Quantum Relative Lorenz Curves

Abstract

The theory of majorization and its variants, including thermomajorization, have been found to play a central role in the formulation of many physical resource theories, ranging from entanglement theory to quantum thermodynamics. Here we formulate the framework of quantum relative Lorenz curves, and show how it is able to unify majorization, thermomajorization, and their noncommutative analogues. In doing so, we define the family of Hilbert $\alpha$-divergences and show how it relates with other divergences used in quantum information theory. We then apply these tools to the problem of deciding the existence of a suitable transformation from an initial pair of quantum states to a final one, focusing in particular on applications to the resource theory of athermality, a precursor of quantum thermodynamics.

ver2: 14 pages, 3 figures, published version; ver1: 5 pages + 2 figures + 15 more pages + 1 more figure

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Cited by in corpus (46)

• Quantum Resource Theories
• Quantum majorization and a complete set of entropic conditions for quantum thermodynamics
• General Resource Theories in Quantum Mechanics and Beyond: Operational Characterization via Discrimination Tasks
• Quantifying the magic of quantum channels
• Amortized Channel Divergence for Asymptotic Quantum Channel Discrimination
• A resource theory of quantum memories and their faithful verification with minimal assumptions
• Probabilistic distillation of quantum coherence
• Quantum resource theories in the single-shot regime
• Resource theory of asymmetric distinguishability for quantum channels
• Quantum thermodynamics of correlated-catalytic state conversion at small-scale
• Third Law of Thermodynamics as a Single Inequality
• Resource theory of asymmetric distinguishability
• Catalysis of entanglement and other quantum resources
• Fundamental work cost of quantum processes
• Probabilistic transformations of quantum resources
• Fundamental Limits on Correlated Catalytic State Transformations
• An information-theoretic treatment of quantum dichotomies
• Tight constraints on probabilistic convertibility of quantum states
• Unifying different notions of quantum incompatibility into a strict hierarchy of resource theories of communication
• Is there a finite complete set of monotones in any quantum resource theory?
• Relative Entropy and Catalytic Relative Majorization
• Approximate Majorization
• Constraints on magic state protocols from the statistical mechanics of Wigner negativity
• Structure of the thermodynamic arrow of time in classical and quantum theories
• Coherence manipulation with dephasing-covariant operations
• The variance of relative surprisal as single-shot quantifier
• Anomalous mobility of a driven active particle in a steady laminar flow
• Two constructive proofs on d-majorization and thermo-majorization
• A complete and operational resource theory of measurement sharpness
• Exact quantum sensing limits for bosonic dephasing channels
• General state transitions with exact resource morphisms: a unified resource-theoretic approach
• Spins-based Quantum Otto Engines and Majorisation
• Complexity-constrained quantum thermodynamics
• Extension of the Alberti-Uhlmann criterion beyond qubit dichotomies
• Data-Driven Inference, Reconstruction, and Observational Completeness of Quantum Devices
• Device-independent tests of quantum states
• Locally-Measured Rényi Divergences
• A Compendious Review of Majorization-Based Resource Theories: Quantum Information and Quantum Thermodynamics
• Projective robustness for quantum channels and measurements and their operational significance
• Thermodynamic state convertibility is determined by qubit cooling and heating
• Towards the ultimate limits of quantum channel discrimination and quantum communication
• Extending Resource Monotones using Kan Extensions
• Quantum hypothesis testing between qubit states with parity
• Classical communication cost of a bipartite quantum channel assisted by non-signalling correlations
• Tight conic approximation of testing regions for quantum statistical models and measurements
• Conditions for Large-Sample Majorization of Pairs of Flat States in Terms of $\alpha$-z Relative Entropies