Related papers: Weak multiplicativity for random quantum channels
We study the problem of efficient compression of a stochastic source of probability distributions. It can be viewed as a generalization of Shannon's source coding problem. It has relation to the theory of common randomness, as well as to…
It is well known, both theoretically and experimentally, that the survival probability for an unstable quantum state, formed at $t=0,$ is not a simple exponential function, even if the latter is a good approximation for intermediate times.…
The highest fidelity of quantum error-correcting codes of length n and rate R is proven to be lower bounded by 1 - exp [-n E(R)+ o(n)] for some function E(R) on noisy quantum channels that are subject to not necessarily independent errors.…
We show that unbounded number of channel uses may be necessary for perfect transmission of quantum information. For any n we explicitly construct low-dimensional quantum channels ($d_A$=4, $d_E$=2 or 4) whose quantum zero-error capacity is…
A strong converse theorem for channel capacity establishes that the error probability in any communication scheme for a given channel necessarily tends to one if the rate of communication exceeds the channel's capacity. Establishing such a…
This paper is motivated by the problem of error control in network coding when errors are introduced in a random fashion (rather than chosen by an adversary). An additive-multiplicative matrix channel is considered as a model for random…
It is known that the minimal output entropy is additive for any product of entanglement breaking (EB) channels. The same is true for the Renyi entropy, where additivity is equivalent to multiplicativity of the $1 \rightarrow q$ norm for all…
In this work, we study two different approaches to defining the entropy of a quantum channel. One of these is based on the von Neumann entropy of the corresponding Choi-Jamio{\l}kowski state. The second one is based on the relative entropy…
The channel output entropy of a transmitted sequence is the entropy of the possible channel outputs and similarly the channel input entropy of a received sequence is the entropy of all possible transmitted sequences. The goal of this work…
Incorporating sample efficiency, by requiring the number of states consumed by broadcasting does not exceed that of a naive prepare-and-distribute strategy, gives rise to the no practical quantum broadcasting theorem. To navigate this…
We show that a quantum channel $\mathcal{N}$ constructed by averaging over $\mathcal{O}(\log d/\epsilon^2)$ randomly chosen unitaries gives a local $\epsilon$-randomizing map with non-negative probability. The idea comes from a small…
We investigate the fundamental limits of reliable communication over multi-view channels, in which the channel output is comprised of a large number of independent noisy views of a transmitted symbol. We consider first the setting of…
We derive several efficiently computable converse bounds for quantum communication over quantum channels in both the one-shot and asymptotic regime. First, we derive one-shot semidefinite programming (SDP) converse bounds on the amount of…
The maximum rate at which classical information can be reliably transmitted per use of a quantum channel strictly increases in general with $N$, the number of channel outputs that are detected jointly by the quantum joint-detection receiver…
We give a short proof that the coherent information is an achievable rate for the transmission of quantum information through a noisy quantum channel. Our method is to produce random codes by performing a unitarily covariant projective…
Some new examples of quantum channels for which the infimum of the output entropy is additive under taking a tensor product of channels are given.
We establish the capacity of a class of communication channels introduced in [1]. The $n$-letter input from a finite alphabet is passed through a discrete memoryless channel $P_{Z|X}$ and then the output $n$-letter sequence is uniformly…
In analogy with its classical counterpart, a noisy quantum channel is characterized by a loss, a quantity that depends on the channel input and the quantum operation performed by the channel. The loss reflects the transmission quality: if…
We give a simple and conceptual proof of the fact that random unitary channels yield violation of the Minimum Output Entropy additivity. The proof relies on strong convergence of random unitary matrices and Haagerup's inequality.
We consider generalizations of depolarizing channels to maps in which the identity channel is replaced by a convex combinations of unitary conjugations. We show that one can construct unital channels of this type for which the input which…