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.
Highlights
One of the central problems in quantum theory is to characterize, detect, and quantify quantumness in terms of classical strategies
As was shown recently[17], such presence or absence of nonclassical system–environment correlations is intimately linked to thepossibility to simulate the open system dynamics with a Hamiltonian ensemble (HE), which may serve as the classical strategy to witness the nonclassicality of the open system dynamics
A seminal and intriguing example is a single qubit subject to spectral disorder with HE given by fðpðωÞ; hωσ^z=2Þgω, the averaged dynamics describes pure dephasing:
Summary
One of the central problems in quantum theory is to characterize, detect, and quantify quantumness in terms of classical strategies. Whenever the inequality is violated, one cannot reproduce the correlations by using a local hidden variable model, the latter serving as the classical strategy for mimicking the measurement statistics Another important paradigm is the quantumness of a boson field, which is formulated in terms of the Wigner function or the Glauber–Sudarshan P representation[6,7,8]. Whenever these functions exhibit negative values, the classical explanation in terms of a probability distribution over phase space fails to represent the boson field Following this spirit, one may ask for a classical strategy to frame the “quantumness” of open system dynamics. HEs, which are used to describe disordered quantum systems, attribute to each member of a collection of (time-independent) Hamiltonians a probability of occurrence, giving rise to an effective average dynamics
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