Quantum Ranking and Selection under Stochastic Constraints

胡琡苓, Mingjie Hu, Jian-Qiang Hu

Bruno Apolloni, C. Carvalho, D. de Falco

Chuanxin Bian, Guofeng Zhang

The purpose of this paper is to investigate an efficient coherent controller design scheme for the general mixed LQG/H∞control problem of the linear quantum stochastic systems. To solve the specific difficulty of the physical realizability constraints, the problem is reformulated as a rank constraint LMI problem, and numerical solution can be attained by using Matlab and softwares therein.

Paweł Caban, Jakub Rembieliński, Kordian A. Smoliński +1 more

We study selected aspects of non-classical correlations of arbitrary states from the stochastic local operations and classical communication orbit of rank-deficient two-qubit states. In particular, we find explicitly entanglement of formation and quantum discord for these states. Moreover, we determine and analyze the Einstein–Podolsky–Rosen steering ellipsoids corresponding to these states.

G. O. S. Ekhaguere

Tomo Munehisa, Yasuko Munehisa

We describe a further development of the stochastic state selection method, which is a kind of Monte Carlo method we have proposed in order to numerically study large quantum spin systems. In the stochastic state selection method we make a sampling which is simultaneous for many states. This feature enables us to modify the method so that a number of given constraints are satisfied in each sampling. In this paper we discuss this modified stochastic state selection method that will be called the constrained stochastic state selection method in distinction from the previously proposed one (the conventional stochastic state selection method) in this paper. We argue that, by virtue of the constrained sampling, some quantities obtained in each sampling become more reliable, i.e. their statistical fluctuations are less than those from the conventional stochastic state selection method. In numerical calculations of the spin- 1/2 quantum Heisenberg antiferromagnet on a 36-site triangular lattice we explicitly show that data errors in our estimation of the ground state energy are reduced. Then we successfully evaluate several low-lying energy eigenvalues of the model on a 48-site lattice. Our results support that this system can be described by the theory based on the spontaneous symmetry breaking in the semiclassical Néel ordered antiferromagnet.