Unified-entropy trade-off relations for a single quantum channel

Abstract

Many important properties of quantum channels are quantified by means of entropic functionals. Characteristics of such a kind are closely related to different representations of a quantum channel. In the Jamiołkowski-Choi representation, the given quantum channel is described by the so-called dynamical matrix. Entropies of the rescaled dynamical matrix known as map entropies describe a degree of introduced decoherence. Within the so-called natural representation, the quantum channel is formally posed by another matrix obtained as reshuffling of the dynamical matrix. The corresponding entropies characterize an amount, with which the receiver a priori knows the channel output. As was previously shown, the map and receiver entropies are mutually complementary characteristics. Indeed, there exists a non-trivial lower bound on their sum. First, we extend the concept of receiver entropy to the family of unified entropies. Developing the previous results, we further derive non-trivial lower bounds on the sum of the map and receiver $(q,s)$-entropies. The derivation is essentially based on some inequalities with the Schatten norms and anti-norms.

8 pages, no figures. The title is slightly changes. Minor grammatical improvements are made. The bibliography is updated

References in corpus (10)

• Heisenberg's Uncertainty Principle
• Competitions between quantum correlations in the quantum-memory-assisted entropic uncertainty relation
• Some general properties of unified entropies
• Unified entropy, entanglement measures and monogamy of multi-party entanglement
• A min-entropy uncertainty relation for finite size cryptography
• Higher entropic uncertainty relations for anti-commuting observables
• Numerical shadow and geometry of quantum states
• Composition of quantum states and dynamical subadditivity
• Entropic trade-off relations for quantum operations
• Notes on entropic characteristics of quantum channels

Cited by in corpus (6)

• Notes on general SIC-POVMs
• On uncertainty relations and entanglement detection with mutually unbiased measurements
• Majorization entropic uncertainty relations for quantum operations
• Unified entropies and quantum speed limits for nonunitary dynamics
• Uncertainty and certainty relations for the Pauli observables in terms of the Rényi entropies of order $\alpha \in (0;1]$
• Family of two-parameter multipartite entanglement measures