Scalable programmable quantum gates and a new aspect of the additivity problem for the classical capacity of quantum channels

Abstract

We consider two apparently separated problems: in the first part of the paper we study the concept of a scalable (approximate) programmable quantum gate (SPQG). These are special (approximate) programmable quantum gates, with nice properties that could have implications on the theory of universal computation. Unfortunately, as we prove, such objects do not exist in the domain of usual quantum theory. In the second part the problem of noisy dense coding (and generalizations) is addressed. We observe that the additivity problem for the classical capacity obtained is of apparently greater generality than for the usual quantum channel (completely positive maps): i.e., the latter occurs as a special case of the former, but, as we shall argue with the help of the non-existence result of the first part, the former cannot be reduced to an instance of the latter. We conclude by suggesting that the additivity problem for the classical capacity of quantum channels, as posed until now, may conceptually not be in its appropriate generality.

9 pages, revtex4. Added a few references and updated others. Extended discussion a bit

References in corpus (5)

• Additivity of the Classical Capacity of Entanglement-Breaking Quantum Channels
• Storing quantum dynamics in quantum states: stochastic programmable gate for U(1) operations
• Classical information capacity of superdense coding
• On the multiplicativity conjecture for quantum channels
• Storage of quantum dynamics on quantum states: a quasi-perfect programmable quantum gate

Cited by in corpus (17)

• The classical-quantum boundary for correlations: discord and related measures
• Operational interpretations of quantum discord
• Remarks on additivity of the Holevo channel capacity and of the entanglement of formation
• Optimal super dense coding over noisy quantum channels
• Dense coding with multipartite quantum states
• Second-order asymptotics for source coding, dense coding and pure-state entanglement conversions
• On quantum advantage in dense coding
• Reducing the entropic uncertainty lower bound in the presence of quantum memory via local operation and classical communication
• Optimal super dense coding over memory channels
• Dense Coding with Locality Restriction for Decoder: Quantum Encoders vs. Super-Quantum Encoders
• Non-optimality of unitary operations for dense coding
• Every entangled state provides an advantage in classical communication
• Quantum Wiretap Channel Coding Assisted by Noisy Correlation
• Classical Capacity of Quantum Binary Adder Channels
• When quantum memory is useful for dense coding
• Quantum Advantage in Storage and Retrieval of Isometry Channels
• Analysis of the Entanglement Cost and Calculation of the Holevo Capacity