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Zhi-Xi Wang

Publications and source records attributed to Zhi-Xi Wang.

At least 91 records · Page 5Linked to original sources
arXiv2016

Trace distance measure of coherence for a class of qudit states

Recently, trace distance measure of coherence has been proposed for characterizing the coherence of a given quantum state. However, it seems difficult to estimate the optimal incoherent state for high dimensional states. An explicit expression for the trace distance measure of coherence for a class of qudit states is provided. We show that the closest incoherent state to the class of qudit states is just the diagonal matrix obtained from it by deleting all off-diagonal elements. It is also shown that the measure of coherence induced by trace distance can act as a measure of coherence for this class of qudit states with some restrictions on the strictly incoherent operations.

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arXiv2016

Strong entropic uncertainty relations for multiple measurements

In this paper, we study entropic uncertainty relations on a finite-dimensional Hilbert space and provide several tighter bounds for multi-measurements, with some of them also valid for Rényi and Tsallis entropies besides the Shannon entropy. We employ majorization theory and actions of the symmetric group to obtain an {\it admixture bound} for entropic uncertainty relations for multi-measurements. Comparisons among all bounds for multi-measurements are shown in figures in our favor.

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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.

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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.

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arXiv2015

Maximal Holevo quantity based on weak measurements

The Holevo bound is a keystone in many applications of quantum information theory. We propose "weak maximal Holevo quantity" with weak measurements as the generalization of the standard Holevo quantity which is defined as the optimal projective measurements. The scenarios that weak measurements is necessary are that only the weak measurements can be performed because for example the system is macroscopic or that one intentionally tries to do so such that the disturbance on the measured system can be controlled for example in quantum key distribution protocols. We evaluate systematically the weak maximal Holevo quantity for Bell-diagonal states and find a series of results. Furthermore, we find that weak measurements can be realized by noise and project measurements.

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arXiv2014

Inequalities detecting entanglement for arbitrary bipartite systems

Based on the generators of $SU(n)$ we present inequalities for detecting quantum entanglement for $2 \otimes d$ and $M \otimes N$ systems. These inequalities provide a sufficient condition of entanglement for bipartite mixed states and give rise to an experimental way of entanglement detection.

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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.

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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.

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arXiv2013

A diagrammatic categorification of the fermion algebra

In this paper, we study the diagrammatic categorification of the fermion algebra. We construct a graphical category corresponding to the one-dimensional fermion algebra, and we investigate the properties of this category. The categorical analogues of the Fock states are some kind of 1-morphisms in our category, and the dimension of the vector space of 2-morphisms is exactly the inner product of the corresponding Fock states. All the results in our categorical framework coincide exactly with those in normal quantum mechanics.

math-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.

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arXiv2013

The One-Way Information Deficit and Geometry for a Class of Two-qubit States

The work deficit, as introduced by Jonathan Oppenheim \emph{et al}[Phys. Rev. Lett. \textbf{89}, 180402 (2002)] is a good measure of the quantum correlations in a state and provides a new standpoint for understanding quantum non-locality. In this paper, we analytically evaluate the one-way information deficit (OWID) for the Bell-diagonal states and a class of two-qubit states and further give the geometry picture for OWID. The dynamic behavior of the OWID under decoherence channel is investigated and it is shown that the OWID of some classes of $X$ states is more robust against the decoherence than the entanglement.

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arXiv2012

Monogamous property of generalized W states in three-qubit systems in terms of relative entropy of entanglement

Because of the difficulty in getting the analytic formula of relative entropy of entanglement, it becomes troublesome to study the monogamy relations of relative entropy of entanglement for three-qubit pure states. However, we find that all generalized W states have the monogamous property for relative entropy of entanglement by calculating the relative entropy of entanglement for the reduced states of the generalized W states in three-qubit systems.

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arXiv2012

Assisted state discrimination without entanglement

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.

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arXiv2011

Nonlocality of two-qubit and three-qubit Schmidt-Correlated states

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.

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arXiv2011

Inequalities Detecting Quantum Entanglement for $2\otimes d$ Systems

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.

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arXiv2011

Faithful teleportation with arbitrary pure or mixed resource states

We study faithful teleportation systematically with arbitrary entangled states as resources. The necessary conditions of mixed states to complete perfect teleportation are proved. Based on these results, the necessary and sufficient conditions of faithful teleportation of an unknown state |ϕ> in C^d with an entangled resource ρ in C^m \otimes C^d and C^d \otimes C^n are derived. It is shown that for ρ in C^m\otimesC^d, ρ must be a maximally entangled state, while for ρ in C^d \otimes C^n, ρ must be a puremaximally entangled state. Moreover, we show that the sender's measurements must be all projectors of maximally entangled pure states. The relations between the entanglement of the formation of the resource states and faithful teleportation are also discussed.

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arXiv2011

Quantum discord and geometry for a class of two-qubit states

We study the level surfaces of quantum discord for a class of two-qubit states with parallel nonzero Bloch vectors. The dynamic behavior of quantum discord under decoherence is investigated. It is shown that a class of X states has sudden transition between classical and quantum correlations under decoherence. Our results include the ones in M. D. Lang and C. M. Caves [Phys. Rev. Lett. 105, 150501 (2010)] as a special case and show new pictures and structures of quantum discord.

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