162 research outputs found

    Optimal States for Bell inequality Violations using Quadrature Phase Homodyne Measurements

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    We identify what ideal correlated photon number states are to required to maximize the discrepancy between local realism and quantum mechanics when a quadrature homodyne phase measurement is used. Various Bell inequality tests are considered.Comment: 6 pages, 5 Figure

    Parallel Repetition of Entangled Games with Exponential Decay via the Superposed Information Cost

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    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 ω(G)\omega^*(G) of a game GG 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 nn-fold parallel repetition GnG^n of GG consists of nn instances of GG where the players receive all the inputs at the same time and produce all the outputs at the same time. They win GnG^n if they win each instance of GG. In this paper we show that for any game GG such that ω(G)=1ε<1\omega^*(G) = 1 - \varepsilon < 1, ω(Gn)\omega^*(G^n) decreases exponentially in nn. First, for any game GG on the uniform distribution, we show that ω(Gn)=(1ε2)Ω(nlog(IO)log(ε))\omega^*(G^n) = (1 - \varepsilon^2)^{\Omega\left(\frac{n}{\log(|I||O|)} - |\log(\varepsilon)|\right)}, where I|I| and O|O| are the sizes of the input and output sets. From this result, we show that for any entangled game GG, ω(Gn)(1ε2)Ω(nQlog(IO)log(ε)Q)\omega^*(G^n) \le (1 - \varepsilon^2)^{\Omega(\frac{n}{Q\log(|I||O|)} - \frac{|\log(\varepsilon)|}{Q})} where pp is the input distribution of GG and Q=I2maxxypxy2minxypxyQ= \frac{|I|^2 \max_{xy} p_{xy}^2 }{\min_{xy} p_{xy} }. This implies parallel repetition with exponential decay as long as minxy{pxy}0\min_{xy} \{p_{xy}\} \neq 0 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

    Entangled qutrits violate local realism stronger than qubits - an analytical proof

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    In Kaszlikowski [Phys. Rev. Lett. {\bf 85}, 4418 (2000)], it has been shown numerically that the violation of local realism for two maximally entangled NN-dimensional (3N3 \leq N) quantum objects is stronger than for two maximally entangled qubits and grows with NN. In this paper we present the analytical proof of this fact for N=3.Comment: 5 page

    Quantum analogues of Hardy's nonlocality paradox

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    Hardy's nonlocality is a "nonlocality proof without inequalities": it exemplifies that quantum correlations can be qualitatively stronger than classical correlations. This paper introduces variants of Hardy's nonlocality in the CHSH scenario which are realized by the PR-box, but not by quantum correlations. Hence this new kind of Hardy-type nonlocality is a proof without inequalities showing that superquantum correlations can be qualitatively stronger than quantum correlations.Comment: minor fixe

    Qubits from Number States and Bell Inequalities for Number Measurements

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    Bell inequalities for number measurements are derived via the observation that the bits of the number indexing a number state are proper qubits. Violations of these inequalities are obtained from the output state of the nondegenerate optical parametric amplifier.Comment: revtex4, 7 pages, v2: results identical but extended presentation, v3: published versio

    Two qubits of a W state violate Bell's inequality beyond Cirel'son's bound

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    It is shown that the correlations between two qubits selected from a trio prepared in a W state violate the Clauser-Horne-Shimony-Holt inequality more than the correlations between two qubits in any quantum state. Such a violation beyond Cirel'son's bound is smaller than the one achieved by two qubits selected from a trio in a Greenberger-Horne-Zeilinger state [A. Cabello, Phys. Rev. Lett. 88, 060403 (2002)]. However, it has the advantage that all local observers can know from their own measurements whether their qubits belongs or not to the selected pair.Comment: REVTeX4, 5 page

    Characterization of Binary Constraint System Games

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    We consider a class of nonlocal games that are related to binary constraint systems (BCSs) in a manner similar to the games implicit in the work of Mermin [N.D. Mermin, "Simple unified form for the major no-hidden-variables theorems," Phys. Rev. Lett., 65(27):3373-3376, 1990], but generalized to n binary variables and m constraints. We show that, whenever there is a perfect entangled protocol for such a game, there exists a set of binary observables with commutations and products similar to those exhibited by Mermin. We also show how to derive upper bounds strictly below 1 for the the maximum entangled success probability of some BCS games. These results are partial progress towards a larger project to determine the computational complexity of deciding whether a given instance of a BCS game admits a perfect entangled strategy or not.Comment: Revised version corrects an error in the previous version of the proof of Theorem 1 that arises in the case of POVM measurement

    Maximal Violation of Bell Inequalities using Continuous Variables Measurements

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    We propose a whole family of physical states that yield a violation of the Bell CHSH inequality arbitrarily close to its maximum value, when using quadrature phase homodyne detection. This result is based on a new binning process called root binning, that is used to transform the continuous variables measurements into binary results needed for the tests of quantum mechanics versus local realistic theories. A physical process in order to produce such states is also suggested. The use of high-efficiency spacelike separated homodyne detections with these states and this binning process would result in a conclusive loophole-free test of quantum mechanics.Comment: 7 pages, 5 figures, to appear in PRA in a slightly different versio

    Two roles of relativistic spin operators

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    Operators that are associated with several important quantities, like angular momentum, play a double role: they are both generators of the symmetry group and ``observables.'' The analysis of different splittings of angular momentum into "spin" and "orbital" parts reveals the difference between these two roles. We also discuss a relation of different choices of spin observables to the violation of Bell inequalities.Comment: RevTeX 4, 4 pages A discussion on relation of different choices of spin observables to the observed violation of Bell inequalities is added, some misprints corrected and the presentation is clarifie
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