also derived for $N=2\ifmmode\times\else\texttimes\fi{}2$ and $N=2\ifmmode\times\else\texttimes\fi{}3$ cases. Finally, numerical Monte Carlo calculations allow us to estimate the volume of separable states, providing numerical evidence that it decreases exponentially with the dimension of the composite system. We have also analyzed a conditional measure of separability under the condition of fixed purity. Our results display a clear dualism between purity and separability: entanglement is typical of pure states, while separability is connected with quantum mixtures. In particular, states of sufficiently low purity are necessarily separable.
1,232 citations
TL;DR: This work devise a quantum-mechanical algorithm that evolves a state, initially localized at the root, through the tree, and proves that if the classical strategy succeeds in reaching level $n$ in time polynomial in $n,$ then so does the quantum algorithm.
Abstract: Many interesting computational problems can be reformulated in terms of decision trees. A natural classical algorithm is to then run a random walk on the tree, starting at the root, to see if the tree contains a node $n$ level from the root. We devise a quantum-mechanical algorithm that evolves a state, initially localized at the root, through the tree. We prove that if the classical strategy succeeds in reaching level $n$ in time polynomial in $n,$ then so does the quantum algorithm. Moreover, we find examples of trees for which the classical algorithm requires time exponential in $n,$ but for which the quantum algorithm succeeds in polynomial time. The examples we have so far, however, could also be solved in polynomial time by different classical algorithms.
1,135 citations
TL;DR: It is demonstrated that fault-tolerant universal computation is possible for any stabilizer code, including the five-quantum-bit code.
Abstract: In order to use quantum error-correcting codes to improve the performance of a quantum computer, it is necessary to be able to perform operations fault-tolerantly on encoded states. I present a theory of fault-tolerant operations on stabilizer codes based on symmetries of the code stabilizer. This allows a straightforward determination of which operations can be performed fault-tolerantly on a given code. I demonstrate that fault-tolerant universal computation is possible for any stabilizer code. I discuss a number of examples in more detail, including the five-quantum-bit code.
791 citations
TL;DR: In this paper, the authors investigate the teleportation of a quantum state using three-particle entanglement to either one of two receivers in such a way that, generally, either one or both receivers can fully reconstruct the quantum state conditioned on the measurement outcome of the other.
Abstract: We investigate the ``teleportation'' of a quantum state using three-particle entanglement to either one of two receivers in such a way that, generally, either one of the two, but only one, can fully reconstruct the quantum state conditioned on the measurement outcome of the other. We furthermore delineate the similarities between this process and a quantum nondemolition measurement.
770 citations
TL;DR: This work describes how this scheme allows to establish multiparticle entanglement between particles belonging to distant users in a communication network through a prior distribution of singlets followed by only local measurements.
Abstract: We generalize the procedure of entanglement swapping to obtain a scheme for manipulating entanglement in multiparticle systems. We describe how this scheme allows to establish multiparticle entanglement between particles belonging to distant users in a communication network through a prior distribution of singlets followed by only local measurements. We show that this scheme can be regarded as a method of generating entangled states of many particles and compare it with existing schemes using simple quantum computational networks. We highlight the practical advantages of using a series of entanglement swappings during the distribution of entangled particles between two parties. Applications of multiparticle entangled states in cryptographic conferencing and in reading messages from more than one source through a single measurement are also described.
588 citations
TL;DR: The best possible approximation to a perfect quantum cloning machine that produces two clones out of a single input is established and an upper bound on the quantum capacity of the depolarizing quantum channel is derived.
Abstract: We establish the best possible approximation to a perfect quantum cloning machine that produces two clones out of a single input. We analyze both universal and state-dependent cloners. The maximal fidelity of cloning is shown to be 5/6 for universal cloners. It can be achieved either by a special unitary evolution or by a teleportation scheme. We construct the optimal state-dependent cloners operating on any prescribed two nonorthogonal states and discuss their fidelities and the use of auxiliary physical resources in the process of cloning. The optimal universal cloners permit us to derive an upper bound on the quantum capacity of the depolarizing quantum channel.
468 citations
TL;DR: In this paper, the authors constructed the unique optimal quantum device for turning a finite number of d-level quantum systems in the same unknown pure state σ into M systems of the same kind, in an approximation of the M-fold tensor product of σ.
Abstract: We construct the unique optimal quantum device for turning a finite number of d-level quantum systems in the same unknown pure state \sigma into M systems of the same kind, in an approximation of the M-fold tensor product of the state \sigma.
468 citations
TL;DR: It is shown that different applications may result in different channel capacities, and upper bounds on several of these capacities are proved based on the coherent information, which plays a role in quantum information theory analogous to that played by the mutual information in classical information theory.
Abstract: Noisy quantum channels may be used in many information-carrying applications. We show that different applications may result in different channel capacities. Upper bounds on several of these capacities are proved. These bounds are based on the coherent information, which plays a role in quantum information theory analogous to that played by the mutual information in classical information theory. Many new properties of the coherent information and entanglement fidelity are proved. Two nonclassical features of the coherent information are demonstrated: the failure of subadditivity, and the failure of the pipelining inequality. Both properties arise as a consequence of quantum entanglement, and give quantum information new features not found in classical information theory. The problem of a noisy quantum channel with a classical observer measuring the environment is introduced, and bounds on the corresponding channel capacity proved. These bounds are always greater than for the unobserved channel. We conclude with a summary of open problems.
TL;DR: In this paper, Grover's algorithm was shown to be optimally short in the case of a quantum system with a Hamiltonian of the form $E|w〉〈w|$ where W is an unknown state and W is a normalized state.
Abstract: We solve a problem, which while not fitting into the usual paradigm, can be viewed as a quantum computation. Suppose we are given a quantum system with a Hamiltonian of the form $E|w〉〈w|$ where $|w〉$ is an unknown (normalized) state. The problem is to produce $|w〉$ by adding a Hamiltonian (independent of $|w〉)$ and evolving the system. If $|w〉$ is chosen uniformly at random we can (with high probability) produce $|w〉$ in a time proportional to ${N}^{1/2}/E$. If $|w〉$ is instead chosen from a fixed, known orthonormal basis we can also produce $|w〉$ in a time proportional to ${N}^{1/2}/E$ and we show that this time is optimally short. This restricted problem is an analog analogue to Grover's algorithm, a computation on a conventional (!) quantum computer that locates a marked item from an unsorted list of $N$ items in a number of steps proportional to ${N}^{1/2}$.
TL;DR: In this article, positive and negative subnatural width resonances were observed in the absorption and fluorescence of rubidium vapor under excitation by two copropagating optical waves with variable frequency offset.
Abstract: Positive and negative subnatural-width resonances (SNWR) were observed in the absorption and fluorescence of rubidium vapor under excitation by two copropagating optical waves with variable frequency offset. The two optical fields resonantly couple Zeeman sublevels, belonging to the same ground-state hyperfine level (GSHL), to an intermediate excited state. The SNWR present opposite signs depending on which GSHL participates in the interaction with the two optical waves. For both Rb isotopes an increase in the transparency with reduced fluorescence occurs for the lower GSHL while the absorption and fluorescence are increased for the upper GSHL. The influence of external magnetic field, polarization, and intensity of applied optical fields on the SNWR is examined. The narrowest observed resonance has a width of 10 kHz (full width at half maximum). The origin of the SNWR is discussed in terms of coherent processes involving ground-state Zeeman sublevels.
TL;DR: In this paper, a nonlinear stochastic Schrodinger equation for pure states describing non-Markovian diffusion of quantum trajectories and compatible with non-markovian master equations is presented, providing an unraveling of the evolution of any quantum system coupled to a finite or infinite number of harmonic oscillators.
Abstract: A nonlinear stochastic Schr\"odinger equation for pure states describing non-Markovian diffusion of quantum trajectories and compatible with non-Markovian master equations is presented. This provides an unraveling of the evolution of any quantum system coupled to a finite or infinite number of harmonic oscillators without any approximation. Its power is illustrated by several examples, including measurementlike situations, dissipation, and quantum Brownian motion. Some examples treat this environment phenomenologically as an infinite reservoir with fluctuations of arbitrary correlation. In other examples the environment consists of a finite number of oscillators. In such a quasiperiodic case we see the reversible decay of a macroscopic quantum-superposition (``Schr\"odinger cat''). Finally, our description of open systems is compatible with different positions of the ``Heisenberg cut'' between system and environment.
TL;DR: In this article, a scheme to create a macroscopic ''Schr''odinger-cat state formed by two interacting Bose condensates was proposed, which can be seen as an example of quantum atom optics at work.
Abstract: We propose a scheme to create a macroscopic ``Schr\"odinger-cat'' state formed by two interacting Bose condensates. In analogy with quantum optics, where the control and engineering of quantum states can be maintained to a large extent, we consider the present scheme to be an example of quantum atom optics at work.
Abstract: We experimentally study the use of two-dimensional magneto-optical trapping (2D-MOT) for the generation of slow beams of cold atoms out of a vapor cell. A particularly high flux of $9\ifmmode\times\else\texttimes\fi{}{10}^{9}$ rubidium atoms/s at a mean velocity of 8 m/s is obtained using a combination of magneto-optical trapping in two dimensions and Doppler cooling in the third dimension $({2\mathrm{D}}^{+}\ensuremath{-}\mathrm{MOT}).$ The resulting width of the velocity distribution is 3.3 m/s [full width at half maximum (FWHM)] with a beam divergence of 43 mrad (FWHM). We investigate the total flux as a function of vapor cell pressure and determine the velocity distribution of our slow atom sources. For comparison, we also realized a low-velocity intense source (LVIS), first reported by Lu et al. [Phys. Rev. Lett. 77, 3331 (1996)]. We find that the ${2\mathrm{D}}^{+}\ensuremath{-}\mathrm{MOT}$ yields a significantly higher flux than the LVIS, even when used with an order of magnitude less laser power.
TL;DR: In this paper, the authors introduce the study of dynamical quantum noise in Bose-Einstein condensates through numerical simulation of stochastic partial differential equations obtained using phase-space representations.
Abstract: We introduce the study of dynamical quantum noise in Bose-Einstein condensates through numerical simulation of stochastic partial differential equations obtained using phase-space representations. We derive evolution equations for a single trapped condensate in both the positive-P and Wigner representations and perform simulations to compare the predictions of the two methods. The positive-P approach is found to be highly susceptible to the stability problems that have been observed in other strongly nonlinear, weakly damped systems. Using the Wigner representation, we examine the evolution of several quantities of interest using from a variety of choices of initial stare for the condensate and compare results to those for single-mode models. [S1050-2947(98)06612-8].
TL;DR: In this paper, the authors present a method to calculate the dynamics of very low-temperature Bose-Einstein condensates in time-dependent traps using a systematic asymptotic expansion in the square root of the fraction of noncondensed particles.
Abstract: We present a method to calculate the dynamics of very-low-temperature Bose-Einstein condensates in time-dependent traps. We consider a system with a well-defined number of particles, rather than a system in a coherent state with a well-defined phase. This preserves the $U(1)$ symmetry of the problem. We use a systematic asymptotic expansion in the square root of the fraction of noncondensed particles. In lowest order we recover the time-dependent Gross-Pitaevskii equation for the condensate wave function. The next order gives the linear dynamics of noncondensed particles. The higher order gives corrections to the time-dependent Gross-Pitaevskii equation including the effects of noncondensed particles on the condensate. We compare this method with the Bogoliubov--de Gennes approach.
TL;DR: In this paper, the authors obtained analytic solutions to the Gross-Pitaevskii equation with negative scattering length in highly asymmetric traps and found that Bose-Einstein condensates behave like quasiparticles and do not expand when the trapping in one direction is eliminated.
Abstract: We obtain analytic solutions to the Gross-Pitaevskii equation with negative scattering length in highly asymmetric traps. We find that in these traps the Bose-Einstein condensates behave like quasiparticles and do not expand when the trapping in one direction is eliminated. The results can be applicable to the control of the motion of Bose-Einstein condensates.
TL;DR: In this paper, a comprehensive theory of nuclear spin polarization of gases by spin-exchange collisions with optically pumped alkali-metal vapors is presented. But the most important physical processes considered are spin-conserving spin exchange collisions between like or unlike atoms, spin-destroying collisions of the alkali metal atoms with each other and with buffer-gas atoms, electron-nuclear spin exchange collision, spin interactions in van der Waals molecules, optical pumping by laser photons, and spatial diffusion.
Abstract: We present a comprehensive theory of nuclear spin polarization of ${}^{3}\mathrm{He}$ and ${}^{129}\mathrm{Xe}$ gases by spin-exchange collisions with optically pumped alkali-metal vapors. The most important physical processes considered are (1) spin-conserving spin-exchange collisions between like or unlike alkali-metal atoms; (2) spin-destroying collisions of the alkali-metal atoms with each other and with buffer-gas atoms; (3) electron-nuclear spin-exchange collisions between alkali-metal atoms and ${}^{3}\mathrm{He}$ or ${}^{129}\mathrm{Xe}$ atoms; (4) spin interactions in van der Waals molecules consisting of a Xe atom bound to an alkali-metal atom; (5) optical pumping by laser photons; (6) spatial diffusion. The static magnetic field is assumed to be small enough that the nuclear spin of the alkali-metal atom is well coupled to the electron spin and the total spin is very nearly a good quantum number. Conditions appropriate for the production of large quantities of spin-polarized ${}^{3}\mathrm{He}$ or ${}^{129}\mathrm{Xe}$ gas are assumed, namely, atmospheres of gas pressure and nearly complete quenching of the optically excited alkali-metal atoms by collisions with ${\mathrm{N}}_{2}$ or ${\mathrm{H}}_{2}$ gas. Some of the more important results of this work are as follows: (1) Most of the pumping and relaxation processes are sudden with respect to the nuclear polarization. Consequently, the steady-state population distribution of alkali-metal atoms is well described by a spin temperature, whether the rate of spin-exchange collisions between alkali-metal atoms is large or small compared to the optical pumping rate or the collisional spin-relaxation rates. (2) The population distributions that characterize the response to sudden changes in the intensity of the pumping light are not described by a spin temperature, except in the limit of very rapid spin exchange. (3) Expressions given for the radio-frequency (rf) resonance linewidths and areas can be used to make reliable estimates of the local spin polarization of the alkali-metal atoms. (4) Diffusion effects for these high-pressure conditions are mainly limited to thin layers at the cell surface and at internal resonant surfaces generated by radio-frequency magnetic fields when the static magnetic field has substantial spatial inhomogeneities. The highly localized effects of diffusion at these surfaces are described with closed-form analytic functions instead of the spatial eigenmode expansions that are appropriate for lower-pressure cells.
TL;DR: A family of additive quantum error-correcting codes whose capacities exceed those of quantum random coding (hashing) for very noisy channels are presented and a general relation between the capacity attainable by these concatenation schemes and the coherent information of the inner code states is derived.
Abstract: We present a family of additive quantum error-correcting codes whose capacities exceed those of quantum random coding (hashing) for very noisy channels. These codes provide nonzero capacity in a depolarizing channel for fidelity parameters $f$ when $fg0.80944$. Random coding has nonzero capacity only for $fg0.81071$; by analogy to the classical Shannon coding limit, this value had previously been conjectured to be a lower bound. We use the method introduced by Shor and Smolin of concatenating a nonrandom repetition (cat) code within a random code to obtain good codes. The cat code with block size five is shown to be optimal for single concatenation. The best known multiple-concatenated code we found has a block size of 25. We derive a general relation between the capacity attainable by these concatenation schemes and the coherent information of the inner code states.
TL;DR: In this paper, Colmenero et al. provided theoretical foundations through a reconstruction theorem for recent attempts at generating higher RDMs from the 2RDM to remove the indeterminacy of the CSE.
Abstract: The contracted Schr\"odinger equation (CSE) technique through its direct determination of the two-particle reduced density matrix (2RDM) without the wave function may offer a fresh alternative to traditional many-body quantum calculations. Without additional information the CSE, also known as the density equation, cannot be solved for the 2RDM because it also requires a knowledge of the 4RDM. We provide theoretical foundations through a reconstruction theorem for recent attempts at generating higher RDMs from the 2RDM to remove the indeterminacy of the CSE. With Grassmann algebra a more concise representation for Valdemoro's reconstruction functionals [F. Colmenero, C. Perez del Valle, and C. Valdemoro, Phys. Rev. A 47, 971 (1993)] is presented. From the perspective of the particle-hole equivalence we obtain Nakatsuji and Yasuda's correction for the 4RDM formula [H. Nakatsuji and K. Yasuda, Phys. Rev. Lett. 76, 1039 (1996)] as well as a corrective approach for the 3RDM functional. A different reconstruction strategy, the ensemble representability method (ERM), is introduced to build the 3- and 4-RDMs by enforcing four-ensemble representability and contraction conditions. We derive the CSE in second quantization without Valdemoro's matrix contraction mapping and offer the first proof of Nakatsuji's theorem for the second-quantized CSE. Both the functional and ERM reconstruction strategies are employed with the CSE to solve for the energies and the 2RDMs of a quasispin model without wave functions. We elucidate the iterative solution of the CSE through an analogy with the power method for eigenvalue equations. Resulting energies of the CSE methods are comparable to single-double configuration-interaction (SDCI) energies, and the 2RDMs are more accurate by an order of magnitude than those from SDCI. While the CSE has been applied to systems with 14 electrons, we present results for as many as 40 particles. Results indicate that the 2RDM remains accurate as the number of particles increases. We also report a direct determination of excited-state 2RDMs through the CSE. By circumventing the wave function, the CSE presents new possibilities for treating electron correlation.
TL;DR: In this paper, cavity-QED effects for the radiative coupling of atoms in a dilute vapor to the external evanescent field of a whisperinggallery mode (WGM) in a fused silica microsphere were investigated.
Abstract: We report measurements of cavity-QED effects for the radiative coupling of atoms in a dilute vapor to the external evanescent field of a whispering-gallery mode (WGM) in a fused silica microsphere. The high Q (5 x 10^(7)), small mode volume (10^(-8) cm^(3)), and unusual symmetry of the microcavity evanescent field enable velocity-selective interactions between fields with photon number of order unity in the WGM and (N) over bar(T) similar to 1 atoms in the surrounding vapor.
TL;DR: In this article, a quantization scheme for the phenomenological Maxwell theory of the full electromagnetic field in an inhomogeneous three-dimensional, dispersive and absorbing dielectric medium is developed.
Abstract: A quantization scheme for the phenomenological Maxwell theory of the full electromagnetic field in an inhomogeneous three-dimensional, dispersive and absorbing dielectric medium is developed. The classical Maxwell equations with spatially varying and Kramers-Kronig consistent permittivity are regarded as operator-valued field equations, introducing additional current- and charge-density operator fields in order to take into account the noise associated with the dissipation in the medium. It is shown that the equal-time commutation relations between the fundamental electromagnetic fields $\hat E$ and $\hat B$ and the potentials $\hat A$ and $\hat \phi$ in the Coulomb gauge can be expressed in terms of the Green tensor of the classical problem. From the Green tensors for bulk material and an inhomogeneous medium consisting of two bulk dielectrics with a common planar interface it is explicitly proven that the well-known equal-time commutation relations of QED are preserved.
TL;DR: In this article, it was shown that the two-photon state generated in the process of spontaneous parametric down-conversion in a thin crystal carries information about the angular spectrum of the pump beam.
Abstract: We show that the two-photon state generated in the process of spontaneous parametric down-conversion in a thin crystal carries information about the angular spectrum of the pump beam. This information transfer allows one to control the transverse correlation properties of the down-converted fields by manipulating the pump field, with consequences for a broad class of experiments. The effect is demonstrated theoretically and experimentally, in connection with the formation of fourth-order images by the down-converted beams.
TL;DR: In this article, the authors derived the quantum phase-noise limit to the sensitivity of a Mach-Zehnder interferometer in which the incident quantum particles enter via both input ports and showed that if the incident particles are entangled and correlated properly, then the phase sensitivity scales asymptotically like the Heisenberg-limited Ω(1/N), where N is the number of particles incident per unit time.
Abstract: I derive the quantum phase-noise limit to the sensitivity of a Mach-Zehnder interferometer in which the incident quantum particles enter via both input ports I show that if the incident particles are entangled and correlated properly, then the phase sensitivity scales asymptotically like the Heisenberg-limited $\ensuremath{\Delta}\ensuremath{\varphi}=O(1/N),$ for large $N,$ where $N$ is the number of particles incident per unit time (In a one-input-port device, the sensitivity can be at best $\ensuremath{\Delta}\ensuremath{\varphi}=1/\sqrt{N}$) My calculation applies to bosons or fermions of arbitrary integer or half-integer spin Applications to optical, atom-beam, and atom-laser gyroscopes are discussed---in particular, an atom-laser can be used to obtain the required entanglements for achieving this Heisenberg-limited sensitivity with atomic matter waves
TL;DR: In this article, strong-field single ionization and double ionization of two diatomic molecules were studied and compared to Xe and Ar, using an intense ultrashort pulse Ti:sapphire laser in the $2.5 to $8.5 GHz range.
Abstract: Strong-field single ionization and double ionization of two diatomic molecules, ${\mathrm{O}}_{2}$ and ${\mathrm{N}}_{2},$ are studied and compared to Xe and Ar, using an intense ultrashort pulse Ti:sapphire laser in the $2\ifmmode\times\else\texttimes\fi{}{10}^{13}$ to $8\ifmmode\times\else\texttimes\fi{}{10}^{14}{\mathrm{W}/\mathrm{c}\mathrm{m}}^{2}$ intensity range. ${\mathrm{N}}_{2}$ behaves like a structureless atom for both single and double ionization. The recently reported suppression of the ${\mathrm{O}}_{2}^{+}$ ion yield compared to ${\mathrm{Xe}}^{+}$ is confirmed in our experiment, but we show that the suppression is not due to dissociative recombination. Rather, we conclude that the ionization rate of ${\mathrm{O}}_{2}$ is below that predicted by tunneling ionization. We extend the study to the double ionization of ${\mathrm{O}}_{2}$ and find a distinctly reduced nonsequential double-ionization rate. We find evidence that electronic structure influences strong-field tunneling ionization in molecules.
TL;DR: In this article, it was shown that the Wigner function of the Einstein-Podolsky-Rosen state, though positive definite, provides direct evidence of the nonlocal character of this state.
Abstract: We demonstrate that the Wigner function of the Einstein-Podolsky-Rosen state, though positive definite, provides direct evidence of the nonlocal character of this state. The proof is based on an observation that the Wigner function describes correlations in the joint measurement of the phase-space displaced parity operator.
TL;DR: In this paper, a constructive method for simulating small-scale quantum circuits by use of linear optical devices is presented, which relies on the representation of several quantum bits by a single photon and on the implementation of universal quantum gates using simple optical components (beam splitters, phase shifters, etc.).
Abstract: A constructive method for simulating small-scale quantum circuits by use of linear optical devices is presented. It relies on the representation of several quantum bits by a single photon, and on the implementation of universal quantum gates using simple optical components (beam splitters, phase shifters, etc.). This suggests that the optical realization of small quantum networks with present-day quantum optics technology is a reasonable goal. This technique could be useful for demonstrating basic concepts of simple quantum algorithms or error-correction schemes. The optical analog of a nontrivial three-bit quantum circuit is presented as an illustration.
TL;DR: In this article, a mean field study of the binary Bose-Einstein condensate mixtures was performed as a function of the mutual repulsive interaction strength, and it was shown that there are two distinct phases: the weakly segregated phase characterized by a ''penetration depth'' and the strongly segregated phase characterised by a healing length.
Abstract: We perform a mean-field study of the binary Bose-Einstein condensate mixtures as a function of the mutual repulsive interaction strength. In the phase segregated regime, we find that there are two distinct phases: the weakly segregated phase characterized by a ``penetration depth'' and the strongly segregated phase characterized by a healing length. In the weakly segregated phase the symmetry of the shape of each condensate will not take that of the trap because of the finite surface tension, but its total density profile still does. In the strongly segregated phase even the total density profile takes a different symmetry from that of the trap because of the mutual exclusion of the condensates. The lower critical condensate-atom number to observe the complete phase segregation is discussed. A comparison to recent experimental data suggests that the weakly segregated phase has been observed.