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arXiv:2104.13237 · Scientific Reports

Effects of symmetry breaking of the structurally-disordered Hamiltonian ensembles on the anisotropic decoherence of qubits

Hongbin Chen

Published Feb 21, 2022• 7 citations
arXivHTMLPDF

Abstract

It is commonly known that the dephasing in open quantum systems is due to the establishment of bipartite correlations with ambient environments, which are typically difficult to be fully characterized. Recently, a new approach of average over disordered Hamiltonian ensemble is developed and shown to be capable of describing the nonclassicality of incoherent dynamics based on inferring the nonclassical nature of the correlations. Here we further extend the approach of Hamiltonian ensemble in the canonical form to the realm of structural disorder. Under the variable separation of the probability distribution within the Hamiltonian ensemble, the geometrical structure is easily visualized and can be characterized according to the degree of symmetry. We demonstrate four degrees and investigate the effects of different types of symmetry breaking on the incoherent dynamics. We show that these effects are easily understood from the emergences of additional terms in the master equations, leading to rather general master equations and, consequently, going beyond the previous frameworks of pure dephasing or isotropic depolarization.

DOI
10.1038/s41598-022-06891-4

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It is commonly known that the dephasing in open quantum systems is due to the establishment of bipartite correlations with ambient environments, which are typically difficult to be fully characterized. Recently, a new approach of average over disordered Hamiltonian ensemble is developed and shown to be capable of describing the nonclassicality of incoherent dynamics based on inferring the nonclassical nature of the correlations. Here we further extend the approach of Hamiltonian ensemble in the canonical form to the realm of structural disorder. Under the variable separation of the probability distribution within the Hamiltonian ensemble, the geometrical structure is easily visualized and can be characterized according to the degree of symmetry. We demonstrate four degrees and investigate the effects of different types of symmetry breaking on the incoherent dynamics. We show that these effects are easily understood from the emergences of additional terms in the master equations, leading to rather general master equations and, consequently, going beyond the previous frameworks of pure dephasing or isotropic depolarization.
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.
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.
Decoherence is conventionally regarded as an obstacle to realizing topological quantum phases. This has motivated extensive efforts to suppress noise in candidate topological materials and devices. Here, we show that decoherence can instead induce topological phenomena. We demonstrate this in a lattice system subject to environment-induced dephasing. The noise-averaged dynamics, governed by an interacting quantum master equation, realize a topological phase characterized by a winding number and the non-Hermitian skin effect. The dynamical consequence is striking: the correlated nature of the stochastic noise yields asymmetric diffusion, whose direction is fixed by the winding number and is reversible only through a topological phase transition. This effect is induced purely by interactions, distinguishing it from previous studies of free, effectively single-particle systems. It also disappears upon postselecting measurement outcomes, confirming that it is a genuinely open-system phenomenon with no effective Hamiltonian description. Remarkably, the model remains analytically tractable. Our results establish correlated quantum noise as a route to topology in open many-body systems, beyond free-particle and non-Hermitian Hamiltonian paradigms.
We derive a quantum master equation which describes the dynamics of the ensemble-averaged state of homogeneous disorder models at short times, and mediates a transition from coherent superpositions into classical mixtures. While each single realization follows unitary dynamics, this decoherencelike behavior arises as a consequence of the ensemble average. The master equation manifestly reflects the translational invariance of the disorder correlations and allows us to relate the disorder-induced dynamics to a collisional decoherence process, where the disorder correlations determine the spatial decay of coherences. We apply our theory to the (one-dimensional) Anderson model.
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.
Abstract Decoherence is conventionally regarded as an obstacle to realizing topological quantum phases. This has motivated extensive efforts to suppress noise in candidate topological materials and devices. Here, we show that decoherence can instead induce topological phenomena. We demonstrate this in a lattice system subject to environment-induced dephasing. The noise-averaged dynamics, governed by an interacting quantum master equation, realize a topological phase characterized by a winding number and the non-Hermitian skin effect. The dynamical consequence is striking: the correlated nature of the stochastic noise yields asymmetric diffusion, whose direction is fixed by the winding number and is reversible only through a topological phase transition. This effect is induced purely by interactions, distinguishing it from previous studies of free, effectively single-particle systems. It also disappears upon postselecting measurement outcomes, confirming that it is a genuinely open-system phenomenon with no effective Hamiltonian description. Remarkably, the model remains analytically tractable. Our results establish correlated quantum noise as a route to topology in open many-body systems, beyond free-particle and non-Hermitian Hamiltonian paradigms.