arXiv:quant-ph/0112030 · Journal of Optics B Quantum and Semiclassical Optics

A random matrix approach to decoherence

T. Gorin, T. H. Seligman

Published Aug 1, 2002• 36 citations

Abstract

In order to analyse the effect of chaos or order on the rate of decoherence in a subsystem, we aim to distinguish the effects of the two types of dynamics by choosing initial states as random product states from two factor spaces representing two subsystems. We introduce a random matrix model that allows us to vary the coupling strength between the subsystems. The case of strong coupling is analysed in detail, and we find no significant differences except for very low-dimensional spaces.

DOI: 10.1088/1464-4266/4/4/325

Related papers

Decoherence in chaotic and integrable systems: A random matrix approach

T. Gorin, T. H. Seligman

In order to analyze the effect of chaos or order on the rate of decoherence in a subsystem we aim to distinguish effects of the two types of dynamics from those depending on the choice of the wave packet. To isolate the former we introduce a random matrix model that permits to vary the coupling strength between the subsystems. The case of strong coupling is analyzed in detail, and we find at intermediate times a weak effect of spectral correlations that is reminiscent of the correlation hole.

arXiv:nlin/0101018Jan 9, 20011 citation

Decoherence of two-qubit systems: a random matrix description

C Pineda, T Gorin, T H Seligman

We study decoherence of two non-interacting qubits. The environment and its interaction with the qubits are modelled by random matrices. Decoherence, measured in terms of purity, is calculated in linear response approximation. Monte Carlo simulations illustrate the validity of this approximation and of its extension by exponentiation. The results up to this point are also used to study one-qubit decoherence. Purity decay of entangled and product states are qualitatively similar though for the latter case it is slower. Numerical studies for a Bell pair as initial state reveal a one to one correspondence between its decoherence and its internal entanglement decay. For strong and intermediate coupling to the environment this correspondence agrees with the one for Werner states. In the limit of a large environment the evolution induces a unital channel in the two qubits, providing a partial explanation for the above relation.

arXiv:quant-ph/0702161New Journal of PhysicsApr 27, 200743 citations

Decoherence of two qubit systems: A random matrix description

Carlos Pineda, T. Gorin, T. H. Seligman

We study decoherence of two non-interacting qubits. The environment and its interaction with the qubits are modelled by random matrices. Decoherence, measured in terms of purity, is calculated in linear response approximation. Monte Carlo simulations illustrate the validity of this approximation and of its extension by exponentiation. The results up to this point are also used to study one qubit decoherence. Purity decay of entangled and product states are qualitatively similar though for the latter case it is slower. Numerical studies for a Bell pair as initial state reveal a one to one correspondence between its decoherence and its internal entanglement decay. For strong and intermediate coupling to the environment this correspondence agrees with the one for Werner states. In the limit of a large environment the evolution induces a unital channel in the two qubits, providing a partial explanation for the relation above.

Feb 15, 200723 citations

A random matrix theory of decoherence

T. Gorin, Carlos Pineda, Heiner Kohler +1 more

Random matrix theory is used to represent generic loss of coherence of a fixed central system coupled to a quantum-chaotic environment, represented by a random matrix ensemble, via random interactions. We study the average density matrix arising from the ensemble induced, in contrast to previous studies where the average values of purity, concurrence, and entropy were considered; we further discuss when one or the other approach is relevant. The two approaches agree in the limit of large environments. Analytic results for the average density matrix and its purity are presented in linear response approximation. The two-qubit system is analysed, mainly numerically, in more detail.

arXiv:0807.4913New Journal of PhysicsNov 20, 200822 citations

A general and solvable random matrix model for spin decoherence

François David

We propose and solve a simple but very general quantum model of a SU (2) spin interacting with a large external system with N states. The coupling is described by a random Hamiltonian in a new general Gaussian SU (2) × U ( N ) random matrix ensemble, that we introduce in this paper. We solve the model in the large N limit, for any value of the spin j and for any choice of the coupling matrix element distributions in the different possible angular momentum channels l (and provided that the internal dynamics of the spin is slow). Besides its mathematical interest as a non-trivial random matrix model, it allows us to study and illustrate in a simple framework various phenomena: the decoherence dynamics, the conditions of emergence of the classical phase space for the spin, and the properties of quantum diffusion in phase space. The large time evolution for the spin is shown to be non-Markovian in general, the Markov property emerging in some specific cases for the dynamics and the initial conditions.

arXiv:1009.1282Journal of Statistical Mechanics Theory and ExperimentJan 6, 20112 citations

Studies in a Random Noise Model of Decoherence

Piotr Korcyl, J. Wosiek, Leo Stodolsky

We study the effects of noise and decoherence for a double-potential well system, suitable for the fabrication of qubits and quantum logic elements. A random noise term is added to the hamiltonian, the resulting wavefunction found numerically and the density matrix obtained by averaging over noise signals. Analytic solutions using the two-state model are obtained and found to be generally in agreement. In particular, a simple formula for the decoherence rate in terms of the noise parameters in the two-state model is reviewed and verified for the full simulation with the multi-level system. The formalism is extended to describe multiple sources of noise or different "dephasing" axes at the same time. Furthermore, the old formula for the "Turing-Watched Pot" effect is generalized to the case where the environmental interactions do not conserve the "quality" in question. Various forms for the noise signal are investigated. An interesting result is the importance of the noise power at low frequency. If it vanishes there is, in leading order, no decoherence. This is verified in a numerical simulation where two apparently similar noise signals, but differing in the power at zero frequency, give strikingly different decoherence effects. A short discussion of situations dominated by low frequency noise is given.

Jan 1, 20101 citation