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

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.

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Controllability of quantum systems with switching control

International Journal of Control ◽

10.1080/00207179.2010.538437 ◽

2011 ◽

Vol 84 (1) ◽

pp. 37-46 ◽

Cited By ~ 13

Author(s):

Daoyi Dong ◽

Ian R. Petersen

Keyword(s):

Switching Control ◽

Quantum Systems

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

International Journal of Quantum Information ◽

10.1142/s0219749903000103 ◽

2003 ◽

Vol 01 (01) ◽

pp. 135-152 ◽

Cited By ~ 12

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.

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A Geometric View on Quantum Tensor Networks

EPJ Web of Conferences ◽

10.1051/epjconf/202022602022 ◽

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.

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