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Physical Review A

Decorrelating capabilities of operations with application to decoherence

Shunlong Luo, Shuangshuang Fu, Nan Li

Published Nov 30, 2010• 38 citations

Abstract

Decoherence, interpreted broadly, is essentially the leakage of system information into the environment and is often accompanied by dissipation. The basic questions arise: how to quantify decoherence induced by an operation and how to quantitatively compare decoherence induced by different operations. In this paper, based on a joint ancilla-system-environment tripartite purification for the initial system state and the operation, and by exploiting the intrinsic relations between the loss of correlations in the ancilla--system and the correlations established in the system-environment, we characterize and quantify decoherence from a decorrelating perspective. For this purpose, we first address the issue of separating and quantifying the classical and quantum parts of decorrelation. By use of the canonical isomorphism between operations and bipartite states, we propose two intrinsic decorrelation measures: One is the classical decorrelation based on the loss of classical correlations, and the other is the quantum decorrelation based on the loss of quantum correlations. With the help of quantum decorrelation, we introduce an intuitive measure of (quantum) decoherence. We further employ these informational quantities to analyze some widely used channels such as the complete decoherent channel, the depolarizing channel, the bit-flip channel, the transpose depolarizing channel, the amplitude damping channel, and the phase damping channel. Our analysis illustrates the intriguing interplay between classical and quantum decorrelations and sheds some light on the informational nature of decoherence.

DOI: 10.1103/physreva.82.052122

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Decoherence, interpreted broadly, is essentially the leakage of system information into the environment and is often accompanied by dissipation. The basic questions arise: how to quantify decoherence induced by an operation and how to quantitatively compare decoherence induced by different operations. In this paper, based on a joint ancilla-system-environment tripartite purification for the initial system state and the operation, and by exploiting the intrinsic relations between the loss of correlations in the ancilla--system and the correlations established in the system-environment, we characterize and quantify decoherence from a decorrelating perspective. For this purpose, we first address the issue of separating and quantifying the classical and quantum parts of decorrelation. By use of the canonical isomorphism between operations and bipartite states, we propose two intrinsic decorrelation measures: One is the classical decorrelation based on the loss of classical correlations, and the other is the quantum decorrelation based on the loss of quantum correlations. With the help of quantum decorrelation, we introduce an intuitive measure of (quantum) decoherence. We further employ these informational quantities to analyze some widely used channels such as the complete decoherent channel, the depolarizing channel, the bit-flip channel, the transpose depolarizing channel, the amplitude damping channel, and the phase damping channel. Our analysis illustrates the intriguing interplay between classical and quantum decorrelations and sheds some light on the informational nature of decoherence.

Quantum channels, in general, will disturb quantum states and will lead to decoherence (i.e., information leakage to the environment). For bipartite systems, local channels often cause more decoherence for global states than for local states due to correlations. Intuitively, the difference between these two kinds of decoherence (i.e., global and local ones) may be regarded as a quantifier characterizing certain aspects of correlations in the global bipartite states. Based on this idea, we introduce a quantifier of correlations (relative to a local channel) as the coherence difference and investigate its basic properties. We probe and quantify correlations relative to various channels including the unitary channels, the twirling channels, the projective measurements, and the weak measurements. In particular, we show that both product states and some natural classical-quantum states can be operationally characterized in terms of local channels: The product states are just those states with vanishing coherence difference relative to the twirling channel induced by the unitary group, whereas these natural classical-quantum states are just those states with vanishing coherence difference relative to the twirling channel induced by the subgroup of the unitary group that does not disturb the local states. We further illustrate the results by various examples.

We examine the system-reservoir dynamics of classical and quantum correlations in the decoherence phenomenon within a two-qubit composite system interacting with two independent environments. The most common noise channels (amplitude damping, phase damping, bit flip, bit-phase flip, and phase flip) are analyzed. By analytical and numerical analyses we find that, contrary to what is usually stated in the literature, decoherence may occur without entanglement between the system and the environment. We also show that, in some cases, the bipartite quantum correlation initially present in the system is completely evaporated and not transferred to the environments.

Decoherence arises from the interaction of a quantum system with the environment or, more precisely, from the measurement in which the environment ``measures'' the quantum system and establishes correlations with it. In this work, we first quantify measurement-induced correlations from both classical and quantum perspectives. Then we quantify decoherence via measurement-induced classical correlations. By virtue of an intrinsic and powerful link between entanglement (as quantified by entanglement of formation) and classical correlations (as quantified by the difference between the total correlations and quantum discord) in pure tripartite systems, we present general analytical formulas for measurement-induced correlations and decoherence measures for qubit systems and, furthermore, reveal a conservation relation for the information-disturbance tradeoff.

As a direct consequence of the interplay between the superposition principle of quantum mechanics and the dynamics of open systems, decoherence is a recurring theme in both foundational and experimental exploration of the quantum realm. Decoherence is intimately related to information leakage of open systems and is usually formulated in the setup of "system + environment" as information acquisition of the environment (observer) from the system. As such, it has been mainly characterized via correlations (e.g., quantum mutual information, discord, and entanglement). Decoherence combined with redundant proliferation of the system information to multiple fragments of environment yields the scenario of quantum Darwinism, which is now a widely recognized framework for addressing the quantum-to-classical transition: the emergence of the apparent classical reality from the enigmatic quantum substrate. Despite the half-century development of the notion of decoherence, there are still many aspects awaiting investigations. In this work, we introduce two quantifiers of classicality via the Jordan product and uncertainty, respectively, and then employ them to quantify decoherence from an information-theoretic perspective. As a comparison, we also study the influence of the system on the environment.

We propose relative entropy-based quantifiers for genuine multipartite total, quantum, and classical correlations. These correlation measures are applied to investigate the generation of genuine multiparticle correlations in decoherent dynamics induced by the interaction of two qubits with local-independent environments. We consider amplitude- and phase-damping channels and compare their capabilities to spread information through the creation of many-body correlations. We identify changes in behavior for the genuine four- and three-partite total correlations and show that, contrary to amplitude environments, phase-noise channels transform the bipartite correlation initially shared between the qubits into genuine multiparticle system-environment correlations.

Based on the exact dynamics of a two-qubit system and environment, we investigate system-environment (SE) quantum and classical correlations. The coupling is chosen to represent a dephasing channel for one of the qubits and the environment is a proper thermal bath. First we discuss the general issue of dilation for qubit phase damping. Based on the usual thermal bath of harmonic oscillators, we derive criteria of separability and entanglement between an initial

X

state and the environment. Applying these criteria to initial Werner states, we find that entanglement between the system and environment is built up in time for temperatures below a certain critical temperature

{T}_{\mathrm{crit}}

. On the other hand, the total state remains separable during those short times that are relevant for decoherence and loss of entanglement in the two-qubit state. Close to

{T}_{\mathrm{crit}}

the SE correlations oscillate between separable and entangled. Even though these oscillations are also observed in the entanglement between the two qubits, no simple relation between the loss of entanglement in the two-qubit system and the build-up of entanglement between the system and environment is found.