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)

References in corpus (108)

• Quantum entanglement
• Quantum Cryptography
• Experimental quantum teleportation
• Mixed State Entanglement and Quantum Error Correction
• Quantum information with continuous variables
• Gaussian Quantum Information
• Introducing Quantum Discord
• Entanglement detection
• Classical, quantum and total correlations
• Experimental Realization of Teleporting an Unknown Pure Quantum State via Dual Classical and Einstein-Podolski-Rosen Channels
• Encoding a qubit in an oscillator
• Entanglement Measures and Purification Procedures
• Quantum Computing
• Free-Space distribution of entanglement and single photons over 144 km
• Violation of Bell inequalities by photons more than 10 km apart
• The capacity of the noisy quantum channel
• Quantum key distribution over 40 dB channel loss using superconducting single photon detectors
• Quantum data processing and error correction
• Entanglement-Assisted Classical Capacity of Noisy Quantum Channels
• Quantum cloning
• General Entanglement Breaking Channels
• Superadditivity of communication capacity using entangled inputs
• Long distance quantum teleportation of qubits from photons at 1300 nm to photons at 1550 nm wavelength
• Coding Theorem and Strong Converse for Quantum Channels
• Dense Coding for Continuous Variables
• Characterizing Entanglement
• Quantum Dense Coding Exploiting Bright EPR Beam
• Information transmission through a noisy quantum channel
• Quantum information with Gaussian states
• Codes for the Quantum Erasure Channel
• Capacities of Quantum Erasure Channels
• Quantum Communication With Zero-Capacity Channels
• Classical capacity of the lossy bosonic channel: the exact solution
• Secure key from bound entanglement
• An improved bound on distillable entanglement
• Extremality of Gaussian quantum states
• Fundamentals of Quantum Information Theory
• Quantum Channel Capacity of Very Noisy Channels
• Experimental Free-Space Distribution of Entangled Photon Pairs over a Noisy Ground Atmosphere of 13km
• Quantum state merging and negative information
• Teleportation as a Depolarizing Quantum Channel, Relative Entropy and Classical Capacity
• The mother of all protocols: Restructuring quantum information's family tree
• Coding Theorems for Quantum Channels
• Universal cloning of continuous quantum variables
• Quantum teleportation with squeezed vacuum states
• On the von Neumann capacity of noisy quantum channels
• Additivity for a class of unital qubit channels
• On Quantum Fidelities and Channel Capacities
• Quantum Capacities of Bosonic Channels
• Strong Converse to the Quantum Channel Coding Theorem
• Additivity of the Classical Capacity of Entanglement-Breaking Quantum Channels
• Counterexample to an additivity conjecture for output purity of quantum channels
• One-mode Bosonic Gaussian channels: a full weak-degradability classification
• Information-capacity description of spin-chain correlations
• Minimum output entropy of bosonic channels: a conjecture
• A family of quantum protocols
• Operator-sum Representation for Bosonic Gaussian Channels
• The structure of degradable quantum channels
• Entanglement required in achieving entanglement-assisted channel capacities
• Accessible information and optimal strategies for real symmetrical quantum sources
• Counterexamples to the maximal p-norm multiplicativity conjecture for all p > 1
• Reexamination of Quantum Bit Commitment: the Possible and the Impossible
• On entanglement-assisted classical capacity
• Tema Con Variazioni: Quantum Channel Capacity
• On some additivity problems in quantum information theory
• Quantum privacy and quantum coherence
• Quantum Communication with Correlated Nonclassical States
• Degradability of Bosonic Gaussian channels
• The quantum capacity with symmetric side channels
• Multi-mode bosonic Gaussian channels
• Discrete formulation of teleportation of continuous variables
• Achievable rates for the Gaussian quantum channel
• Multiplicativity of completely bounded p-norms implies a new additivity result
• Experimental demonstration of entanglement assisted coding using a two-mode squeezed vacuum state
• Strong and Electromagnetic Decays of Two New $Lambd{a}_c^{\ast }$ Baryons
• Majorization theory approach to the Gaussian channel minimum entropy conjecture
• Nonadditivity of quantum and classical capacities for entanglement breaking multiple-access channels and butterfly network
• Remarks on additivity of the Holevo channel capacity and of the entanglement of formation
• Multiplicativity of maximal output purities of Gaussian channels under Gaussian inputs
• Broadband channel capacities
• Binding entanglement channels
• Comments on Hastings' Additivity Counterexamples
• Maximization of capacity and p-norms for some product channels
• Unconditional Continuous Variable Dense Coding
• Capacities of Quantum Channels and How to Find Them
• Quantum Feedback Channels
• Counterexamples to additivity of minimum output p-Renyi entropy for p close to 0
• Sequential projective measurements for channel decoding
• Generalized minimal output entropy conjecture for one-mode Gaussian channels: definitions and some exact results
• Unconditional privacy over channels which cannot convey quantum information
• General teleportation channel, singlet fraction and quasi-distillation
• When does noise increase the quantum capacity?
• Another Short and Elementary Proof of Strong Subadditivity of Quantum Entropy
• The entropy gain of infinite-dimensional quantum channels
• Gaussian quantum channels
• The optimal unitary dilation for bosonic Gaussian channels
• Lower Bounds on the Quantum Capacity and Highest Error Exponent of General Memoryless Channels
• The maximal p-norm multiplicativity conjecture is false
• Isotropic quantum spin channels and additivity questions
• Conditions for the multiplicativity of maximal l_p-norms of channels for fixed integer p
• Effective field theory and fundamental interactions
• Some Open Problems in Quantum Information Theory
• Entanglement-assisted capacity of a quantum channel and the reverse Shannon theorem
• The capacity of a quantum channel for simultaneous transmission of classical and quantum information
• Inequalities and separations among assisted capacities of quantum channels
• One-mode quantum Gaussian channels
• Optimal signal ensembles
• The Adaptive Classical Capacity of a Quantum Channel, or Information Capacities of Three Symmetric Pure States in Three Dimensions

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