Junde Wu

On conjectures of classical and quantum correlations in bipartite states

In this paper, two conjectures which were proposed in Luo et al (2010 Phys. Rev. A http://dx.doi.org/10.1103/PhysRevA.82.052122) on the correlations in a bipartite state ρAB are studied. If the mutual information I(ρAB) between two quantum systems A and B before any measurement is considered as the total amount of correlations in the state ρAB, then it can be separated into two parts: classical correlations and quantum correlations. The so-called classical correlations C(ρAB) in the state ρAB are defined by the maximizing mutual information between two quantum systems A and B after von Neumann measurements on system B. We show that it is upper bounded by the von Neumann entropies of both subsystems A and B, which answered the conjecture on the classical correlation. If the quantum correlations Q(ρAB) in the state ρAB are defined by Q(ρAB) = I(ρAB) − C(ρAB), we also show that it is upper bounded by the von Neumann entropy of subsystem B. It is also found that Q(ρAB) is upper bounded by the von Neumann entropy of subsystem A for a class of states.

A lower bound of quantum conditional mutual information

In this paper, a lower bound of quantum conditional mutual information is obtained by employing the Peierls–Bogoliubov inequality and the Golden–Thompson inequality. Comparison with the bounds obtained by other researchers indicates that our result is independent of any measurements. It may give some new insights into squashed entanglement and perturbations of Markov chain states.

Cohering power of quantum operations

Abstract Quantum coherence and entanglement, which play a crucial role in quantum information processing tasks, are usually fragile under decoherence. Therefore, the production of quantum coherence by quantum operations is important to preserve quantum correlations including entanglement. In this paper, we study cohering power–the ability of quantum operations to produce coherence. First, we provide an operational interpretation of cohering power. Then, we decompose a generic quantum operation into three basic operations, namely, unitary, appending and dismissal operations, and show that the cohering power of any quantum operation is upper bounded by the corresponding unitary operation. Furthermore, we compare cohering power and generalized cohering power of quantum operations for different measures of coherence.

Max- relative entropy of coherence: an operational coherence measure

The operational characterization of quantum coherence is the cornerstone in the development of the resource theory of coherence. We introduce a new coherence quantifier based on maximum relative entropy. We prove that the maximum relative entropy of coherence is directly related to the maximum overlap with maximally coherent states under a particular class of operations, which provides an operational interpretation of the maximum relative entropy of coherence. Moreover, we show that, for any coherent state, there are examples of subchannel discrimination problems such that this coherent state allows for a higher probability of successfully discriminating subchannels than that of all incoherent states. This advantage of coherent states in subchannel discrimination can be exactly characterized by the maximum relative entropy of coherence. By introducing a suitable smooth maximum relative entropy of coherence, we prove that the smooth maximum relative entropy of coherence provides a lower bound of one-shot coherence cost, and the maximum relative entropy of coherence is equivalent to the relative entropy of coherence in the asymptotic limit. Similar to the maximum relative entropy of coherence, the minimum relative entropy of coherence has also been investigated. We show that the minimum relative entropy of coherence provides an upper bound of one-shot coherence distillation, and in the asymptotic limit the minimum relative entropy of coherence is equivalent to the relative entropy of coherence.

Not each sequential effect algebra is sharply dominating

Let

The Drazin inverse of the linear combinations of two idempotents in the Banach algebra

E

Von Neumann entropy-preserving quantum operations

be an effect algebra and

Coherence-breaking channels and coherence sudden death

E_S

A Generalized Family of Discrete \mathcal{PT}-symmetric Square Wells

be the set of all sharp elements of

All-derivable points in nest algebras

E