Correlations in typicality and an affirmative solution to the exact catalytic entropy conjecture

Abstract

I show that if a finite-dimensional density matrix has strictly smaller von Neumann entropy than a second one of the same dimension (and the rank is not bigger), then sufficiently (but finitely) many tensor-copies of the first density matrix majorize a density matrix whose single-body marginals are all exactly equal to the second density matrix. This implies an affirmative solution of the exact catalytic entropy conjecture (CEC) introduced by Boes et al. [PRL 122, 210402 (2019)]. Both the Lemma and the solution to the CEC transfer to the classical setting of finite-dimensional probability vectors (with permutations of entries instead of unitary transformations for the CEC).

arXiv commentv2: ~3.5 + 1 pages; Improved presentation, additional appendix; final version for publication in Quantum

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Cited by in corpus (14)

• Catalysis of entanglement and other quantum resources
• Arbitrary Amplification of Quantum Coherence in Asymptotic and Catalytic Transformation
• Catalytic advantage in Otto-like two-stroke quantum engines
• Covariant catalysis requires correlations and good quantum reference frames degrade little
• Quantum catalysis in cavity quantum electrodynamics
• Catalytic transformations for thermal operations
• Gibbs-preserving operations requiring infinite amount of quantum coherence
• Teleportation with Embezzling Catalysts
• Quantum thermodynamics with coherence: Covariant Gibbs-preserving operation is characterized by the free energy
• Communication with Quantum Catalysts
• Transcendental properties of entropy-constrained sets: Part II
• Finite-size catalysis in quantum resource theories
• Thermal operations from informational equilibrium
• Information Processing in Quantum Thermodynamic Systems: an Autonomous Hamiltonian Approach