The Capacity of a Quantum Channel for Simultaneous Transmission of Classical and Quantum Information

By Igor Devetak, Peter W. Shor. 2003

428 citations recorded by the source corpus.

An expression is derived characterizing the set of admissible rate pairs for simultaneous transmission of classical and quantum information over a given quantum channel, generalizing both the classical and quantum capacities of the channel. Although our formula involves regularization, i.e. taking a limit over many copies of the channel, it reduces to a single-letter expression in the case of generalized dephasing channels. Analogous formulas are conjectured for the simultaneous public-private capacity of a quantum channel and for the simultaneously 1-way distillable common randomness and entanglement of a bipartite quantum state.

Subfields: Artificial Intelligence, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/be0039807e8480ccb748b20aad6e11621a235411

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Citations in the corpus

The structure of degradable quantum channels (2008, background): “It was shown in [11] that degradable channels satisfy (7).”
A Survey on Quantum Channel Capacities (2018, methodology): “The first,—but yet not complete—definitions of the quantum capacity of the quantum channel can be found in Shor’s work from 1995 [491], in which Shor has introduced a scheme for reducing decoherence in quantum computer memory, and in Schumacher’s articles from one year later [467, 468].”
Advances in quantum cryptography (2019, neutral): “[621].”
Dynamical Purification Phase Transition Induced by Quantum Measurements (2019, background): “[63] Note, unitary-dephasing channels are a distinct class of channels from the generalized dephasing channels introduced in [44].”
Fundamental limits of repeaterless quantum communications (2015, neutral): “edu/people/preskill/ph229/ [33] Devetak, I.”
Strong Converse for the Classical Capacity of Entanglement-Breaking and Hadamard Channels via a Sandwiched Rényi Relative Entropy (2013, background): “Some interesting channels fall into this class: generalized dephasing channels [18,77], cloning channels [6,14], and the so-called Unruh channel [6–8].”
Quantum channels and memory effects (2012, background): “On the other hand the quantum capacity of a phase damping channel Φγ is Q(Φγ) = 1− h(pz) (Devetak and Shor, 2005; Wolf and Pérez-Garćıa, 2007) where h is the binary entropy.”
Quantum Machine Learning for 6G Communication Networks: State-of-the-Art and Vision for the Future (2019, background): “Subsequently, the article [138] investigated the case where both the classical and quantum information can be simultaneously transmitted over a quantum channel by employing a time-sharing strategy.”
The private classical capacity and quantum capacity of a quantum channel (2003, background): “A nontrivial class of channels exists (the so-called degradable channels) for which is efficiently computable [19], and it can be shown that this property extends to (we do not know this to be true for ).”