Ming-Jing Zhao

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.

Complete Entanglement Witness for Quantum Teleportation

We propose a set of linear quantum entanglement witnesses constituted by local quantum-mechanical observables with each two possible measurement outcomes. These witnesses detect all the entangled resources which give rise to a better fidelity than separable states in quantum teleportation and present both sufficient and necessary conditions in experimentally detecting the useful resources for quantum teleportation.

Experimental Determination of Entanglement for Arbitrary Pure States

We present a way of experimentally determining the concurrence in terms of the expectation values of local observables for arbitrary multipartite pure states. Instead of the joint measurements on two copies of a state in the experiment for two-qubit systems [S. P. Walborn et al., Nature (London) 440, 20 (2006)], we only need one copy of the state in every measurement for any arbitrary dimensional multipartite systems, avoiding the preparation of twin states or the imperfect copy of the state.

A note on fully entangled fraction

We investigate the general characteristics of the fully entangled fraction for quantum states. The fully entangled fractions of isotropic states and Werner states are analytically computed.

Non-commutativity and Local Indistinguishability of Quantum States

We study the local indistinguishability problem of quantum states. By introducing an easily calculated quantity, non-commutativity, we present an criterion which is both necessary and sufficient for the local indistinguishability of a complete set of pure orthogonal product states. A constructive distinguishing procedure to obtain the concrete local measurements and classical communications is given. The non-commutativity of ensembles can be also used to characterize the quantumness for classical-quantum or quantum-classical correlated states.

Lower bound on concurrence and distillation for arbitrary-dimensional bipartite quantum states

We present a lower bound of concurrence for arbitrary-dimensional bipartite quantum states. This lower bound may be used to improve all the known lower bounds of concurrence. Moreover, the lower bound gives rise to an operational sufficient criterion of distillability of quantum entanglement. The significance of our result is illustrated by quantitative evaluation of entanglement for entangled states that fail to be identified by the usual concurrence estimation method and by showing the distillability of mixed states that cannot be recognized by other distillability criteria.

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 (m2 − 1) × (m2 − 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.

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.

Multiqubit quantum teleportation

We provide a class of six-qubit states for three-qubit perfect teleportation. These states include the six-qubit cluster states as a special class. We generalize this class of six-qubit states to 2n-qubit pure states for n-qubit teleportation, n ⩾ 1. These states can be also used for 2n-bit classical information transmission in dense coding.

Entanglement of multipartite Schmidt-correlated states

We generalize the Schmidt-correlated states to multipartite systems. The related equivalence under SLOCC, the separability, entanglement witness, entanglement measures of negativity, concurrence and relative entropy are investigated in detail for the generalized Schmidt-correlated states.