870 research outputs found

### 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

### 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

### Bell's Theorem and Nonlinear Systems

For all Einstein-Podolsky-Rosen-type experiments on deterministic systems the
Bell inequality holds, unless non-local interactions exist between certain
parts of the setup. Here we show that in nonlinear systems the Bell inequality
can be violated by non-local effects that are arbitrarily weak. Then we show
that the quantum result of the existing Einstein-Podolsky-Rosen-type
experiments can be reproduced within deterministic models that include
arbitrarily weak non-local effects.Comment: Accepted for publication in Europhysics Letters. 14 pages, no
figures. In the Appendix (not included in the EPL version) the author says
what he really thinks about the subjec

### 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

### Maximal violation of Bell inequality for any given two-qubit pure state

In the case of bipartite two qubits systems, we derive the analytical
expression of bound of Bell operator for any given pure state. Our result not
only manifest some properties of Bell inequality, for example which may be
violated by any pure entangled state and only be maximally violated for a
maximally entangled state, but also give the explicit values of maximal
violation for any pure state. Finally we point out that for two qubits systems
there is no mixed state which can produce maximal violation of Bell inequality.Comment: 3 pages, 1 figure

### 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

### Entropy inequalities and Bell inequalities for two-qubit systems

Sufficient conditions for (the non-violation of) the Bell-CHSH inequalities
in a mixed state of a two-qubit system are: 1) The linear entropy of the state
is not smaller than 0.5, 2) The sum of the conditional linear entropies is
non-negative, 3) The von Neumann entropy is not smaller than 0.833, 4) The sum
of the conditional von Neumann entropies is not smaller than 0.280.Comment: Errors corrected. See L. Jakobcyk, quant-ph/040908

### General criterion for the entanglement of two indistinguishable particles

We relate the notion of entanglement for quantum systems composed of two
identical constituents to the impossibility of attributing a complete set of
properties to both particles. This implies definite constraints on the
mathematical form of the state vector associated with the whole system. We then
analyze separately the cases of fermion and boson systems, and we show how the
consideration of both the Slater-Schmidt number of the fermionic and bosonic
analog of the Schmidt decomposition of the global state vector and the von
Neumann entropy of the one-particle reduced density operators can supply us
with a consistent criterion for detecting entanglement. In particular, the
consideration of the von Neumann entropy is particularly useful in deciding
whether the correlations of the considered states are simply due to the
indistinguishability of the particles involved or are a genuine manifestation
of the entanglement. The treatment leads to a full clarification of the subtle
aspects of entanglement of two identical constituents which have been a source
of embarrassment and of serious misunderstandings in the recent literature.Comment: 18 pages, Latex; revised version: Section 3.2 rewritten, new Theorems
added, reference [1] corrected. To appear on Phys.Rev.A 70, (2004

### Atomic vapor-based high efficiency optical detectors with photon number resolution

We propose a novel approach to the important fundamental problem of detecting
weak optical fields at the few photon level. The ability to detect with high
efficiency (>99%), and to distinguish the number of photons in a given time
interval is a very challenging technical problem with enormous potential
pay-offs in quantum communications and information processing. Our proposal
diverges from standard solid-state photo-detector technology by employing an
atomic vapor as the active medium, prepared in a specific quantum state using
laser radiation. The absorption of a photon will be aided by a dressing laser,
and the presence or absence of an excited atom will be detected using the
``cycling transition'' approach perfected for ion traps. By first incorporating
an appropriate upconversion scheme, our method can be applied to a wide variety
of optical wavelengths.Comment: 4 pages, 2 figure

### Substituting Quantum Entanglement for Communication

We show that quantum entanglement can be used as a substitute for
communication when the goal is to compute a function whose input data is
distributed among remote parties. Specifically, we show that, for a particular
function among three parties (each of which possesses part of the function's
input), a prior quantum entanglement enables one of them to learn the value of
the function with only two bits of communication occurring among the parties,
whereas, without quantum entanglement, three bits of communication are
necessary. This result contrasts the well-known fact that quantum entanglement
cannot be used to simulate communication among remote parties.Comment: 4 pages REVTeX, no figures. Minor correction

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