Bounding generalized relative entropies: Nonasymptotic quantum speed limits

Abstract

Information theory has become an increasingly important research field to better understand quantum mechanics. Noteworthy, it covers both foundational and applied perspectives, also offering a common technical language to study a variety of research areas. Remarkably, one of the key information-theoretic quantities is given by the relative entropy, which quantifies how difficult is to tell apart two probability distributions, or even two quantum states. Such a quantity rests at the core of fields like metrology, quantum thermodynamics, quantum communication and quantum information. Given this broadness of applications, it is desirable to understand how this quantity changes under a quantum process. By considering a general unitary channel, we establish a bound on the generalized relative entropies (Rényi and Tsallis) between the output and the input of the channel. As an application of our bounds, we derive a family of quantum speed limits based on relative entropies. Possible connections between this family with thermodynamics, quantum coherence, asymmetry and single-shot information theory are briefly discussed.

arXiv comment20 pages, 6 figures. Close to published version

References in corpus (64)

• Quantifying Entanglement
• Rényi Divergence and Kullback-Leibler Divergence
• The Role of Relative Entropy in Quantum Information Theory
• The role of quantum information in thermodynamics --- a topical review
• The maximum speed of dynamical evolution
• On quantum Renyi entropies: a new generalization and some properties
• The second laws of quantum thermodynamics
• Quantum speed limits: from Heisenberg's uncertainty principle to optimal quantum control
• Observable measure of quantum coherence in finite dimensional systems
• Dissipation: The phase-space perspective
• Quantum speed limit for physical processes
• Quantum speed limit for non-Markovian dynamics
• Quantum speed limits in open system dynamics
• Min- and Max- Relative Entropies and a New Entanglement Monotone
• How to quantify coherence: Distinguishing speakable and unspeakable notions
• Extending Noether's theorem by quantifying the asymmetry of quantum states
• The fundamental limit on the rate of quantum dynamics: the unified bound is tight
• Quantum speed limits, coherence and asymmetry
• Sandwiched Rényi Divergence Satisfies Data Processing Inequality
• Speed Limit for Classical Stochastic Processes
• Monotonicity of a relative Rényi entropy
• Max- relative entropy of coherence: an operational coherence measure
• Quantum-coherence quantifiers based on the Tsallis relative $\alpha$-entropies
• Fundamental properties of Tsallis relative entropy
• Quantum Speed Limits Across the Quantum-to-Classical Transition
• Quantum Speed Limit is Not Quantum
• Nonextensive statistical mechanics: A brief introduction
• Tightening Quantum Speed Limits for Almost All States
• On the quantum Renyi relative entropies and related capacity formulas
• alpha-z-relative Renyi entropies
• Time-information uncertainty relations in thermodynamics
• Wigner-Yanase information on quantum state space:the geometric approach
• Work fluctuations in slow processes: quantum signatures and optimal control
• Orthogonality Catastrophe as a Consequence of the Quantum Speed Limit
• Tight, robust, and feasible quantum speed limits for open dynamics
• Continuity bounds on the quantum relative entropy
• Quantum work statistics close to equilibrium
• Quantum fluctuations hinder finite-time information erasure near the Landauer limit
• Action quantum speed limits
• Demonstration of quantum brachistochrones between distant states of an atom
• Continuity bounds on the quantum relative entropy - II
• Nonadditive generalization of the quantum Kullback-Leibler divergence for measuring the degree of purification
• Probing Quantum Speed Limits with Ultracold Gases
• The metric property of the quantum Jensen-Shannon divergence
• Relative Entropy in Biological Systems
• Information-theoretical bound of the irreversibility in thermal relaxation processes
• Resource speed limits: Maximal rate of resource variation
• A limit of the quantum Renyi divergence
• Operational definition of a quantum speed limit
• Quantum coherence quantifiers based on the Rényi $\alpha$-relative entropy
• Monotonic decrease of the quantum nonadditive divergence by projective measurements
• Entropic Energy-Time Uncertainty Relation
• Quantum parameter estimation with the Landau-Zener transition
• Kibble-Zurek scaling in quantum speed limits for shortcuts to adiabaticity
• Nonequilibrium uncertainty principle from information geometry
• Renyi relative entropies of quantum Gaussian states
• Quantum work statistics and resource theories: bridging the gap through Renyi divergences
• Quantum gravity, information theory and the CMB
• Geodesic distances on density matrices
• Holographic second laws of black hole thermodynamics
• Quantum speed limit for robust state characterization and engineering
• Bounds of the Pinsker and Fannes Types on the Tsallis Relative Entropy
• Relating relative Rényi entropies and Wigner-Yanase-Dyson skew information to generalized multiple quantum coherences
• Holographic Interpretation of Shannon Entropy of Coherence of Quantum Pure States

Cited by in corpus (17)

• Unifying Quantum and Classical Speed Limits on Observables
• Action quantum speed limits
• Resource speed limits: Maximal rate of resource variation
• Experimental Investigation of Geometric Quantum Speed Limits in an Open Quantum System
• Tight and attainable quantum speed limit for open systems
• Unified entropies and quantum speed limits for nonunitary dynamics
• Quantum Velocity Limits for Multiple Observables: Conservation Laws, Correlations, and Macroscopic Systems
• Fundamental speed limits on entanglement dynamics of bipartite quantum systems
• Quantum Speed Limits Based on Schatten Norms: Universality and Tightness
• Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe
• Quantum-imaginarity-based quantum speed limit
• Generalized Entropic Quantum Speed Limits
• Quantum Speed Limits Based on the Sharma-Mittal Entropy
• Quantum speed limits based on Jensen-Shannon and Jeffreys divergences for general physical processes
• Speed limits on classical chaos
• Asymmetry and dynamical criticality
• Approaching the Quantum Speed Limit in Quantum Gates with Geometric Control