Quantum channels and their entropic characteristics

Abstract

One of the major achievements of the recently emerged quantum information theory is the introduction and thorough investigation of the notion of quantum channel which is a basic building block of any data-transmitting or data-processing system. This development resulted in an elaborated structural theory and was accompanied by the discovery of a whole spectrum of entropic quantities, notably the channel capacities, characterizing information-processing performance of the channels. This paper gives a survey of the main properties of quantum channels and of their entropic characterization, with a variety of examples for finite dimensional quantum systems. We also touch upon the "continuous-variables" case, which provides an arena for quantum Gaussian systems. Most of the practical realizations of quantum information processing were implemented in such systems, in particular based on principles of quantum optics. Several important entropic quantities are introduced and used to describe the basic channel capacity formulas. The remarkable role of the specific quantum correlations - entanglement - as a novel communication resource, is stressed.

review article, 60 pages, 5 figures, 194 references; Rep. Prog. Phys. (in press)

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• Quantum work extraction efficiency for noisy quantum batteries: the role of coherence
• Quantum Work Capacitances: ultimate limits for energy extraction on noisy quantum batteries
• Gaussian states and geometrically uniform symmetry
• Optimizing state-discrimination receivers for continuous-variable quantum key distribution over a wiretap channel
• Maximum tolerable excess noise in continuous-variable quantum key distribution and improved lower bound on two-way capacities
• Resonant Multilevel Amplitude Damping Channels
• Quantum probabilities and entanglement for multimode quantum systems
• Quantum states tomography with noisy measurement channels
• Non-Markovianity as a Resource for Quantum Technologies
• Modeling and simulation of a quantum thermal noise on the qubit
• Non-Markovianity in High-Dimensional Open Quantum Systems using Next-generation Multicore Optical Fibers
• Deterministic preparation of superpositions of vacuum plus one photon by adaptive homodyne detection: experimental considerations
• Exploring Non-Markovianity in Ergodic Channels: Measuring Memory Retention through Ergotropy
• Phase-transition-like behavior in information retrieval of a quantum scrambled random circuit system
• Dynamical phase transitions of information flow in random quantum circuits
• Controlling gain with loss: Bounds on localizable entanglement in multi-qubit systems
• Quantum Wasserstein distance of order 1 between channels
• Dual nature of localization in guiding systems with randomly corrugated boundaries: Anderson-type versus entropic
• Process Tomography for Systems in a Thermal State
• Transmission distance in the space of quantum channels
• Employing weak-field homodyne detection for quantum communications
• Localizing genuine multiparty entanglement in noisy stabilizer states
• Effects of Quantum Communication in Large-Scale Networks at Minimum Latency
• Five Starter Pieces: Quantum Information Science via Semi-definite Programs
• Quantum theory of measurements as quantum decision theory
• Limitations for adaptive quantum state tomography in the presence of detector noise
• Maximum expectation of observables with restricted purity states
• Positive operator-valued measures in quantum decision theory
• Decoding Protocols for Classical Communication on Quantum Channels
• On the additivity of the minimum output entropy