Sixia Yu

Quantum discord of two-qubitXstates

Quantum discord provides a measure for quantifying quantum correlations beyond entanglement and is very hard to compute even for two-qubit states because of the minimization over all possible measurements. Recently a simple algorithm to evaluate the quantum discord for two-qubit X states was proposed by Ali, Rau, and Alber [Phys. Rev. A 81, 042105 (2010)] with minimization taken over only a few cases. Here we shall at first identify a class of X states, whose quantum discord can be evaluated analytically without any minimization, for which their algorithm is valid, and also identify a family of X states for which their algorithm fails. And then we demonstrate that this special family of X states provides furthermore an explicit example for the inequivalence between the minimization over positive operator-valued measures and that over von Neumann measurements.

State-independent proof of Kochen-Specker theorem with 13 rays.

Quantum contextuality, as proved by Kochen and Specker, and also by Bell, should manifest itself in any state in any system with more than two distinguishable states and recently has been experimentally verified. However, for the simplest system capable of exhibiting contextuality, a qutrit, the quantum contextuality is verified only state dependently in experiment because too many (at least 31) observables are involved in all the known state-independent tests. Here we report an experimentally testable inequality involving only 13 observables that is satisfied by all noncontextual realistic models while being violated by all qutrit states. Thus our inequality facilitates a state-independent test of the quantum contextuality for an indivisible quantum system. We also provide a record-breaking state-independent proof of the Kochen-Specker theorem with 13 directions determined by 26 points on the surface of a magic cube.

Graphical Nonbinary Quantum Error-Correcting Codes

In this paper, we present a systematic way based on the nonbinary graph state of constructing good nonbinary quantum codes, both additive and nonadditive, for systems with integer dimensions. With a computer search, which results in many interesting codes including some nonadditive codes meeting the Singleton bounds, we are able to construct explicitly four families of optimal codes, namely,

All Entangled Pure States Violate a Single Bell’s Inequality

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Nonadditive Quantum Error-Correcting Code

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Entanglement detection by local orthogonal observables.

{[[7,3,3]]}_{p}

Entropic uncertainty relation for mutually unbiased bases

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Comprehensive test of entanglement for two-level systems via the indeterminacy relationship.

{[[8,2,4]]}_{p}

Classifying N-qubit entanglement via Bell's inequalities.

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Greenberger-Horne-Zeilinger paradoxes from qudit graph states.

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