Additivity for unital qubit channels

By Christopher K. King. 2001

194 citations recorded by the source corpus.

Additivity of the Holevo capacity is proved for product channels, under the condition that one of the channels is a unital qubit channel, with the other completely arbitrary. As a byproduct this proves that the Holevo bound is the classical information capacity of such qubit channels, and provides an explicit formula for this classical capacity. Additivity of minimal entropy and multiplicativity of p-norms are also proved under the same assumptions. The proof relies on a new bound for the p-norm of an output state from the half-noisy phase-damping channel.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/4891f5f4707b2696fd705c51b5b902b58da040e2

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

In Atomic and Molecular Physics, and Optics

Citations in the corpus

Additivity of the classical capacity of entanglement-breaking quantum channels (2002, background): “Holevo calls a c-q or q-c channel (these terms wil l be defined later) [6, 7], and when one of the channels is a unital qubit channel [8].”
General formulas for capacity of classical-quantum channels (2002, unknown): “See, for instance, [22, 23, 24 , 25] and the references cited there.”
Geometry of Quantum States: Index (2007, background): “This was known to hold for some particular class of channels [32, 530, 836], so it was tempting to speculate that it is true in general.”
From Classical to Quantum Shannon Theory (2011, unknown): “King et al. (2007) studied the quantum Hadamard channels.”
Inequalities for quantum entropy: A review with conditions for equality (2002, methodology): “Using a different approach, King [20, 21 ] recently proved several additivity results for the minimal entropy and Holevo capacity of a noisy channel by using Lp inequalities in which Epstein’s technique provided a critical estimate.”
Quantum channels and memory effects (2012, background): “For these channels the Holevo information has been proven to be additive (King, 2002, 2003).”
Properties of Conjugate Channels with Applications to Additivity and Multiplicativity (2005, methodology): “In Section 3 we study the conjugates of EBT channels, and extend King’s results [21] about Hadamard diagonal channels to a larger class, which we call simply Hadamard channels.”
Unital Quantum Channels – Convex Structure and Revivals of Birkhoff’s Theorem (2008, background): “, regarding contractivity [1] or fixed points [2] — often allowing for a more geometric intuition, (ii) for small dimensions their additional constraint is strong enough to considerably simplify problems [3], and (iii) for sufficiently large dimensions problems on general channels can often be reduc”
Strong Converse for the Classical Capacity of Entanglement-Breaking and Hadamard Channels via a Sandwiched Rényi Relative Entropy (2013, background): “For certain quantum channels, the HSW formula is equal to the classical capacity of the channel [1,4,17,24,36,38,40,62].”
Inequalities for Trace Norms of 2 × 2 Block Matrices (2003, methodology): “This result was derived previously using a lengthier argument [7], and the purpose of this presentation is to explore an alternative method which may allow new approaches to the additivity problem.”
Entanglement-assisted capacity of a quantum channel and the reverse Shannon theorem (2001, background): “2075 Noiseless bit channel = 0 0 1 1 100% dephasing qubit channel Proved in [24].”