Decoherence of two qubit systems: A random matrix description

Abstract

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.

32 pages, 11 figures

References in corpus (38)

• Entanglement of Formation of an Arbitrary State of Two Qubits
• Decoherence, einselection, and the quantum origins of the classical
• Entanglement of a Pair of Quantum Bits
• Finite-Time Disentanglement via Spontaneous Emission
• Scalable multi-particle entanglement of trapped ions
• Dynamics of Loschmidt echoes and fidelity decay
• Experimental Demonstration of Five-photon Entanglement and Open-destination Teleportation
• Environment-independent decoherence rate in classically chaotic systems
• Measures and dynamics of entangled states
• Maximal entanglement versus entropy for mixed quantum states
• Golden rule decay versus Lyapunov decay of the quantum Loschmidt echo
• Decoherence and the Loschmidt echo
• Stability of quantum motion and correlation decay
• Quantum Chaotic Environments, The Butterfly Effect, And Decoherence
• Robust entanglement
• Measuring the Lyapunov exponent using quantum mechanics
• A random matrix formulation of fidelity decay
• Universality of the Lyapunov regime for the Loschmidt echo
• Quantum chaos and random matrix theoryfor fidelity decay in quantum computationswith static imperfections
• Decoherence as Decay of the Loschmidt Echo in a Lorentz Gas
• Dephasing representation: Employing the shadowing theorem to calculate quantum correlation functions
• A Uniform Approximation for the Fidelity in Chaotic Systems
• Decoherence by a chaotic many-spin bath
• Can quantum chaos enhance stability of quantum computation?
• Fidelity amplitude of the scattering matrix in microwave cavities
• Concurrence vs. purity: Influence of local channels on Bell states of two qubits
• Dephasing representation of quantum fidelity for general pure and mixed states
• Experimental verification of fidelity decay: From perturbative to Fermi Golden Rule regime
• Decoherence of spin echoes
• Decoherence alias Loschmidt echo of the environment
• Fidelity recovery in chaotic systems and the Debye-Waller factor
• Scattering fidelity in elastodynamics
• A random matrix approach to decoherence
• Evolution of pairwise entanglement in a coupled n-body system
• A Bell pair in a generic random matrix environment
• Anomalous slow fidelity decay for symmetry breaking perturbations
• Estimating purity in terms of correlation functions
• Stability of wave packet dynamics under perturbations

Cited by in corpus (29)

• Open-System Dynamics of Entanglement
• Non-Markovian behavior of small and large complex quantum systems
• Decoherence effects in interacting qubits under the influence of various environments
• Experimental investigation of enviroment--induced entanglement using an all--optical setup
• Relaxation due to random collisions with a many-qudit environment
• Relations between entanglement and purity in non-Markovian dynamics
• Entanglement dynamics and relaxation in a few qubit system interacting with random collisions
• Decoherence and Entanglement Dynamics in Fluctuating Fields
• Decoherence of an $n$-qubit quantum memory
• A random matrix theory of decoherence
• Extracting work from random collisions: A model of a quantum heat engine
• Quantum chaotic system as a model of decohering environment
• Single qubit decoherence under a separable coupling to a random matrix environment
• Quantum kicked harmonic oscillator in contact with a heat bath
• The two-body random spin ensemble and a new type of quantum phase transition
• Improving coherence with nested environments
• Structural change in multipartite entanglement sharing: a random matrix approach
• Random Matrix Ensembles For Many-Body Quantum Systems
• Dissipative dynamics of quantum discord under quantum chaotic environment
• Quantum homogenization and state randomization in semi-quantal spin systems
• Stabilizing coherence with nested environments: a numerical study using kicked Ising models
• A generalized fidelity amplitude for open systems
• Random density matrices versus random evolution of open systems
• A trivial observation on time reversal in random matrix theory
• The transition from non-Markovian to Markovian dynamics for generic environments
• Markovian and non-Markovian dynamics induced by a generic environment
• Initial-state randomness as a universal source of decoherence
• Quantum birthmarks: Ergodicity breaking beyond scarring
• Partial thermalisation of a two-state system coupled to a finite quantum bath