969 research outputs found
Parallel Repetition of Entangled Games with Exponential Decay via the Superposed Information Cost
In a two-player game, two cooperating but non communicating players, Alice
and Bob, receive inputs taken from a probability distribution. Each of them
produces an output and they win the game if they satisfy some predicate on
their inputs/outputs. The entangled value of a game is the
maximum probability that Alice and Bob can win the game if they are allowed to
share an entangled state prior to receiving their inputs.
The -fold parallel repetition of consists of instances of
where the players receive all the inputs at the same time and produce all
the outputs at the same time. They win if they win each instance of .
In this paper we show that for any game such that , decreases exponentially in . First, for
any game on the uniform distribution, we show that , where and are the sizes of the input
and output sets. From this result, we show that for any entangled game ,
where is the input distribution of and
. This implies parallel
repetition with exponential decay as long as for
general games. To prove this parallel repetition, we introduce the concept of
\emph{Superposed Information Cost} for entangled games which is inspired from
the information cost used in communication complexity.Comment: In the first version of this paper we presented a different, stronger
Corollary 1 but due to an error in the proof we had to modify it in the
second version. This third version is a minor update. We correct some typos
and re-introduce a proof accidentally commented out in the second versio
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
Implications of Teleportation for Nonlocality
Adopting an approach similar to that of Zukowski [Phys. Rev. A 62, 032101
(2000)], we investigate connections between teleportation and nonlocality. We
derive a Bell-type inequality pertaining to the teleportation scenario and show
that it is violated in the case of teleportation using a perfect singlet. We
also investigate teleportation using `Werner states' of the form x P + (1-x)
I/4, where P is the projector corresponding to a singlet state and I is the
identity. We find that our inequality is violated, implying nonlocality, if x >
1/sqrt(2). In addition, we extend Werner's local hidden variable model to
simulation of teleportation with the x = 1/2 Werner state. Thus teleportation
using this state does not involve nonlocality even though the fidelity achieved
is 3/4 which is greater than the `classical limit' of 2/3. Finally, we comment
on a result of Gisin's and offer some philosophical remarks on teleportation
and nonlocality generally.Comment: 10 pages, no figures. Title changed to accord with Phys. Rev. A
version. A note and an extra reference have been added. Journal reference
adde
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
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
Retrieval of phase memory in two independent atomic ensembles by Raman process
In spontaneous Raman process in atomic cell at high gain, both the Stokes
field and the accompanying collective atomic excitation (atomic spin wave) are
coherent. We find that, due to the spontaneous nature of the process, the
phases of the Stokes field and the atomic spin wave change randomly from one
realization to another but are anti-correlated. The phases of the atomic
ensembles are read out via another Raman process at a later time, thus
realizing phase memory in atoms. The observation of phase correlation between
the Stokes field and the collective atomic excitations is an important step
towards macroscopic EPR-type entanglement of continuous variables between light
and atoms
Site-specific identification and quantitation of endogenous SUMO modifications under native conditions.
Small ubiquitin-like modifier (SUMO) modification regulates numerous cellular processes. Unlike ubiquitin, detection of endogenous SUMOylated proteins is limited by the lack of naturally occurring protease sites in the C-terminal tail of SUMO proteins. Proteome-wide detection of SUMOylation sites on target proteins typically requires ectopic expression of mutant SUMOs with introduced tryptic sites. Here, we report a method for proteome-wide, site-level detection of endogenous SUMOylation that uses α-lytic protease, WaLP. WaLP digestion of SUMOylated proteins generates peptides containing SUMO-remnant diglycyl-lysine (KGG) at the site of SUMO modification. Using previously developed immuno-affinity isolation of KGG-containing peptides followed by mass spectrometry, we identified 1209 unique endogenous SUMO modification sites. We also demonstrate the impact of proteasome inhibition on ubiquitin and SUMO-modified proteomes using parallel quantitation of ubiquitylated and SUMOylated peptides. This methodological advancement enables determination of endogenous SUMOylated proteins under completely native conditions
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]
Generic Bell correlation between arbitrary local algebras in quantum field theory
We prove that for any two commuting von Neumann algebras of infinite type,
the open set of Bell correlated states for the two algebras is norm dense. We
then apply this result to algebraic quantum field theory -- where all local
algebras are of infinite type -- in order to show that for any two spacelike
separated regions, there is an open dense set of field states that dictate Bell
correlations between the regions. We also show that any vector state cyclic for
one of a pair of commuting nonabelian von Neumann algebras is entangled (i.e.,
nonseparable) across the algebras -- from which it follows that every field
state with bounded energy is entangled across any two spacelike separated
regions.Comment: Third version; correction in the proof of Proposition
Nonsequential positive-operator-valued measurements on entangled mixed states do not always violate a Bell inequality
We present a local-hidden-variable model for positive-operator-valued
measurements (an LHVPOV model) on a class of entangled generalized Werner
states, thus demonstrating that such measurements do not always violate a
Bell-type inequality. We also show that, in general, if the state can
be obtained from with certainty by local quantum operations without
classical communication then an LHVPOV model for the state implies the
existence of such a model for .Comment: 4 pages, no figures. Title changed to accord with Phys. Rev. A
version. Journal reference adde
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