Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Physics A Mathematical and Theoretical

Qubits in a random environment

Ismail Yunus Akhalwaya, M. Fannes, Francesco Petruccione

Published Jun 27, 2007• 5 citations
Publisher

Abstract

Decoherence phenomena in a small quantum system coupled to a complex environment can be modelled with random matrices. We propose a simple deterministic model in the limit of a high dimensional environment. The model is investigated numerically and some analytically addressable questions are singled out.
DOI
10.1088/1751-8113/40/28/s15

Related papers

Single-qubit decoherence under a separable coupling to a random matrix environment

M. Carrera-Núñez, T. Gorin, T. H. Seligman

This paper describes the dynamics of a quantum two-level system (qubit) under the influence of an environment modeled by an ensemble of random matrices. In distinction to earlier work, we consider here separable couplings and focus on a regime where the decoherence time is of the same order of magnitude as the environmental Heisenberg time. We derive an analytical expression in the linear response approximation, and study its accuracy by comparison with numerical simulations. We discuss a series of unusual properties, such as purity oscillations, strong signatures of spectral correlations (in the environment Hamiltonian), memory effects, and symmetry-breaking equilibrium states.

arXiv:1405.4448•Physical Review A•Aug 11, 2014•13 citations

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/0702161•New Journal of Physics•Apr 27, 2007•43 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, 2007•23 citations

Random matrix models for decoherence and fidelity decay in quantum information systems

Carlos Pineda, T. H. Seligman, Rocio R. Jauregui +2 more

This course aims to introduce the student to random matrix models for decoherence and fidelity decay. They present a very powerful alternate approach, that emphasizes the disordered character of many environments and uncontrollable perturbations/couplings. The inherent integrability of such models makes analytic studies possible. We limit our considerations to linear response treatment, as high fidelity and small decoherence are the backbone of quantum information processes. For fidelity decay, where experimental results are available, a comparison with experiments shows excellent agreement with random matrix theory predictions.

arXiv:0711.1503•AIP conference proceedings•Jan 1, 2008•2 citations

The Dynamics of Quantum Correlations of Two Qubits in a Common Environment Modeled by Large Random Matrices

E. N. Bratus’, Leonid Andreevich Pastur

This paper is a continuation of our previous paper [8], in which we have studied the dynamics of quantum correlations of two qubits embedded each into its own disordered multiconnected environment. We modeled the environment by random matrices of large size allowing for a possibility to describe meso- and even nanoenvironments. In this paper we also study the dynamics of quantum correlations of two qubits but embedded into a common environment which we also model by random matrices of large size. We obtain the large size limit of the reduced density matrix of two qubits. We then use an analog of the Bogolyubov-van Hove (also known as the Born-Markov) approximation of the theory of open systems and statistical mechanics. The approximation does not imply in general the Markovian evolution in our model but allows for sufficiently detailed analysis both analytical and numerical of the evolution of several widely used quantifiers of quantum correlation, mainly entanglement. We find a number of new patterns of qubits dynamics comparing with the case of independent environments studied in [8] and displaying the role of dynamical (indirect, via the environment) correlations in the enhancing and diversification of qubit evolution. Our results, (announced in [9]), can be viewed as a manifestation of the universality of certain properties of the decoherent qubit evolution which have been found previously in various exact and approximate versions of two-qubit models with macroscopic bosonic environment.

arXiv:2005.05222•May 11, 2020•0 citations

Dynamical control of qubit coherence: Random versus deterministic schemes

Léa Ferreira dos Santos, Lorenza Viola

We reexamine the problem of switching off unwanted phase evolution and decoherence in a single two-state quantum system in the light of recent results on random dynamical decoupling methods [L. Viola and E. Knill, Phys. Rev. Lett. 94, 060502 (2005)]. A systematic comparison with standard cyclic decoupling is effected for a variety of dynamical regimes, including the case of both semiclassical and fully quantum decoherence models. In particular, exact analytical expressions are derived for randomized control of decoherence from a bosonic environment. We investigate quantitatively control protocols based on purely deterministic, purely random, as well as hybrid design, and identify their relative merits and weaknesses at improving system performance. We find that for time-independent systems, hybrid protocols tend to perform better than pure random and may improve over standard asymmetric schemes, whereas random protocols can be considerably more stable against fluctuations in the system parameters. Beside shedding light on the physical requirements underlying randomized control, our analysis further demonstrates the potential for explicit control settings where the latter may significantly improve over conventional schemes.

arXiv:quant-ph/0511121•Physical Review A•Dec 5, 2005•59 citations
This paper describes the dynamics of a quantum two-level system (qubit) under the influence of an environment modeled by an ensemble of random matrices. In distinction to earlier work, we consider here separable couplings and focus on a regime where the decoherence time is of the same order of magnitude as the environmental Heisenberg time. We derive an analytical expression in the linear response approximation, and study its accuracy by comparison with numerical simulations. We discuss a series of unusual properties, such as purity oscillations, strong signatures of spectral correlations (in the environment Hamiltonian), memory effects, and symmetry-breaking equilibrium states.
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.
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.
This course aims to introduce the student to random matrix models for decoherence and fidelity decay. They present a very powerful alternate approach, that emphasizes the disordered character of many environments and uncontrollable perturbations/couplings. The inherent integrability of such models makes analytic studies possible. We limit our considerations to linear response treatment, as high fidelity and small decoherence are the backbone of quantum information processes. For fidelity decay, where experimental results are available, a comparison with experiments shows excellent agreement with random matrix theory predictions.
This paper is a continuation of our previous paper [8], in which we have studied the dynamics of quantum correlations of two qubits embedded each into its own disordered multiconnected environment. We modeled the environment by random matrices of large size allowing for a possibility to describe meso- and even nanoenvironments. In this paper we also study the dynamics of quantum correlations of two qubits but embedded into a common environment which we also model by random matrices of large size. We obtain the large size limit of the reduced density matrix of two qubits. We then use an analog of the Bogolyubov-van Hove (also known as the Born-Markov) approximation of the theory of open systems and statistical mechanics. The approximation does not imply in general the Markovian evolution in our model but allows for sufficiently detailed analysis both analytical and numerical of the evolution of several widely used quantifiers of quantum correlation, mainly entanglement. We find a number of new patterns of qubits dynamics comparing with the case of independent environments studied in [8] and displaying the role of dynamical (indirect, via the environment) correlations in the enhancing and diversification of qubit evolution. Our results, (announced in [9]), can be viewed as a manifestation of the universality of certain properties of the decoherent qubit evolution which have been found previously in various exact and approximate versions of two-qubit models with macroscopic bosonic environment.
We reexamine the problem of switching off unwanted phase evolution and decoherence in a single two-state quantum system in the light of recent results on random dynamical decoupling methods [L. Viola and E. Knill, Phys. Rev. Lett. 94, 060502 (2005)]. A systematic comparison with standard cyclic decoupling is effected for a variety of dynamical regimes, including the case of both semiclassical and fully quantum decoherence models. In particular, exact analytical expressions are derived for randomized control of decoherence from a bosonic environment. We investigate quantitatively control protocols based on purely deterministic, purely random, as well as hybrid design, and identify their relative merits and weaknesses at improving system performance. We find that for time-independent systems, hybrid protocols tend to perform better than pure random and may improve over standard asymmetric schemes, whereas random protocols can be considerably more stable against fluctuations in the system parameters. Beside shedding light on the physical requirements underlying randomized control, our analysis further demonstrates the potential for explicit control settings where the latter may significantly improve over conventional schemes.