No abstract

Quantum coherence is an essential ingredient in quantum information processing and plays an important role in quantum computation. Therefore, it is a hot issue about how to quantify the coherence of quantum states in theoretical framework. The coherence effect of a state is usually described by the off-diagonal elements of its density matrix with respect to a particular reference basis. Recently, based on the established notions from quantitative theory of entanglement, a resource theory of coherence quantification has been proposed[1,2]. In the theory framework, a proper measure of coherence should satisfy three criteria: the coherence should be zero for all incoherent state; the coherence should not increase under mixing quantum states; the coherence should not increase under incoherent operations. Then, a number of coherence measures have been suggested, such as l1 norm of coherence and the relative entropy of coherence[2]. Wigner function is known as an important tool to study the non-classical property of quantum states for continuous-variable quantum systems. It has been generalized to finite-dimensional Hilbert spaces, and named as discrete Wigner function[9-16]. The magic property of quantum states, which promotes stabilizer computation to universal quantum computation, can be generally measured by the absolute sum of the negative items (negativity sum) in the discrete Wigner function of the observed quantum states. In this paper we investigate quantum coherence from the view of discrete Wigner function. From the definition of the discrete Wigner function of the quantum systems with odd prime dimensions, for a given density matrix we analyze in phase space the performance of its diagonal and off-diagonal items. We find that, the discrete Wigner function of a quantum state contains two aspects: the true quantum coherence and the classical mixture, where the part of classical mixture can be excluded by only considering the discrete Wigner function of the diagonal items of the density matrix. Thus, we propose a possible measure method for quantum coherence from the discrete Wigner function of the off-diagonal items of the density matrix. We show that the proposed measure method satisfies the criteria (C1) and (C2) of coherence measure perfectly. For the criteria (C3), we give a numerical proof in three-dimensional quantum system. Meanwhile, we compare the proposed coherence measure with l1 norm coherence, and get an inequality relationship between them. Finally, an inequality is obtained to discuss the relation between quantum coherence and the negativity sum of discrete Wigner function, which shows that the quantum coherence is only necessary but not sufficient for quantum computation speed-up.

The relation between discrete Wigner function and quantum contextuality based on graph theory has been studied, following the work in [Nature 510,351(2014)]. To do this, non-stabilizer projectors have been introduced to a series of non-contextuality graphs based on stabilizer projectors for a single qudit with odd prime dimension. It has been found that, for a phase space point defined by Wootters, there exists a given set of states for an odd-prime qudit where the negative discrete Wigner function on the phase space point means its quantum contextuality under measurements on the graphs designed by a specific method. To implement this method, a subset of non-stabilizer projectors has been found. In the union of the set of states for all phase space points, there exists a negativity-to-violation map between Wigner function and quantum contextuality inequality. The robustness of the equivalence under depolarizing noise has been analyzed and discussed. For demonstration purposes, the graphs with different independence numbers and the corresponding set of states have been established on a single qutrit. Different to the cited work, this method involves only a single qudit, then is experimentally feasible for a qutrit.

The light-atom interaction is the major research subject in atomic-based optical devices. In this study, we develop a Monte Carlo simulation of light-atom interaction to study the transmission properties of the Anti-Resonant Reflective Optical Waveguides with a thermal-atomic-vapor core. The surface-atom interaction is considered in the simulation by calculating Green's tensor through a numerical method. And this interaction causes a shift of resonance frequency and modified spontaneous emission rate of the atoms close to the surface. Further, we run some simulations for the different input light power. And these simulation results show a nonlinear relation between input light power and the amplitude of absorption. We also simulate power transmission versus the traveling length of light in the core, where we obtain the longitudinal penetration depth of light. These results and Monte Carlo simulations pave the way to design other optical devices and establish integrated optical circuits.