662 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 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 . 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 . Thus the magnitude of violation
of the inequality derived in this paper is approximately 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 of pure singlets ()
distillable from mixed states , showing 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
and 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 can be transmitted at some rate Q through a
noisy channel without degradation. We prove that an EPP involving one-
way classical communication and acting on mixed state (obtained
by sharing halves of EPR pairs through a channel ) yields a QECC on
with rate , and vice versa. We compare the amount of entanglement
E(M) required to prepare a mixed state M by local actions with the amounts
and that can be locally distilled from it by EPPs using one-
and two-way classical communication respectively, and give an exact expression
for when 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 (or ) 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
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