Searcharxiv⌕ Search

arXiv subjects

Shao-Ming Fei

Publications and source records attributed to Shao-Ming Fei.

At least 415 records · Page 23Linked to original sources
arXiv2013

Super-quantum correlation and geometry for Bell-diagonal states with weak measurements

We propose "super one-way deficit" by weak measurement as the generalization of one-way deficit defined for standard projective measurement. The super one-way deficit for Werner state is obtained analytically. We find that super one-way deficit is smaller than the standard one-way deficit, which contrasts with a straightforward expectation based on the known fact that super-quantum discord by weak measurement is always larger than the quantum discord defined by projective measurement. On the other hand, by tuning the weak measurement continuously to the projective measurement, both super one-way deficit and super-quantum discord converge to the same value, which is either the one-way deficit or the quantum discord both quantifying quantum correlation. In this sense, weak measurement does not necessarily capture more quantumness of correlations. We also give the geometry of super- quantum discord of the Bell-diagonal states with explicit geometrical figures. As an application, the dynamic behavior of super- quantum correlation including super-quantum discord and super one-way deficit under decoherence is investigated. We find that the order relation of the super-quantum correlation and the quantum correlation keep unchanged under the phase flipping channel for the Bell-diagonal states and the Werner states.

quant-ph↗
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.

quant-ph↗
arXiv2013

Geometry of Quantum Computation with Qutrits

Determining the quantum circuit complexity of a unitary operation is an important problem in quantum computation. By using the mathematical techniques of Riemannian geometry, we investigate the efficient quantum circuits in quantum computation with $n$ qutrits. We show that the optimal quantum circuits are essentially equivalent to the shortest path between two points in a certain curved geometry of $SU(3^n)$. As an example, three-qutrit systems are investigated in detail.

quant-ph↗
arXiv2013

Unextendible maximally entangled bases and mutually unbiased bases

We study unextendible maximally entangled basis in arbitrary bipartite spaces. A systematic way of constructing a set of $d^{2}$ orthonormal maximally entangled states in $\mathbb{C}^{d}\bigotimes\mathbb{C}^{d'}(\frac{d'}{2}<d<d')$ is provided. The complementary space of the set of these $d^{2}$ orthonormal maximally entangled states contains no maximally entangled states that are orthogonal to all of them. Furthermore, we investigate mutually unbiased bases in which all the bases are unextendible maximally entangled ones. We present two unextendible maximally entangled bases in $\mathbb{C}^{2}\bigotimes\mathbb{C}^{3}$ which are mutually unbiased.

quant-ph↗
arXiv2013

Characterization of four-qubit states via Bell inequalities

A set of Bell inequalities classifying the quantum entanglement of four-qubit states is presented. These inequalities involve only two measurement settings per observer and can characterize fully separable, bi-separable and tri-separable quantum states. In addition, a quadratic inequality of the Bell operators for four-qubit systems is derived.

quant-ph↗
arXiv2013

A Note on Resistance of NPT to Mixture of Separable States

We study the stability of NPT property of an arbitrary pure entangled state under the mixture of arbitrary pure separable states. For bipartite pure states with Schmidt number $n$ $(n>1)$ which is NPT, we show that this state is still NPT when it is mixed with no more than $\frac{n(n-1)}{2}-1$ arbitrary pure separable states. This result is generalized to multipartite case.

quant-ph↗
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.

quant-ph↗
arXiv2013

One-way Unlocalizable Information Deficit

We introduce one-way unlocalizable information deficit with respect to the one-way information deficit, similar to the definition of one-way unlocalizable quantum discord with respect to one-way quantum discord. The properties of the one-way unlocalizable information deficit and the relations among one-way unlocalizable information deficit, one-way unlocalizable quantum discord, one-way quantum discord, one-way information deficit and other quantum correlations are investigated. Analytical formulas of the one-way unlocalizable quantum discord are given to detailed examples.

quant-ph↗
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.

quant-ph↗
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.

quant-ph↗
arXiv2013

One-way deficit of SU(2) invariant states

We calculate analytically the one-way deficit for systems consisting spin-$j$ and spin-${1}{2}$ subsystems with SU(2) symmetry. Comparing our results with the quantum discord of SU(2) invariant states, we show that the one-way deficit is equal to the quantum discord for half-integer $j$, and is larger than the quantum discord for integer $j$. Moreover, we also compare the one-way deficit with entanglement of formation. The quantum entanglement tends to zero as $j$ increases, while the one-way deficit can remain significantly large.

quant-ph↗
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.

quant-ph↗
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.

quant-ph↗
arXiv2013

Three-tangle and Three-π for a class of tripartite mixed states

We study the tripartite entanglement for a class of mixed states defined by the mixture of GHZ and W states, ρ=p|GHZ> <W|. Based on the Caratheodory theorem and the periodicity assumption, the possible optimal decomposition of the states has been derived, which is not independent on the detailed measure of entanglement. We find that, according to p, there are two different decompositions containing 3 or 4 quantum states in the decomposition respectively. When the decomposition contains 3 quantum states, the tripartite entanglement of the mixed state is simply the entanglement of superposition states of GHZ and W. When the decomposition contains 4 quantum states, the tripartite entanglement of the mixed state is a liner function of p. We also study the relations between the three-tangle and three-π. It is shown that the three-tangle is smaller than the three-π. Moreover, the three-π has a minimal point in the interval 0 and 1, while the three-tangle is a non decreasing function of p.

quant-ph↗
arXiv2013

A Note on Locally Unextendible Non-Maximally Entangled Basis

We study the locally unextendible non-maximally entangled basis (LUNMEB) in $H^{d}\bigotimes H^{d}$. We point out that there exists an error in the proof of the main result of LUNMEB [Quant. Inf. Comput. 12, 0271(2012)], which claims that there are at most $d$ orthogonal vectors in a LUNMEB, constructed from a given non-maximally entangled state. We show that both the proof and the main result are not correct in general. We present a counter example for $d=4$, in which five orthogonal vectors from a specific non-maximally entangled state are constructed. Besides, we completely solve the problem of LUNMEB for the case of $d=2$.

quant-ph↗
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.

quant-ph↗
arXiv2012

Bell inequalities for multipartite qubit quantum systems and their maximal violation

We present a set of Bell inequalities for multiqubit quantum systems. These Bell inequalities are shown to be able to detect multiqubit entanglement better than previous Bell inequalities such as Werner-Wolf-Zukowski- Brukner ones. Computable formulas are presented for calculating the maximal violations of these Bell inequalities for any multiqubit states.

quant-ph↗