We discuss the local equilibration of closed systems using the relative purity, a paradigmatic information-theoretic distinguishability measure that finds applications ranging from quantum metrology to quantum speed limits. First we obtain an upper bound on the average size of the fluctuations on the relative purity: it depends on the effective dimension resembling the bound obtained with the trace distance. Second, we investigate the dynamics of relative purity and its rate of change as a probe of the speed of fluctuations around the equilibrium. In turn, such speed captures the notion of how fast some nonequilibrium state approaches the steady state under the local nonunitary dynamics, somehow giving the information of the quantum speed limit towards the equilibration. We show that the size of fluctuations depends on the quantum coherences of the initial state with respect to the eigenbasis of the Hamiltonian, also addressing the role played by the correlations between system and reservoir into the averaged speed. Finally, we have derived a family of lower bounds on the time of evolution between these states, thus obtaining an estimate for the equilibration time at the local level. These results could be of interest to the subjects of equilibration, quantum speed limits, and also quantum metrology.
The environment of an open quantum system is usually modelled as a large many-body quantum system. However, when an isolated quantum system itself is a many-body quantum system, the question of how large and complex it must be in order to generate internal equilibration is an open key-point in the literature. In this work, by monitoring the degree of equilibration of a single spin through its purity degradation, we are able to sense the chaotic behaviour of the generic spin chain to which it is coupled. Quite remarkably, this holds even in the case of extremely short spin chains composed of th…
We introduce the concept of Magic Subspaces for the control of dissipative N- level quantum systems whose dynamics are governed by Lindblad equation. For a given purity, these subspaces can be defined as the set of density matrices for which the rate of purity change is maximum or minimum. Adding fictitious control fields to the system so that two density operators with the same purity can be connected in a very short time, we show that magic subspaces allow to derive a purity speed limit, which only depends on the relaxation rates. We emphasize the superiority of this limit with respect to es…
Out-of-time-ordered correlators (OTOCs) have been extensively studied in recent years as a diagnostic of quantum information scrambling. In this paper, we study quantum information-theoretic aspects of the regularized finite-temperature OTOC. We introduce analytical results for the bipartite regularized OTOC (BROTOC): the regularized OTOC averaged over random unitaries supported over a bipartition. We show that the BROTOC has several interesting properties, for example, it quantifies the purity of the associated thermofield double state and the operator purity of the analytically continued tim…
We discuss our recent study of local quantum mechanical uncertainty relations in quantum many body systems. These lead to fundamental bounds for quantities such as the speed, acceleration, relaxation times, spatial gradients and the Lyapunov exponents. We additionally obtain bounds on various transport coefficients like the viscosity, the diffusion constant, and the thermal conductivity. Some of these bounds are related to earlier conjectures, such as the bound on chaos by Maldacena, Shenker and Stanford while others are new. Our approach is a direct way of obtaining exact bounds in fairly gen…
The minimum time a system needs to change from an initial state to a final orthogonal state is called quantum speed limit time. Quantum speed limit time can be used to quantify the speed of the quantum evolution. The speed of the quantum evolution will increase, if the quantum speed limit time decreases. In this work we will use relative purity based bound for quantum speed limit time. It is applicable for any arbitrary initial state. Here, we investigate the effects of filtering operation on quantum speed limit time. It will be observed that for some intervals of filtering operation parameter…
The new bound on quantum speed limit (in terms of relative purity) is derived by applying the original Mandelstam-Tamm one to the evolution in the space of Hilbert-Schmidt operators acting in the initial space of states. It is shown that it provides the quantum counterpart of the classical speed limit derived in Phys. Rev. Lett. 120 (2018), 070402 and the $\hbar\rightarrow 0$ limit of the former yields the latter. The existence of classical limit is related to the degree of mixing of the quantum state.
Information-theoretic derivation of energy, speed bounds, and quantum theory
The University of Hong Kong（香港大学）；QICI Quantum Information and Computation Initiative, Department of Computer Science, The University of Hong Kong（香港大学计算机科学与量子信息计算倡议）；HKU-Oxford Joint Laboratory for Quantum Information and Computation（港大-牛津量子信息计算联合实验室）；University of Oxford（牛津大学）；Perimeter Institute for Theoretical Physics（理论物理前沿研究所）
We discuss a class of quantum speed limits (QSLs) based on unified quantum ($α,μ$)-entropy for nonunitary physical processes. The bounds depend on both the Schatten speed and the smallest eigenvalue of the evolved state, and the two-parametric unified entropy. We specialize these results to quantum channels and non-Hermitian evolutions. In the first case, the QSL depends on the Kraus operators related to the quantum channel, while in the second case the speed limit is recast in terms of the non-Hermitian Hamiltonian. To illustrate these findings, we consider a single-qubit state evolving under…
The quantum speed limit is a fundamental concept in quantum mechanics, which aims at finding the minimum time scale or the maximum dynamical speed for some fixed targets. In a large number of studies in this field, the construction of valid bounds for the evolution time is always the core mission, yet the physics behind it and some fundamental questions like which states can really fulfill the target, are ignored. Understanding the physics behind the bounds is at least as important as constructing attainable bounds. Here we provide an operational approach for the definition of the quantum spee…
Dynamical irreversibility and local decoherence in quantum many-body chaos
Instituto de Física, Universidad Nacional Autónoma de México（墨西哥国立自治大学物理研究所）；Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México（墨西哥国立自治大学核科学研究所）；Center for Theoretical Physics of Complex Systems, Institute for Basic Science (IBS)（基础科学研究院复杂系统理论物理中心）
Experimental demonstration of non-local magic in a superconducting quantum processor
Università degli Studi di Napoli “Federico II”（那不勒斯费德里科二世大学）；Scuola Superiore Meridionale（南方高等学院）；Istituto Nazionale di Fisica Nucleare (INFN)（意大利国家核物理研究所）
