On the Minimum Output Entropy of Random Orthogonal Quantum Channels

Abstract

Abstract. We consider sequences of random quantum channels defined using the Stinespring formula with Haar-distributed random orthogonal matrices. For any fixed sequence of input states, we study the asymptotic eigenvalue distribution of the outputs through tensor powers of random channels. We show that the input states achieving minimum output entropy are tensor products of maximally entangled states (Bell states) when the tensor power is even. This phenomenon is completely different from the one for random quantum channels constructed from Haar-distributed random unitary matrices, which leads us to formulate some conjectures about the regularized minimum output entropy.

Geometry of phase-covariant qubit channels

“…, similarly to the case of three-parameter phase-covariant maps in equation (28). Just like in figure 5(b), we again have the complete positivity region that has two axes of symmetry.…”

“…Random quantum channels find applications in qubit encryption [23] and superdense coding [24]. The authors prove that even incomplete information about quantum evolution can be sufficient to determine its characteristics, such as bounds on minimal output entropy and its asymptotic behavior [25][26][27][28]. Their generation methods, spectral properties, and state transformations were analyzed in [13,29,30].…”

Black hole microstates vs. the additivity conjectures

“…Nonetheless the known violations of additivity are small, improving capacity by less than a bit no matter how large the channel N is. This has continued to be true despite significant efforts over a number of years to find larger violations [20][21][22][23][24][25][26][27][28][29]. There are some indications that larger violations could be found, however.…”

Random positive operator valued measures

“…In the last few years, significant developments have been reported in Quantum Information Theory as a consequence of applying sophisticated techniques coming from Random Matrix Theory and Free Probability Theory. Indeed, the introduction of suitable models for random quantum states and channels has generated results in various topics, such as: quantum entanglement [ASY14], classical capacity of quantum channels [FN18], additivity question [Has09,CN16]. It is of interest to apply such methods to other concepts or open problems from quantum information, such as, for example, positive operator-valued measures (POVMs) [HZ12].…”