Stabilizing a class of mixed states for stochastic quantum systems via switching control

2018 ◽  
Vol 355 (5) ◽  
pp. 2562-2582 ◽  
Author(s):  
Jie WEN ◽  
Yuanhao SHI ◽  
Xiaonong LU
Keyword(s):  
Switching Control ◽  
Quantum Systems ◽  
Mixed States ◽  
Stochastic Quantum Systems

scholarly journals Global Stabilization of Mixed-states for Stochastic Quantum Systems via Switching Control

2017 ◽  
Vol 50 (1) ◽  
pp. 13032-13037
Author(s):  
Shuang Cong ◽  
Jie Wen ◽  
Fangfang Meng ◽  
Kezhi Li
Keyword(s):  
Switching Control ◽  
Quantum Systems ◽  
Global Stabilization ◽  
Mixed States ◽  
Stochastic Quantum Systems

Horodeckis criterion of separability of mixed states in von Neumann and C*-algebras

2014 ◽  
Vol 17 (04) ◽  
pp. 1450028 ◽  
Author(s):  
Marek Miller ◽  
Robert Olkiewicz
Keyword(s):  
Quantum Systems ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Mixed States ◽  
Von Neumann ◽  
C Algebras ◽  
Necessary And Sufficient

The Horodeckis necessary and sufficient condition of separability of mixed states is generalized to arbitrary composite quantum systems.

scholarly journals On the Generation of Random Ensembles of Qubits and Qutrits Computing Separability Probabilities for Fixed Rank States

2018 ◽  
Vol 173 ◽  
pp. 02010 ◽  
Author(s):  
Arsen Khvedelidze ◽  
Ilya Rogojin
Keyword(s):  
Quantum Systems ◽  
Separable State ◽  
Mixed States ◽  
Finite Dimensional ◽  
Fixed Rank

The generation of random mixed states is discussed, aiming for the computation of probabilistic characteristics of composite finite dimensional quantum systems. In particular, we consider the generation of random Hilbert-Schmidt and Bures ensembles of qubit and qutrit pairs and compute the corresponding probabilities to find a separable state among the states of a fixed rank.

Controllability of quantum systems with switching control

2011 ◽  
Vol 84 (1) ◽  
pp. 37-46 ◽  
Author(s):  
Daoyi Dong ◽  
Ian R. Petersen
Keyword(s):  
Switching Control ◽  
Quantum Systems

GEOMETRIC PHASES FOR MIXED STATES DURING UNITARY AND NON-UNITARY EVOLUTIONS

2003 ◽  
Vol 01 (01) ◽  
pp. 135-152 ◽  
Author(s):  
ARUN K. PATI
Keyword(s):  
Geometric Phase ◽  
Parallel Transport ◽  
Quantum Systems ◽  
Mixed States ◽  
Completely Positive Maps ◽  
Initial State ◽  
Unitary Evolution ◽  
Completely Positive ◽  
Quantum Operations ◽  
Positive Maps

Mixed states typically arise when quantum systems interact with the outside world. Evolution of open quantum systems in general are described by quantum operations which are represented by completely positive maps. We elucidate the notion of geometric phase for a quantum system described by a mixed state undergoing unitary evolution and non-unitary evolutions. We discuss parallel transport condition for mixed states both in the case of unitary maps and completely positive maps. We find that the relative phase shift of a system not only depends on the state of the system, but also depends on the initial state of the ancilla with which it might have interacted in the past. The geometric phase change during a sequence of quantum operations is shown to be non-additive in nature. This property can attribute a "memory" to a quantum channel. We explore these ideas and illustrate them with simple examples.

scholarly journals A Geometric View on Quantum Tensor Networks

2020 ◽  
Vol 226 ◽  
pp. 02022
Author(s):  
Alexander Tsirulev
Keyword(s):  
Building Blocks ◽  
Quantum Systems ◽  
Mixed States ◽  
Normal Coordinates ◽  
Covariant Derivatives ◽  
Tensor Networks ◽  
Tensor Network ◽  
Network States ◽  
Tensor Network States ◽  
Arbitrary Quantum

Tensor network states and algorithms play a key role in understanding the structure of complex quantum systems and their entanglement properties. This report is devoted to the problem of the construction of an arbitrary quantum state using the differential geometric scheme of covariant series in Riemann normal coordinates. The building blocks of the scheme are polynomials in the Pauli operators with the coefficients specified by the curvature, torsion, and their covariant derivatives on some base manifold. The problem of measuring the entanglement of multipartite mixed states is shortly discussed.

Feedback stabilization of N-dimensional stochastic quantum systems based on bang-bang control

2017 ◽  
Vol 15 (3) ◽  
pp. 206-218 ◽  
Author(s):  
Xiaqing Sun ◽  
Sen Kuang ◽  
Yanan Liu ◽  
Juan Zhou ◽  
Shuang Cong
Keyword(s):  
Quantum Systems ◽  
Feedback Stabilization ◽  
Bang Bang Control ◽  
Stochastic Quantum Systems

scholarly journals Topological Order, Mixed States and Open Systems

2019 ◽  
Vol 26 (03) ◽  
pp. 1950012 ◽  
Author(s):  
Manuel Asorey ◽  
Paolo Facchi ◽  
Giuseppe Marmo
Keyword(s):  
Open Systems ◽  
Quantum Systems ◽  
Topological Phases ◽  
Topological Order ◽  
Mixed States ◽  
Quantum Matter ◽  
Physical Role ◽  
Topological Quantum ◽  
Pure States

The role of mixed states in topological quantum matter is less known than that of pure quantum states. Generalisations of topological phases appearing in pure states have received attention in the literature only quite recently. In particular, it is still unclear whether the generalisation of the Aharonov–Anandan phase for mixed states due to Uhlmann plays any physical role in the behaviour of the quantum systems. We analyse, from a general viewpoint, topological phases of mixed states and the robustness of their invariance. In particular, we analyse the role of these phases in the behaviour of systems with periodic symmetry and their evolution under the influence of an environment preserving its crystalline symmetries.

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