Related papers: Chain rules for quantum channels
We prove that a broad array of capacities of a quantum channel are continuous. That is, two channels that are close with respect to the diamond norm have correspondingly similar communication capabilities. We first show that the classical…
We consider the exact channel synthesis problem. This problem concerns the determination of the minimum amount of information required to create exact correlation remotely when there is a certain rate of randomness shared by two terminals.…
Quantum information theory has generated several interesting conjectures involving products of completely positive maps on matrix algebras, also known as quantum channels. In particular it is conjectured that the output state with maximal…
In this paper, Wielandt's inequality for classical channels is extended to quantum channels. That is, an upper bound to the number of times a channel must be applied, so that it maps any density operator to one with full rank, is found.…
We study binary discrimination of idempotent quantum channels. When the two channels share a common full-rank invariant state, we show that a simple image inclusion condition completely determines the asymptotic behavior: when it holds, a…
Degradable quantum channels are an important class of completely positive trace-preserving maps. Among other properties, they offer a single-letter formula for the quantum and the private classical capacity and are characterized by the fact…
Networks based on entangled quantum systems enable interesting applications in quantum information processing and the understanding of the resulting quantum correlations is essential for advancing the technology. We show that the theory of…
A completely depolarising quantum channel always outputs a fully mixed state and thus cannot transmit any information. In a recent Letter [D. Ebler et al., Phys. Rev. Lett. 120, 120502 (2018)], it was however shown that if a quantum state…
In this paper, we first introduce and define several new information divergences in the space of transition matrices of finite Markov chains which measure the discrepancy between two Markov chains. These divergences offer natural…
By using the Choi-Jamio{\l}kowski isomorphism, we propose two classes of coherence monotones of quantum channels based on the unified $(r,s)$-relative entropy and the sandwiched R\'{e}nyi relative entropy. Elegant properties of the…
The information capacities and ``distillability'' of a quantum channel are studied in the presence of auxiliary resources. These include prior entanglement shared between the sender and receiver and free classical bits of forward and…
We derive a general criterion to detect entangled states in multi-partite systems based on the symmetric logarithmic derivative quantum Fisher information. This criterion is a direct consequence of the fact that separable states do not…
Surprisingly often decoherence is due to classical fluctuations of ambient fields and may thus be described in terms of random unitary (RU) dynamics. However, there are decoherence channels where such a representation cannot exist. Based on…
R\'enyi divergence is related to R\'enyi entropy much like Kullback-Leibler divergence is related to Shannon's entropy, and comes up in many settings. It was introduced by R\'enyi as a measure of information that satisfies almost the same…
Recently, a new notion of quantum R\'enyi divergences has been introduced by M\"uller-Lennert, Dupuis, Szehr, Fehr and Tomamichel, J.Math.Phys. 54:122203, (2013), and Wilde, Winter, Yang, Commun.Math.Phys. 331:593--622, (2014), that has…
The ability to transfer coherent quantum information between systems is a fundamental component of quantum technologies and leads to coherent correlations within the global quantum process. However correlation structures in quantum channels…
A necessary condition for reversibility (sufficiency) of a quantum channel with respect to complete families of states with bounded rank is obtained. A full description (up to isometrical equivalence) of all quantum channels reversible with…
In this work we improve the quantum communication rates of various quantum channels of interest using permutation-invariant quantum codes. We focus in particular on parametrized families of quantum channels and aim to improve bounds on…
The quantum capacity of a noisy quantum channel determines the maximal rate at which we can code reliably over asymptotically many uses of the channel, and it characterizes the channel's ultimate ability to transmit quantum information…
The theory of quantum error correction is a cornerstone of quantum information processing. It shows that quantum data can be protected against decoherence effects, which otherwise would render many of the new quantum applications…