Abstract
Using the graphical calculus and integration techniques introduced by the authors, we study the statistical properties of outputs of products of random quantum channels for entangled inputs. In particular, we revisit and generalize models of relevance for the recent counterexamples to the minimum output entropy additivity problems. Our main result is a classification of regimes for which the von Neumann entropy is lower on average than the elementary bounds that can be obtained with linear algebra techniques.
Highlights
As in classical computer science, randomized proofs and constructions are ubiquitous in quantum information
Quantum information theory provides a rich source of random matrix problems
One of the most important classes of problems in the mathematical aspects of quantum information theory is the study of data transmission through noisy quantum channels
Summary
As in classical computer science, randomized proofs and constructions are ubiquitous in quantum information. If one considers the product channel Φ ⊗ Φ (where Φ is obtained by replacing the Stinespring unitary U defining the channel by its conjugate), if one takes a maximally entangled (or Bell) state as an input, the output density matrix has always a large eigenvalue This second important fact was observed by Winter, and it implies that the output state in question has low entropy, allowing for a violation of additivity. The paper is organized as follows: in Section 2, we first review the tools available to study moments of outputs of random quantum channels These techniques were introduced in [7,8] and [5] and their first applications to quantum information theory were developed in [5,6] and [9]. In subsections 2.4 and 2.5, we recall two applications of these techniques
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