arXiv subjects

Ting-Gui Zhang

Publications and source records attributed to Ting-Gui Zhang.

10 recordsLinked to original sources

arXiv2019

Uncertainties of genuinely incompatible triple measurements based on statistical distance

We investigate the measurement uncertainties of a triple of positive operator-valued measures (POVMs) based on statistical distance, and formulate state-independent tight uncertainty inequalities satisfied by the three measurements in terms of triple-wise joint measurability. Particularly, uncertainty inequalities for three unbiased qubit measurements are presented with analytical lower bounds which relates to the necessary and sufficient condition of the triple-wise joint measurability of the given triple. We show that the measurement uncertainties for a triple measurement are essentially different from the ones obtained by pair wise measurement uncertainties by comparing the lower bounds of different measurement uncertainties.

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arXiv2016

von Neumann measurement-related matrices and the nullity condition for quantum correlation

We study von Neumann measurement-related matrices, and the nullity condition of quantum correlation. We investigate the properties of these matrices that are related to a von Neumann measurement. It is shown that these (m^2-1)* (m^2-1) matrices are idempotent, and have rank m-1. These properties give rise to necessary conditions for the nullity of quantum correlations in bipartite systems. Finally, as an example we discuss quantum correlation in Bell diagonal states.

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arXiv2014

SLOCC Invariants for Multipartite Mixed States

We construct a nontrivial set of invariants for any multipartite mixed states under the SLOCC symmetry. These invariants are given by hyperdeterminants and independent from basis change. In particular, a family of d^2 invariants for arbitrary d-dimensional even partite mixed states are explicitly given.

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arXiv2013

Criterion of Local Unitary Equivalence for Multipartite States

We study the local unitary equivalence of arbitrary dimensional multipartite quantum mixed states. We present a necessary and sufficient criterion of the local unitary equivalence for general multipartite states based on matrix realignment. The criterion is shown to be operational even for particularly degenerated states by detailed examples. Besides, explicit expressions of the local unitary operators are constructed for locally equivalent states. In complement to the criterion, an alternative approach based on partial transposition of matrices is also given, which makes the criterion more effective in dealing with generally degenerated mixed states.

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arXiv2013

Local unitary invariants for multipartite states

We study the invariants of arbitrary dimensional multipartite quantum states under local unitary transformations. For multipartite pure states, we give a set of invariants in terms of singular values of coefficient matrices. For multipartite mixed states, we propose a set of invariants in terms of the trace of coefficient matrices. For full ranked mixed states with nondegenerate eigenvalues, this set of invariants is also the necessary and sufficient conditions for the local unitary equivalence of such two states.

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arXiv2013

Separable State Decompositions for a Class of Mixed States

We study certain quantum states for which the PPT criterion is both sufficient and necessary for separability. A class of $n\times n$ bipartite mixed states is presented and the conditions of PPT for these states are derived. The separable pure state decompositions of these states are explicitly constructed when they are PPT.

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arXiv2013

A Note on State Decomposition Independent Local Invariants

We derive a set of invariants under local unitary transformations for arbitrary dimensional quantum systems. These invariants are given by hyperdeterminants and independent from the detailed pure state decompositions of a given quantum state. They also give rise to necessary conditions for the equivalence of quantum states under local unitary transformations.

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arXiv2013

Entanglement Detection and Distillation for Arbitrary Bipartite Systems

We present an inequality for detecting entanglement and distillability of arbitrary dimensional bipartite systems. This inequality provides a sufficient condition of entanglement for bipartite mixed states, and a necessary and sufficient condition of entanglement for bipartite pure states. Moreover, the inequality also gives a necessary and sufficient condition for distillability.

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arXiv2013

Quantum Correlations Induced by Local von Neumann Measurement

We study the total quantum correlation, semiquantum correlation and joint quantum correlation induced by local von Neumann measurement in bipartite system.We analyze the properties of these quantum correlations and obtain analytical formula for pure states. The experimental witness for these quantum correlations is further provided and the significance of these quantum correlations is discussed in the context of local distinguishability of quantum states.

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arXiv2013

Identification of three-qubit entanglement

We present a way of identifying all kinds of entanglement for three-qubit pure states in terms of the expectation values of Pauli operators. The necessary and sufficient conditions to classify the fully separable, biseparable, and genuine entangled states are explicitly given. The approach can be generalized to multipartite high-dimensional cases. For three-qubit mixed states, we propose two kinds of inequalities in terms of the expectation values of complementary observables. One inequality has advantages in entanglement detection of the quantum state with positive partial transpositions, and the other is able to detect genuine entanglement. The results give an effective method for experimental entanglement identification.

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