Additivity for unital qubit channels

  title={Additivity for unital qubit channels},
  author={Christopher King},
  journal={Journal of Mathematical Physics},
  • C. King
  • Published 28 March 2001
  • Mathematics, Physics
  • Journal of Mathematical Physics
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… 
Qubit channels which require four inputs to achieve capacity: implications for additivity conjectures
An example is given of a qubit quantum channel which requires four inputs to maximize the Holevo capacity and a conjecture about the concavity of output entropy as a function of entanglement parameters is supported.
Additivity of the classical capacity of entanglement-breaking quantum channels
We show that for the tensor product of an entanglement-breaking quantum channel with an arbitrary quantum channel, both the minimum entropy of an output of the channel and the
Counterexample to an additivity conjecture for output purity of quantum channels
A conjecture arising naturally in the investigation of additivity of classical information capacity of quantum channels states that the maximal purity of outputs from a quantum channel, as measured
A strong converse for classical channel coding using entangled inputs.
It is shown that a strong converse holds for a large class of channels, including all unital qubit channels, the d-dimensional depolarizing channel and the Werner-Holevo channel, which justifies the interpretation of the classical capacity as a sharp threshold for information transmission.
Conditions for multiplicativity of maximal ℓp-norms of channels for fixed integer p
We introduce a condition for memoryless quantum channels which, when satisfied guarantees the multiplicativity of the maximal lp-norm with p a fixed integer. By applying the condition to qubit
Classical information capacity of a class of quantum channels
We consider the additivity of the minimal output entropy and the classical information capacity of a class of quantum channels. For this class of channels, the norm of the output is maximized for the
Numerical Experiments on The Capacity of Quantum Channel with Entangled Input States
The capacity of quantum channel with product input states was formulated by the quantum coding theorem. However, whether entangled input states can enhance the quantum channel is still open. It turns
Additivity and distinguishability of random unitary channels
A random unitary channel is one that is given by a convex combination of unitary channels. It is shown that the conjectures on the additivity of the minimum output entropy and the multiplicativity of
Maximal output purity and capacity for asymmetric unital qudit channels
We consider generalizations of depolarizing channels to maps of the form with Vk being unitary and ∑kak = a < 1. We show that one can construct unital channels of this type for which the input which
Additive Bounds of Minimum Output Entropies for Unital Channels and an Exact Qubit Formula
  • M. Fukuda, G. Gour
  • Mathematics, Computer Science
    IEEE Transactions on Information Theory
  • 2017
An upper bound for the minimum output entropy of a unital quantum channel is found, and an exact formula for general qubit channels is obtained that gives the precise quantity of classical capacity of the Werner–Holevo channel.


Counterexample to an additivity conjecture for output purity of quantum channels
A conjecture arising naturally in the investigation of additivity of classical information capacity of quantum channels states that the maximal purity of outputs from a quantum channel, as measured
Maximization of capacity and lp norms for some product channels
It is conjectured that the Holevo capacity of a product channel Ω⊗Φ is achieved when product states are used as input. Amosov, Holevo, and Werner have also conjectured that the maximal lp norm of a
Minimal entropy of states emerging from noisy quantum channels
It is proved that for a tensor product of two unital stochastic maps on qubit states, using an entanglement that involves only states which emerge with minimal entropy cannot decrease the entropy below the minimum achievable using product states.
On Some Additivity Problems in Quantum Information Theory
A class of problems in quantum information theory, having an elementary formulation but still resisting solution, concerns the additivity properties of various quantities characterizing quantum
Coding Theorems for Quantum Channels
The more than thirty years old issue of the (classical) information capacity of quantum communication channels was dramatically clarified during the last years, when a number of direct quantum coding
On the multiplicativity conjecture for quantum channels
A multiplicativity conjecture for quantum communication channels is formulated, validity of which for the values of parameter $p$ close to 1 is related to the solution of the fundamental problem of
The Capacity of the Quantum Channel with General Signal States
  • A. Holevo
  • Physics, Computer Science
    IEEE Trans. Inf. Theory
  • 1998
It is shown that the capacity of a classical-quantum channel with arbitrary (possibly mixed) states equals the maximum of the entropy bound with respect to all a priori distributions. This completes
Entanglement-Enhanced Classical Communication on a Noisy Quantum Channel
We consider the problem of sending a single classical bit through a noisy quantum channel, when two uses of the channel are available as a resource. For a quantum channel, the possibility exists of
Quantum coding theorems
ContentsI. IntroductionII. General considerations § 1. Quantum communication channel § 2. Entropy bound and channel capacity § 3. Formulation of the quantum coding theorem. Weak conversionIII. Proof
Quantum entanglement and classical communication through a depolarizing channel
Abstract We analyse the role of entanglement for transmission of classical information through a memoryless depolarizing channel. Using the isotropic character of this channel we prove analytically