Quantifying the nonclassicality of pure dephasing

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.

Measure of qubit-environment entanglement for pure dephasing evolutions

“…The density matrix is written in matrix form only in terms of qubit pointer states. As shown previously [11,12], for this class of problems the if and only if criterion of separability at time t is (it is also the criterion for zero discord [15,16])…”

How to detect qubit environment entanglement in pure dephasing evolutions

“…It has been shown previously [10,11] that for this class of interactions and initial states, the if and only if criterion of QE separability at time t is (it is also the criterion for zero-discord [16,17]…”

Protecting quantum coherences from static noise and disorder

“…A convenient model for quantum systems with static noise are ensembles of time-independent, random Hamiltonians [4], each one characterizing a realization of the noise. This description can, among others, be applied to disordered quantum systems [4], random unitary maps [4,8], or open quantum systems experiencing noise from the coupling to a timeindependent, classical [9] environment [10].…”

“…Another example is when variations between successive runs of the same measurement [14] to accumulate statistics cannot be resolved, such as when using a photon beam for quantum communication through the (turbulent) atmosphere [15]. A central consequence of the ensemble average is the averaging over the accumulated phases associated with the eigenstates of the underlying random Hamiltonian for each realization of the static noise [4,9,16]. This averaging induces a loss of phase information.…”