arXiv subjects

Shao-Ming Fei

Publications and source records attributed to Shao-Ming Fei.

At least 379 records · Page 21Linked to original sources

arXiv2016

Uniform Entanglement Frames

We present several criteria for genuine multipartite entanglement from universal uncertainty relations based on majorization theory. Under non-negative Schur-concave functions, the vector-type uncertainty relation generates a family of infinitely many detectors to check genuine multipartite entanglement. We also introduce the concept of $k$-separable circles via geometric distance for probability vectors, which include at most $(k-1)$-separable states. The entanglement witness is also generalized to a universal entanglement witness which is able to detect the $k$-separable states more accurately.

quant-ph↗

arXiv2016

The local indistinguishability of multipartite product states

In this paper, we mainly study the local indistinguishability of multipartite product states. Firstly, we follow the method of Z.-C. Zhang \emph{et al}[Phys. Rev. A 93, 012314(2016)] to give another more concise set of $2n-1$ orthogonal product states in $\mathbb{C}^m\otimes\mathbb{C}^n(4\leq m\leq n)$ which can not be distinguished by local operations and classical communication(LOCC). Then we use the 3 dimension cubes to present some product states which give us an intuitive view how to construct locally indistinguishable product states in tripartite quantum system. At last, we give an explicit construction of locally indistinguishable orthogonal product states for general multipartite system.

quant-ph↗

arXiv2016

Steering Bell-diagonal states

We investigate the steerability of two-qubit Bell-diagonal states under projective measurements by the steering party. In the simplest nontrivial scenario of two projective measurements, we solve this problem completely by virtue of the connection between the steering problem and the joint-measurement problem. A necessary and sufficient criterion is derived together with a simple geometrical interpretation. Our study shows that a Bell-diagonal state is steerable by two projective measurements iff it violates the Clauser-Horne-Shimony-Holt (CHSH) inequality, in sharp contrast with the strict hierarchy expected between steering and Bell nonlocality. We also introduce a steering measure and clarify its connections with concurrence and the volume of the steering ellipsoid. In particular, we determine the maximal concurrence and ellipsoid volume of Bell-diagonal states that are not steerable by two projective measurements. Finally, we explore the steerability of Bell-diagonal states under three projective measurements. A simple sufficient criterion is derived, which can detect the steerability of many states that are not steerable by two projective measurements. Our study offers valuable insight on steering of Bell-diagonal states as well as the connections between entanglement, steering, and Bell nonlocality.

quant-ph↗

arXiv2016

Geometric Global Quantum Discord of Two-qubit States

We consider the geometric global quantum discord (GGQD) of two-qubit systems. By analyzing the symmetry of geometric global quantum discord we give an approach for deriving analytical formulae of the extremum problem which lies at the core of computing the GGQD for arbitrary two-qubit states. Furthermore, formulae of GGQD of arbitrary two-qubit states and some concrete examples are presented.

quant-ph↗

arXiv2016

A note on one-way quantum deficit and quantum discord

One-way quantum deficit and quantum discord are two important measures of quantum correlations. We revisit the relationship between them in two-qubit systems. We investigate the conditions that both one-way quantum deficit and quantum discord have the same optimal measurement ensembles, and demonstrate that one-way quantum deficit can be derived from the quantum discord for a class of X states. Moreover, we give an explicit relation between one-way quantum deficit and entanglement of formation. We show that under phase damping channel both one-way quantum deficit and quantum discord evolve exactly in the same way for four parameters X states. Some examples are presented in details.

quant-ph↗

arXiv2015

Generalized Monogamy Relations of Concurrence for N-qubit Systems

We present a new kind of monogamous relations based on concurrence and concurrence of assistance. For $N$-qubit systems $ABC_1...C_{N-2}$, the monogamy relations satisfied by the concurrence of $N$-qubit pure states under the partition $AB$ and $C_1...C_{N-2}$, as well as under the partition $ABC_1$ and $C_2...C_{N-2}$ are established, which give rise to a kind of restrictions on the entanglement distribution and trade off among the subsystems.

quant-ph↗

arXiv2015

Genuine multipartite entanglement detection and lower bound of multipartite concurrence

The problems of genuine multipartite entanglement detection and classification are challenging. We show that a multipartite quantum state is genuine multipartite entangled if the multipartite concurrence is larger than certain quantities given by the number and the dimension of the subsystems. This result also provides a classification of various genuine multipartite entanglement. Then, we present a lower bound of the multipartite concurrence in terms of bipartite concurrences. While various operational approaches are available for providing lower bounds of bipartite concurrences, our results give an effective operational way to detect and classify the genuine multipartite entanglement. As applications, the genuine multipartite entanglement of tripartite systems is analyzed in detail.

quant-ph↗

arXiv2015

Trade-off Relations of Bell Violations among Pairwise Qubit Systems

We investigate the nonlocality distributions among multiqubit systems based on the maximal violations of the Clauser-Horne-Shimony-Holt (CHSH) inequality of reduced pairwise qubit systems. We present a trade-off relation satisfied by these maximal violations, which gives rise to restrictions on the distribution of nonlocality among the subqubit systems. For a three-qubit system, it is impossible that all pairs of qubits violate the CHSH inequality, and once a pair of qubits violates the CHSH inequality maximally, the other two pairs of qubits must both obey the CHSH inequality. Detailed examples are given to illustrate the trade-off relations, and the trade-off relations are generalized to arbitrary multiqubit systems.

quant-ph↗

arXiv2015

Separability criteria based on the realignment of density matrices and reduced density matrices

By combining a parameterized Hermitian matrix, the realignment matrix of the bipartite density matrix $ρ$ and the vectorization of its reduced density matrices, we present a family of separability criteria, which are stronger than the computable cross norm or realignment (CCNR) criterion. With linear contraction methods, the proposed criteria can be used to detect the multipartite entangled states that are biseparable under any bipartite partitions. Moreover, we show by examples that the presented multipartite separability criteria can be more efficient than the corresponding multipartite realignment criterion based on CCNR, multipartite correlation tensor criterion and multipartite covariance matrix criterion.

quant-ph↗

arXiv2015

Sum uncertainty relations for arbitrary $N$ incompatible observables

We formulate uncertainty relations for arbitrary $N$ observables. Two uncertainty inequalities are presented in terms of the sum of variances and standard deviations, respectively. The lower bounds of the corresponding sum uncertainty relations are explicitly derived. These bounds are shown to be tighter than the ones such as derived from the uncertainty inequality for two observables [Phys. Rev. Lett. 113, 260401 (2014)]. Detailed examples are presented to compare among our results with some existing ones.

quant-ph↗

arXiv2015

Nonlocality of orthogonal product basis quantum states

We study the local indistinguishability of mutually orthogonal product basis quantum states in the high-dimensional quantum system. In the quantum system of $\mathbb{C}^d\otimes\mathbb{C}^d$, where $d$ is odd, Zhang \emph{et al} have constructed $d^2$ orthogonal product basis quantum states which are locally indistinguishable in [Phys. Rev. A. {\bf 90}, 022313(2014)]. We find a subset contains with $6d-9$ orthogonal product states which are still locally indistinguishable. Then we generalize our method to arbitrary bipartite quantum system $\mathbb{C}^m\otimes\mathbb{C}^n$. We present a small set with only $3(m+n)-9$ orthogonal product states and prove these states are LOCC indistinguishable. Even though these $3(m+n)-9$ product states are LOCC indistinguishable, they can be distinguished by separable measurements. This shows that separable operations are strictly stronger than the local operations and classical communication.

quant-ph↗

arXiv2015

Quantum Discord for $d\otimes2$ Systems

We present an analytical solution for classical correlation, defined in terms of linear entropy, in an arbitrary $d\otimes 2$ system when the second subsystem is measured. We show that the optimal measurements used in the maximization of the classical correlation in terms of linear entropy, when used to calculate the quantum discord in terms of von Neumann entropy, result in a tight upper bound for arbitrary $d\otimes 2$ systems. This bound agrees with all known analytical results about quantum discord in terms of von Neumann entropy and, when comparing it with the numerical results for $10^6$ two-qubit random density matrices, we obtain an average deviation of order $10^{-4}$. Furthermore, our results give a way to calculate the quantum discord for arbitrary $n$-qubit GHZ and W states evolving under the action of the amplitude damping noisy channel.

quant-ph↗

arXiv2015

Quantum Nonlocality of Arbitrary Dimensional Bipartite States

We study the nonlocality of arbitrary dimensional bipartite quantum states. By computing the maximal violation of a set of multi-setting Bell inequalities, an analytical and computable lower bound has been derived for general two-qubit states. This bound gives the necessary condition that a two-qubit state admits no local hidden variable models. The lower bound is shown to be better than that from the CHSH inequality in judging the nonlocality of some quantum states. The results are generalized to the case of high dimensional quantum states, and a sufficient condition for detecting the non-locality has been presented.

quant-ph↗

arXiv2015

Local Unitary Invariants of Generic Multi-qubit States

We present a complete set of local unitary invariants for generic multi-qubit systems which gives necessary and sufficient conditions for two states being local unitary equivalent. These invariants are canonical polynomial functions in terms of the generalized Bloch representation of the quantum states. In particular, we prove that there are at most 12 polynomial local unitary invariants for two-qubit states and at most 90 polynomials for three-qubit states. Comparison with Makhlin's 18 local unitary invariants is given for two-quibit systems.

quant-ph↗

arXiv2015

Detection of Ideal Resource for Multiqubit Teleportation

We give a sufficient condition in detecting entanglement resource for perfect multiqubit teleportation. The criterion involves only local measurements on some complementary observables and can be experimentally implemented. It is also a necessary condition for fully separability of multiqubit states. Moreover, by proving the optimality of teleportation witnesses, we solve the open problem in [Phys. Rev. A {\bf 86}, 032315 (2012)].

quant-ph↗

arXiv2015

One-Way Deficit of Two Qubit X States

Quantum deficit originates in questions regarding work extraction from quantum systems coupled to a heat bath [Phys. Rev. Lett. 89, 180402 (2002)]. It links quantum correlations with quantum thermodynamics and provides a new standpoint for understanding quantum non-locality. In this paper, we propose a new method to evaluate the one-way deficit for a class of two-qubit states. The dynamic behavior of the one-way deficit under decoherence channel is investigated and it is shown that the one-way deficit of the X states with five parameters is more robust against the decoherence than the entanglement.

quant-ph↗

arXiv2015

The Saturation of Several Universal Inequalities in Information-Processing

In this paper, we characterize the saturation of four universal inequalities in quantum information theory, including a variant version of strong subadditivity inequality for von Neumann entropy, the coherent information inequality, the Holevo quantity and average entropy inequalities. These results shed new light on quantum information inequalities.

quant-ph↗

arXiv2015

A Note on Mutually Unbiased Unextendible Maximally Entangled Bases in $\mathbb{C}^{2}\bigotimes \mathbb{C}^{3}$

We systematically study the construction of mutually unbiased bases in $\mathbb{C}^{2}\bigotimes\mathbb{C}^{3}$, such that all the bases are unextendible maximally entangled ones. Necessary conditions of constructing a pair of mutually unbiased unextendible maximally entangled bases in $\mathbb{C}^{2}\bigotimes\mathbb{C}^{3}$ are derived. Explicit examples are presented.

quant-ph↗