Zhengjun Xi

Quantum coherence and correlations in quantum system.

Criteria of measure quantifying quantum coherence, a unique property of quantum system, are proposed recently. In this paper, we first give an uncertainty-like expression relating the coherence and the entropy of quantum system. This finding allows us to discuss the relations between the entanglement and the coherence. Further, we discuss in detail the relations among the coherence, the discord and the deficit in the bipartite quantum system. We show that, the one-way quantum deficit is equal to the sum between quantum discord and the relative entropy of coherence of measured subsystem.

Fidelity and trace-norm distances for quantifying coherence

We investigate the coherence measures induced by fidelity and trace norm, based on the recent proposed coherence quantification in [Phys. Rev. Lett. 113, 140401, 2014]. We show that the fidelity of coherence does not in general satisfy the monotonicity requirement as a measure of coherence under the subselection of measurements condition. We find that the trace norm of coherence can act as a measure of coherence for qubit case and some special class of qutrits.

Quantum Coherence Quantifiers Based on Rényi α-Relative Entropy*

The resource theories of quantum coherence attract a lot of attention in recent years. Especially, the monotonicity property plays a crucial role here. In this paper we investigate the monotonicity property for the coherence measures induced by the Renyi α-relative entropy, which present in [Phys. Rev. A 94 (2016) 052336]. We show that the Renyi α-relative entropy of coherence does not in general satisfy the monotonicity requirement under the subselection of measurements condition and it also does not satisfy the extension of monotonicity requirement, which presents in [Phys. Rev. A 93 (2016) 032136]. Due to the Renyi α-relative entropy of coherence can act as a coherence monotone quantifier, we examine the trade-off relations between coherence and mixedness. Finally, some properties for the single qubit of Renyi 2-relative entropy of coherence are derived.

One-way unlocalizable quantum discord

We present the in-plane optical reflectance measurement on single crystals of URu2Si2. The study revealed a strong temperature-dependent spectral evolution. Above 50 K, the low frequency optical conductivity is rather flat without a clear Drude-like response, indicating a very short transport lifetime of the free carriers. Well below thecoherence temperature, there appears an abrupt spectral weight suppression below 400 cm(-1), yielding evidence for the formation of a hybridization energy gap arising from the mixing of the conduction electron and narrow f-electron bands. A small part of the suppressed spectral weight was transferred to the low frequency side, leading to a narrow Drude component, while the majority of the suppressed spectral weight was transferred to the high frequency side centered near 3500 cm(-1). Below the hidden order temperature, another very prominent energy gap structure was observed, which leads to the removal of a large part of the Drude component and a sharp reduction of the carrier scattering rate. The study revealed that the hybridization gap and the hidden order gap are distinctly different: they occur at different energy scales and exhibit completely different spectral characteristics.

Entropic cohering power in quantum operations

Coherence is a basic feature of quantum systems and a common necessary condition for quantum correlations. It is also an important physical resource in quantum information processing. In this paper, using relative entropy, we consider a more general definition of the cohering power of quantum operations. First, we calculate the cohering power of unitary quantum operations and show that the amount of distributed coherence caused by non-unitary quantum operations cannot exceed the quantum-incoherent relative entropy between system of interest and its environment. We then find that the difference between the distributed coherence and the cohering power is larger than the quantum-incoherent relative entropy. As an application, we consider the distributed coherence caused by purification.

Some algebraic properties of measure-once two-way quantum finite automata

Quantum finite automata (QFA) can be divided into four kinds depend upon the head-directions and the measure times. They are measure-once one way QFA (MO-1QFA) introduced by Moore and Crutchfield (Theor Comput Sci 237: 275–306, 2000); measure-many one way QFA (MM-1QFA) and measure-many two-way QFA (MM-2QFA) introduced by Kondacs and Watrous (Proceedings of the 38th IEEE annual symposium on 433 foundations of computer science, 66–75, 1997); and measure-once two-way QFA (MO-2QFA) which were not given until now. The purpose of this work is mainly to discuss one kind of QFA, which is called MO-2QFA for brief. First of all, the definition of MO-2QFA is given and the conditions for preserving unitary properties are shown. Then, we analysis the basic algebraic properties of the class of languages which can be recognized by MO-2QFA, such as the union, intersection, complement and reversal operations. As well, we consider the catenation operation on the class of quantum languages recognized by MO-2QFA is closed in the generalized conditions.