Superactivation of the Asymptotic Zero-Error Classical Capacity of a Quantum Channel

Abstract

The zero-error classical capacity of a quantum channel is the asymptotic rate at which it can be used to send classical bits perfectly, so that they can be decoded with zero probability of error. We show that there exist pairs of quantum channels, neither of which individually have any zero-error capacity whatsoever (even if arbitrarily many uses of the channels are available), but such that access to even a single copy of both channels allows classical information to be sent perfectly reliably. In other words, we prove that the zero-error classical capacity can be superactivated. This result is the first example of superactivation of a classical capacity of a quantum channel.

24 pages. Despite the similar title, contains different results from arXiv:0906.2527. See "Note Added" at end of paper for details. V2: Includes significantly revised proof of Theorem 27. V3: Includes expanded explanation of some of the technical details

References in corpus (8)

• Superadditivity of communication capacity using entangled inputs
• Quantum Communication With Zero-Capacity Channels
• Counterexamples to the maximal p-norm multiplicativity conjecture for all p > 1
• On the dimension of subspaces with bounded Schmidt rank
• Extensive nonadditivity of privacy
• Counterexamples to additivity of minimum output p-Renyi entropy for p close to 0
• For quantum information, two wrongs can make a right
• Entanglement between Two Uses of a Noisy Multipartite Quantum Channel Enables Perfect Transmission of Classical Information

Cited by in corpus (30)

• Quantum Resource Theories
• A Survey on Quantum Channel Capacities
• Super-activation of quantum non-locality
• Zero-error communication via quantum channels, non-commutative graphs and a quantum Lovasz theta function
• Unbounded number of channel uses are required to see quantum capacity
• Semidefinite programming strong converse bounds for classical capacity
• No-Signalling Assisted Zero-Error Capacity of Quantum Channels and an Information Theoretic Interpretation of the Lovasz Number
• Positivity of linear maps under tensor powers
• Quantum source-channel coding and non-commutative graph theory
• On superactivation of zero-error capacities and reversibility of a quantum channel
• Memory effects can make the transmission capability of a communication channel uncomputable
• Indistinguishability of bipartite states by positive-partial-transpose operations in the many-copy scenario
• On zero-error communication via quantum channels in the presence of noiseless feedback
• Positive tensor products of qubit maps and n-tensor-stable positive qubit maps
• Uniform Additivity in Classical and Quantum Information
• Quantum graphs: different perspectives, homomorphisms and quantum automorphisms
• On channels with positive quantum zero-error capacity having vanishing n-shot capacity
• Separation between quantum Lovász number and entanglement-assisted zero-error classical capacity
• Certifying the Classical Simulation Cost of a Quantum Channel
• On non-commutative operator graphs generated by reducible unitary representation of the Heisenberg-Weyl group
• Quasi-Superactivation of Classical Capacity of Zero-Capacity Quantum Channels
• On the quantum no-signalling assisted zero-error classical simulation cost of non-commutative bipartite graphs
• Maximum privacy without coherence, zero-error
• How Deep the Theory of Quantum Communications Goes: Superadditivity, Superactivation and Causal Activation
• On n-partite superactivation of quantum channel capacities
• Quantum non-signalling assisted zero-error classical capacity of qubit channels
• Information theoretic parameters of non-commutative graphs and convex corners
• Activation of zero-error classical capacity in low-dimensional quantum systems
• Information storage and transmission under Markovian noise
• Conclusive Local State Marking: More Nonlocality With No Entanglement