Random quantum codes from Gaussian ensembles and an uncertainty relation

Abstract

Using random Gaussian vectors and an information-uncertainty relation, we give a proof that the coherent information is an achievable rate for entanglement transmission through a noisy quantum channel. The codes are random subspaces selected according to the Haar measure, but distorted as a function of the sender's input density operator. Using large deviations techniques, we show that classical data transmitted in either of two Fourier-conjugate bases for the coding subspace can be decoded with low probability of error. A recently discovered information-uncertainty relation then implies that the quantum mutual information for entanglement encoded into the subspace and transmitted through the channel will be high. The monogamy of quantum correlations finally implies that the environment of the channel cannot be significantly coupled to the entanglement, and concluding, which ensures the existence of a decoding by the receiver.

9 pages, two-column style. This paper is a companion to quant-ph/0702005 and quant-ph/0702006

References in corpus (4)

• Coding Theorem and Strong Converse for Quantum Channels
• Randomizing quantum states: Constructions and applications
• Remote preparation of quantum states
• Uncertainty, Monogamy, and Locking of Quantum Correlations

Cited by in corpus (22)

• A Survey on Quantum Channel Capacities
• Conjectured Strong Complementary Information Tradeoff
• Fundamental bound on the reliability of quantum information transmission
• On the strong converses for the quantum channel capacity theorems
• Trade-off capacities of the quantum Hadamard channels
• Strong converse rates for quantum communication
• Physical Underpinnings of Privacy
• Privacy Amplification, Private States, and the Uncertainty Principle
• Quantum Communication in Rindler Spacetime
• Achieving the Holevo bound via sequential measurements
• Entanglement transmission and generation under channel uncertainty: Universal quantum channel coding
• Decoding quantum information via the Petz recovery map
• Weak Decoupling Duality and Quantum Identification
• Robust quantum data locking from phase modulation
• RTNI - A symbolic integrator for Haar-random tensor networks
• Classicality with(out) decoherence: Concepts, relation to Markovianity, and a random matrix theory approach
• Activation and superactivation of single-mode Gaussian quantum channels
• Quantum Convolutional Coding with Shared Entanglement: General Structure
• The Physics of Quantum Information: Complementarity, Uncertainty, and Entanglement
• Random coding for sharing bosonic quantum secrets
• Optimal State Merging Without Decoupling
• Eigenstate Thermalization Hypothesis and Approximate Quantum Error Correction