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arXiv:1703.09428 · Physical Review Letters

Simulating Open Quantum Systems with Hamiltonian Ensembles and the Nonclassicality of the Dynamics

Hongbin Chen, Clemens Gneiting, Ping‐Yuan Lo, Yueh-Nan Chen, Franco Nori

Published Jan 19, 2018• 62 citations
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Abstract

The incoherent dynamical properties of open quantum systems are generically attributed to an ongoing correlation between the system and its environment. Here, we propose a novel way to assess the nature of these system-environment correlations by examining the system dynamics alone. Our approach is based on the possibility or impossibility to simulate open-system dynamics with Hamiltonian ensembles. As we show, such (im)possibility to simulate is closely linked to the system-environment correlations. We thus define the nonclassicality of open-system dynamics in terms of the nonexistence of a Hamiltonian-ensemble simulation. This classifies any nonunital open-system dynamics as nonclassical. We give examples for open-system dynamics that are unital and classical, as well as unital and nonclassical.

DOI
10.1103/physrevlett.120.030403

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The incoherent dynamical properties of open quantum systems are generically attributed to an ongoing correlation between the system and its environment. Here, we propose a novel way to assess the nature of these system-environment correlations by examining the system dynamics alone. Our approach is based on the possibility or impossibility to simulate open-system dynamics with Hamiltonian ensembles. As we show, such (im)possibility to simulate is closely linked to the system-environment correlations. We thus define the nonclassicality of open-system dynamics in terms of the nonexistence of a Hamiltonian-ensemble simulation. This classifies any nonunital open-system dynamics as nonclassical. We give examples for open-system dynamics that are unital and classical, as well as unital and nonclassical.
One of the central problems in quantum theory is to characterize, detect, and quantify quantumness in terms of classical strategies. Dephasing processes, caused by non-dissipative information exchange between quantum systems and environments, provides a natural platform for this purpose, as they control the quantum-to-classical transition. Recently, it has been shown that dephasing dynamics itself can exhibit (non)classical traits, depending on the nature of the system-environment correlations and the related (im)possibility to simulate these dynamics with Hamiltonian ensembles-the classical strategy. Here we establish the framework of detecting and quantifying the nonclassicality for pure dephasing dynamics. The uniqueness of the canonical representation of Hamiltonian ensembles is shown, and a constructive method to determine the latter is presented. We illustrate our method for qubit, qutrit, and qubit-pair pure dephasing and describe how to implement our approach with quantum process tomography experiments. Our work is readily applicable to present-day quantum experiments.
Open quantum systems are inherently coupled to their environments, which in turn also obey quantum dynamical rules. Restricting ourselves to dissipative dynamics, here we propose a measure that quantifies how far the action of an environment on a system departs from the influence of classical noise fluctuations. It is based on the lack of commutativity between the initial reservoir state and the total system-environment Hamiltonian. Independently of the nature of the dissipative system evolution, Markovian or non-Markovian, the measure can be written in terms of the dual propagator that defines the evolution of system operators. The physical meaning and properties of the proposed definition are discussed in detail and also characterized through different paradigmatic dissipative Markovian and non-Markovian open quantum dynamics.
Abstract One of the central problems in quantum theory is to characterize, detect, and quantify quantumness in terms of classical strategies. Dephasing processes, caused by non-dissipative information exchange between quantum systems and environments, provides a natural platform for this purpose, as they control the quantum-to-classical transition. Recently, it has been shown that dephasing dynamics itself can exhibit (non)classical traits, depending on the nature of the system-environment correlations and the related (im)possibility to simulate these dynamics with Hamiltonian ensembles–the classical strategy. Here we establish the framework of detecting and quantifying the nonclassicality for pure dephasing dynamics. The uniqueness of the canonical representation of Hamiltonian ensembles is shown, and a constructive method to determine the latter is presented. We illustrate our method for qubit, qutrit, and qubit-pair pure dephasing and describe how to implement our approach with quantum process tomography experiments. Our work is readily applicable to present-day quantum experiments.
Some physical objects are hardly accessible to direct experimentation. It is then desirable to infer their properties based solely on the interactions they have with systems over which we have control. In this spirit, here we introduce schemes for assessing the nonclassicality of the inaccessible objects as characterized by quantum discord. We consider two probes individually interacting with the inaccessible object but not with each other. The schemes are based on monitoring entanglement dynamics between the probes. Our method is robust and experimentally friendly, as it allows the probes and the object to be open systems and makes no assumptions about the initial state, dimensionality of involved Hilbert spaces, and details of the probe-object Hamiltonian. We apply our scheme to a membrane-in-the-middle optomechanical system, to detect system-environment correlations in open system dynamics as well as nonclassicality of the environment, and we foresee potential benefits for the inference of the nonclassical nature of gravity.
The nonclassical nature of quantum states, often illustrated using entanglement measures or quantum discord, constitutes a resource for quantum information protocols. However, the nonclassicality of a quantum system cannot be seen as a property of the state alone, as the set of available measurements used to extract information on the system is typically restricted. In this work we study how the nonclassicality of quantum measurements, quantified via their incompatibility, is influenced by quantum noise and how a non-Markovian environment can be useful for maintaining the measurement resources.
We develop a general strategy for the detection of nonclassical system-environment correlations in the initial states of an open quantum system. The method employs a dephasing map which operates locally on the open system and leads to an experimentally accessible witness for genuine quantum correlations, measuring the Hilbert-Schmidt distance between pairs of open system states. We further derive the expectation value of the witness for various random matrix ensembles modeling generic features of complex quantum systems. This expectation value is shown to be proportional to a measure for the quantum discord which reduces to the concurrence for pure initial states.