Factoring and Fourier Transformation with a Mach-Zehnder Interferometer

The scheme of Clauser and Dowling (Phys. Rev. A 53, 4587 (1996)) for factoring $N$ by means of an N-slit interference experiment is translated into an experiment with a single Mach-Zehnder interferometer. With dispersive phase shifters the ratio of the coherence length to wavelength limits the numbers that can be factored. A conservative estimate permits $N \approx 10^7$. It is furthermore shown, that sine and cosine Fourier coefficients of a real periodic function can be obtained with such an interferometer.Comment: 5 pages, 2 postscript figures; to appear in Phys.Rev.A, Nov. 1997; Figures contained only in replaced versio

Is Quantum Mechanics Compatible with a Deterministic Universe? Two Interpretations of Quantum Probabilities

Two problems will be considered: the question of hidden parameters and the problem of Kolmogorovity of quantum probabilities. Both of them will be analyzed from the point of view of two distinct understandings of quantum mechanical probabilities. Our analysis will be focused, as a particular example, on the Aspect-type EPR experiment. It will be shown that the quantum mechanical probabilities appearing in this experiment can be consistently understood as conditional probabilities without any paradoxical consequences. Therefore, nothing implies in the Aspect experiment that quantum theory is incompatible with a deterministic universe.Comment: REVISED VERSION! ONLY SMALL CHANGES IN THE TEXT! compressed and uuencoded postscript, a uuencoded version of a demo program file (epr.exe for DOS) is attached as a "Figure

Strict detector-efficiency bounds for n-site Clauser-Horne inequalities

An analysis of detector-efficiency in many-site Clauser-Horne inequalities is presented, for the case of perfect visibility. It is shown that there is a violation of the presented n-site Clauser-Horne inequalities if and only if the efficiency is greater than n/(2n-1). Thus, for a two-site two-setting experiment there are no quantum-mechanical predictions that violate local realism unless the efficiency is greater than 2/3. Secondly, there are n-site experiments for which the quantum-mechanical predictions violate local realism whenever the efficiency exceeds 1/2.Comment: revtex, 5 pages, 1 figure (typesetting changes only

Does Clauser-Horne-Shimony-Holt Correlation or Freedman-Clauser Correlation lead to the largest violation of Bell's Inequality?

An inequality is deduced from Einstein's locality and a supplementary assumption. This inequality defines an experiment which can actually be performed with present technology to test local realism. Quantum mechanics violate this inequality a factor of 1.5. In contrast, quantum mechanics violates previous inequalities (for example, Clauser-Horne-Shimony-Holt inequality of 1969, Freedman-Clauser inequality of 1972, Clauser-Horne inequality of 1974) by a factor of $\sqrt 2$. Thus the magnitude of violation of the inequality derived in this paper is approximately $20.7$ larger than the magnitude of violation of previous inequalities. This result can be particularly important for the experimental test of locality.Comment: 15 pages, LaTeX file, no figure

Distillability and positivity of partial transposes in general quantum field systems

Criteria for distillability, and the property of having a positive partial transpose, are introduced for states of general bipartite quantum systems. The framework is sufficiently general to include systems with an infinite number of degrees of freedom, including quantum fields. We show that a large number of states in relativistic quantum field theory, including the vacuum state and thermal equilibrium states, are distillable over subsystems separated by arbitrary spacelike distances. These results apply to any quantum field model. It will also be shown that these results can be generalized to quantum fields in curved spacetime, leading to the conclusion that there is a large number of quantum field states which are distillable over subsystems separated by an event horizon.Comment: 25 pages, 2 figures. v2: Typos removed, references and comments added. v3: Expanded introduction and reference list. To appear in Rev. Math. Phy

Quantum entanglement and Bell violation of two coupled cavity fields in dissipative environment

We study the quantum entanglement between two coupled cavities, in which one is initially prepared in a mesoscopic superposition state and the other is in the vacuum in dissipative environment and show how the entanglement between two cavities can arise in the dissipative environment. The dynamic behavior of the nonlocality for the system is also investigated.Comment: 12 pages, 5 figure

Generalized quantum measurements and local realism

The structure of a local hidden variable model for experiments involving sequences of measurements rigorously is analyzed. Constraints imposed by local realism on the conditional probabilities of the outcomes of such measurement schemes are explicitly derived. The violation of local realism in the case of ``hidden nonlocality'' is illustrated by an operational example.Comment: Revtex, 12 pages; Some modifications of introduction has been made; a note stating that part of results had been obtained earlier by other authors, has been added; one postscript figure available at request from [email protected]

Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels

Two separated observers, by applying local operations to a supply of not-too-impure entangled states ({\em e.g.} singlets shared through a noisy channel), can prepare a smaller number of entangled pairs of arbitrarily high purity ({\em e.g.} near-perfect singlets). These can then be used to faithfully teleport unknown quantum states from one observer to the other, thereby achieving faithful transfrom one observer to the other, thereby achieving faithful transmission of quantum information through a noisy channel. We give upper and lower bounds on the yield $D(M)$ of pure singlets ($\ket{\Psi^-}$) distillable from mixed states $M$, showing $D(M)>0$ if \bra{\Psi^-}M\ket{\Psi^-}>\half.Comment: 4 pages (revtex) plus 1 figure (postscript). See also http://vesta.physics.ucla.edu/~smolin/ . Replaced to correct interchanged $\sigma_x$ and $\sigma_z$ near top of column 2, page

Mixed State Entanglement and Quantum Error Correction

Entanglement purification protocols (EPP) and quantum error-correcting codes (QECC) provide two ways of protecting quantum states from interaction with the environment. In an EPP, perfectly entangled pure states are extracted, with some yield D, from a mixed state M shared by two parties; with a QECC, an arbi- trary quantum state $|\xi\rangle$ can be transmitted at some rate Q through a noisy channel $\chi$ without degradation. We prove that an EPP involving one- way classical communication and acting on mixed state $\hat{M}(\chi)$ (obtained by sharing halves of EPR pairs through a channel $\chi$) yields a QECC on $\chi$ with rate $Q=D$, and vice versa. We compare the amount of entanglement E(M) required to prepare a mixed state M by local actions with the amounts $D_1(M)$ and $D_2(M)$ that can be locally distilled from it by EPPs using one- and two-way classical communication respectively, and give an exact expression for $E(M)$ when $M$ is Bell-diagonal. While EPPs require classical communica- tion, QECCs do not, and we prove Q is not increased by adding one-way classical communication. However, both D and Q can be increased by adding two-way com- munication. We show that certain noisy quantum channels, for example a 50% depolarizing channel, can be used for reliable transmission of quantum states if two-way communication is available, but cannot be used if only one-way com- munication is available. We exhibit a family of codes based on universal hash- ing able toachieve an asymptotic $Q$ (or $D$) of 1-S for simple noise models, where S is the error entropy. We also obtain a specific, simple 5-bit single- error-correcting quantum block code. We prove that {\em iff} a QECC results in high fidelity for the case of no error the QECC can be recast into a form where the encoder is the matrix inverse of the decoder.Comment: Resubmission with various corrections and expansions. See also http://vesta.physics.ucla.edu/~smolin/ for related papers and information. 82 pages latex including 19 postscript figures included using psfig macro

Quantum Nonlocality in Phase Space

We propose an experiment demonstrating the nonlocality of a quantum singlet-like state generated from a single photon incident on a beam splitter. Each of the two spatially separated apparatuses in the setup performs a strongly unbalanced homodyning, employing a single photon counting detector. We show that the correlation functions violating the Bell inequalities in the proposed experiment are given by the joint two-mode Q-function and the Wigner function of the optical singlet-like state. This establishes a direct relationship between two intriguing aspects of quantum mechanics: the nonlocality of entangled states and the noncommutativity of quantum observables, which underlies the nonclassical structure of phase space quasidistribution functions.Comment: 4 pages, REVTe