Rényi generalizations of quantum information measures

Abstract

Quantum information measures such as the entropy and the mutual information find applications in physics, e.g., as correlation measures. Generalizing such measures based on the Rényi entropies is expected to enhance their scope in applications. We prescribe Rényi generalizations for any quantum information measure which consists of a linear combination of von Neumann entropies with coefficients chosen from the set {-1,0,1}. As examples, we describe Rényi generalizations of the conditional quantum mutual information, some quantum multipartite information measures, and the topological entanglement entropy. Among these, we discuss the various properties of the Rényi conditional quantum mutual information and sketch some potential applications. We conjecture that the proposed Rényi conditional quantum mutual informations are monotone increasing in the Rényi parameter, and we have proofs of this conjecture for some special cases.

9 pages, related to and extends the results from arXiv:1403.6102

References in corpus (55)

• Quantum entanglement
• Introducing Quantum Discord
• Entanglement Entropy and Quantum Field Theory
• Area laws for the entanglement entropy - a review
• Entanglement in quantum critical phenomena
• Topological entanglement entropy
• Detecting topological order in a ground state wave function
• Entropy and Area
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Entanglement entropy and conformal field theory
• The classical-quantum boundary for correlations: discord and related measures
• An Area Law for One Dimensional Quantum Systems
• On quantum Renyi entropies: a new generalization and some properties
• Monogamy of entanglement and other correlations
• Entanglement Renyi entropies in holographic theories
• Entanglement entropy of black holes
• Strong converse for the classical capacity of entanglement-breaking and Hadamard channels via a sandwiched Renyi relative entropy
• "Squashed Entanglement" - An Additive Entanglement Measure
• No-local-broadcasting theorem for quantum correlations
• Entropy, entanglement, and area: analytical results for harmonic lattice systems
• Structure of states which satisfy strong subadditivity of quantum entropy with equality
• A holographic proof of the strong subadditivity of entanglement entropy
• A Fully Quantum Asymptotic Equipartition Property
• The problem with the geometric discord
• Continuity of quantum conditional information
• Topological Entanglement Renyi Entropy and Reduced Density Matrix Structure
• Measuring Gaussian quantum information and correlations using the Renyi entropy of order 2
• Monotonicity of a relative Rényi entropy
• Faithful Squashed Entanglement
• Error Exponent in Asymmetric Quantum Hypothesis Testing and Its Application to Classical-Quantum Channel coding
• Quantum hypothesis testing and the operational interpretation of the quantum Renyi relative entropies
• Strong Converse to the Quantum Channel Coding Theorem
• The work value of information
• A Matrix Convexity Approach to Some Celebrated Quantum Inequalities
• The exact cost of redistributing multipartite quantum states
• On the quantum Renyi relative entropies and related capacity formulas
• An area law for entanglement from exponential decay of correlations
• Entanglement in spin chains and lattices with long-range Ising-type interactions
• Optimal quantum source coding with quantum information at the encoder and decoder
• Renyi Entropy of the XY Spin Chain
• Fundamental bound on the reliability of quantum information transmission
• On the strong converses for the quantum channel capacity theorems
• The squashed entanglement of a quantum channel
• A strong converse for classical channel coding using entangled inputs
• Robustness of quantum Markov chains
• Relating different quantum generalizations of the conditional Renyi entropy
• Squashed entanglement for multipartite states and entanglement measures based on the mixed convex roof
• Multiplicativity of completely bounded $p$-norms implies a strong converse for entanglement-assisted capacity
• Renyi generalizations of the conditional quantum mutual information
• An additive and operational entanglement measure: conditional entanglement of mutual information
• The structure of Renyi entropic inequalities
• Reliability function of general classical-quantum channel
• Shell-Filling Effect in the Entanglement Entropies of Spinful Fermions
• Interaction in Quantum Communication
• Quantum Information Complexity and Amortized Communication

Cited by in corpus (14)

• Recoverability in quantum information theory
• A family of generalized quantum entropies: definition and properties
• Rényi squashed entanglement, discord, and relative entropy differences
• Renyi relative entropies of quantum Gaussian states
• Majorization entropic uncertainty relations for quantum operations
• Mutual information and spontaneous symmetry breaking
• Approximate reversal of quantum Gaussian dynamics
• A one-shot achievability result for quantum state redistribution
• Quantifying information scrambling via Classical Shadow Tomography on Programmable Quantum Simulators
• Swiveled Rényi entropies
• On the Strong Subadditivity of the Rényi entropies for bosonic and fermionic Gaussian states
• Monotonic multi-state quantum $f$-divergences
• Quantum information spreading in random spin chains
• Entropy production in a photovoltaic cell