In Valiant's matchgate theory, 2-input 2-output matchgates are 4 4 matrices that satisfy ten so-called matchgate identities. We prove that the set of all such matchgates (including non-unitary and non-invertible ones) ...

The capacity of classical channels is convex. This is not the case for the quantum capacity of a channel: The capacity of a mixture of different quantum channels exceeds the mixture of the individual capacities and thus ...

We introduce an aspect of nonlocality which arises when the task of quantum states distinguishability is considered under local operations and shared entanglement in the absence of classical communication. We find the ...

We obtain a general connection between a large quantum advantage in communication complexity and Bell non-locality. We show that given any protocol offering a sufficiently large quantum advantage in communication complexity, ...

We give two strengthenings of an inequality for the quantum conditional mutual information of a tripartite quantum state recently proved by Fawzi and Renner, connecting it with the ability to reconstruct the state from its ...

We define and study a new type of quantum oracle, the quantum conditional oracle, which provides oracle access to the conditional probabilities associated with an underlying distribution. Amongst other properties, we (a) ...

The quantum capacity of a quantum channel is always smaller than the capacity of the channel for private communication. Both quantities are given by the infinite regularization of the coherent and the private information, ...

Transmitting data reliably over noisy communication channels is one of the most important applications of information theory, and is well understood for channels modelled by classical physics. However, when quantum effects ...