arXiv subjects
Publications and source records attributed to Shao-Ming Fei.
We provide analytical lower and upper bounds for entanglement of formation for bipartite systems, which give a direct relation between the bounds of entanglement of formation and concurrence, and improve the previous results. Detailed examples are presented.
Let $\cH_A\ot \cH_B$ be a bipartite system and $ρ_{AB}$ a quantum state on $\cH_A\ot \cH_B$, $ρ_A = \Ptr{B}{ρ_{AB}}$, $ρ_B = \Ptr{A}{ρ_{AB}}$. Then each quantum operation $Φ_B$ on the quantum system $\cH_B$ can induce a quantum ensemble $\set{(p_μ,ρ_{A,μ})}$ on quantum system $\cH_A$. In this paper, we show that the Holevo quantity $χ\set{(p_μ,ρ_{A,μ})}$ of the quantum ensemble $\set{(p_μ,ρ_{A,μ})}$ can be upper bounded by both subsystem entropies. By using the result, we answer partly a conjecture of Fannes, de Melo, Roga and Życzkowski.
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.
We study the entanglement of tripartite quantum states and provide analytical lower bound of concurrence in terms of the concurrence of sub-states. The lower bound may improve all the existing lower bounds of concurrence. The approach is generalized to arbitrary dimensional multipartite systems.
The nonlocal properties of arbitrary dimensional bipartite quantum systems are investigated. A complete set of invariants under local unitary transformations is presented. These invariants give rise to both sufficient and necessary conditions for the equivalence of quantum states under local unitary transformations: two density matrices are locally equivalent if and only if all these invariants have equal values.
A new form of zero-discord state via Petz's monotonicity condition on relative entropy with equality has been derived systematically. A generalization of symmetric zero-discord states is presented and the related physical implications are discussed.
We study the entanglement of multipartite quantum states. Some lower bounds of the multipartite concurrence are reviewed. We further present more effective lower bounds for detecting and qualifying entanglement, by establishing functional relations between the concurrence and the generalized partial transpositions of the multipartite systems.
We investigate the possibility and conditions to factorize the entanglement evolution of a multiqubit system passing through multi-sided noisy channels. By means of a lower bound of concurrence (LBC) as entanglement measure, we derive an explicit formula of LBC evolution of the N-qubit generalized Greenberger-Horne-Zeilinger (GGHZ) state under some typical noisy channels, based on which two kinds of factorizing conditions for the LBC evolution are presented. In this case, the time-dependent LBC can be determined by a product of initial LBC of the system and the LBC evolution of a maximally entangled GGHZ state under the same multi-sided noisy channels. We analyze the realistic situations where these two kinds of factorizing conditions can be satisfied. In addition, we also discuss the dependence of entanglement robustness on the number of the qubits and that of the noisy channels.
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.
In this paper we point out that the genuine quantum and classical correlations defined by Giorgi et al in two different ways [Phys. Rev. Lett. 107, 190501 (2011), arXiv:1108.0434] do not coincide in general.
We find that the mixed maximally entangled states exist and prove that the form of the mixed maximally entangled states is unique in terms of the entanglement of formation. Moreover, even if the entanglement is quantified by other entanglement measures, this conclusion is still proven right. This result is a supplementary to the generally accepted fact that all maximally entangled states are pure. These states possess important properties of the pure maximally entangled states, for example, these states can be used as a resource for faithful teleportation and they can be distinguished perfectly by local operations and classical communication.
Entanglement of formation is an important measure of quantum entanglement. We present an experimental way to measure the entanglement of formation for arbitrary dimensional pure states. The measurement only evolves local quantum mechanical observables.
It is shown that the dissonance, a quantum correlation which is equal to quantum discord for separable state, is required for assisted optimal state discrimination. We find that only one side discord is required in the optimal process of assisted state discrimination, while another side discord and entanglement is not necessary. We confirm that the quantum discord, which is asymmetric depending on local measurements, is a resource for assisted state discrimination. With the absence of entanglement, we give the necessary and sufficient condition for vanishing one side discord in assisted state discrimination for a class of $d$ nonorthogonal states. As a byproduct, we find that the positive-partial-transposition (PPT) condition is the necessary and sufficient condition for the separability of a class of $2\times d$ states.
We present a set of inequalities based on mean values of quantum mechanical observables nonlinear entanglement witnesses for bipartite quantum systems. These inequalities give rise to sufficient and necessary conditions for separability of all bipartite pure states and even some mixed states. In terms of these mean values of quantum mechanical observables a measurable lower bound of the convex-roof extension of the negativity is derived.
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 can not be recognized by other distillability criteria.
Based on maximally entangled states in the full- and sub-spaces of two qutrits, we present an alternative decomposition of two-qutrit pure states in a form $|Ψ>=\frac{p_{1}}{\sqrt{3}}(|00>+|11>+|22>) +\frac{p_{2}}{\sqrt{2}}(|01>+|12>)+ p_{3}e^{iθ}|02>$. Similar to the Schmidt decomposition, all two-qutrit pure states can be transformed into the alternative decomposition under local unitary transformations, and the parameter $p_1$ is shown to be an entanglement invariant.
We investigate the nonlocality of Schmidt-correlated (SC) states, and present analytical expressions of the maximum violation value of Bell inequalities. It is shown that the violation of Clauser-Horne-Shimony-Holt (CHSH) inequality is necessary and sufficient for the nonlocality of two-qubit SC states, whereas the violation of the Svetlichny inequality is only a sufficient condition for the genuine nonlocality of three-qubit SC states. Furthermore, the relations among the maximum violation values, concurrence and relative entropy entanglement are discussed.
We present a set of inequalities for detecting quantum entanglement of $2\otimes d$ quantum states. For $2\otimes 2$ and $2\otimes 3$ systems, the inequalities give rise to sufficient and necessary separability conditions for both pure and mixed states. For the case of $d>3$, these inequalities are necessary conditions for separability, which detect all entangled states that are not positive under partial transposition and even some entangled states with positive partial transposition. These inequalities are given by mean values of local observables and present an experimental way of detecting the quantum entanglement of $2\otimes d$ quantum states and even multi-qubit pure states.