We investigate the problem of producing local pure states by performing local noisy operations assisted by one-way classical communication on a given bipartite mixed state in the one-shot setting. We consider the following two scenarios:1)Scenario I: A party, say Alice, is provided with a single copy of some quantum state ρAon system A. The task for Alice is to extract pure qubit states using only noisy operations on A. We call this task purity concentration.2)Scenario II: Two parties, Alice and Bob possess the A and B sub-systems, respectively, of a given bipartite quantum state ρAB. They are allowed to perform any local noisy operations and communicate via a one-way dephasing (i.e., classical) channel. The task for them is to design a protocol using these resources such that together they can extract pure local qubit states from the shared state ρAB. We call this task local purity distillation.

The guesswork of a quantum ensemble quantifies the minimum number of guesses needed in average to correctly guess the state of the ensemble, when only one state can be queried at a time. Here, we derive analytical solutions of the guesswork problem subject to a finite set of conditions, including the analytical solution for any qubit ensemble with uniform probability distribution. As explicit examples, we compute the guesswork for any qubit regular polygonal and polyhedral ensemble.

The accessible information and the informational power quantify the maximum amount of information that can be extracted from a quantum ensemble and by a quantum measurement, respectively. Here, we investigate the tradeoff between the accessible information (informational power, respectively) and the purity of the states of the ensemble (the elements of the measurement, respectively). Under any given lower bound on the purity, 1) we compute the minimum informational power and show that it is attained by the depolarized uniformly-distributed measurement; and 2) we give a lower bound on the accessible information. Under any given upper bound on the purity, 1) we compute the maximum accessible information and show that it is attained by an ensemble of pairwise commuting states with at most two distinct non-null eigenvalues; and 2) we give a lower bound on the maximum informational power. The present results provide, as a corollary, novel sufficient conditions for the tightness of the Jozsa-Robb-Wootters lower bound to the accessible information.

This paper considers the comparison of noisy channels from the viewpoint of statistical decision theory. Various orderings are discussed, all formalizing the idea that one channel is “better” than another for information transmission. The main result is an equivalence relation that is proved for classical channels, quantum channels with classical encoding, and quantum channels with quantum encoding.

We evaluate the one-shot entanglement of assistance for an arbitrary bipartite state. This yields another interesting result, namely a characterization of the one-shot distillable entanglement of a bipartite pure state. This result is shown to be stronger than that obtained by specializing the one-shot hashing bound to pure states. Finally, we show how the one-shot result yields the operational interpretation of the asymptotic entanglement of assistance proved by Smolin and coworkers.

We study optimal rates for quantum communication over a single use of a channel, which itself can correspond to a finite number of uses of a channel with arbitrarily correlated noise. The corresponding capacity is often referred to as theone-shotquantum capacity. In this paper, we prove bounds on the one-shot quantum capacity of an arbitrary channel. This allows us to compute the quantum capacity of a channel with arbitrarily correlated noise, in the limit of asymptotically many uses of the channel. In the memoryless case, we explicitly show that our results reduce to known expressions for the quantum capacity.