Heralded channel Holevo superadditivity bounds from entanglement monogamy

Abstract

We show that for a particular class of quantum channels, which we call heralded channels, monogamy of squashed entanglement limits the superadditivity of Holevo capacity. Heralded channels provide a means to understand the quantum erasure channel composed with an arbitrary other quantum channel, as well as common situations in experimental quantum information that involve frequent loss of qubits or failure of trials. We also show how entanglement monogamy applies to non-classicality in quantum games, and we consider how faithful, monogamous entanglement measures may bound other entanglement-dependent quantities in many-party scenarios.

Monogamy relations and upper bounds for the generalized $W$-class states using Rényi-$α$ entropy

“…Our result is also tighter than the result in Ref. [32]. Moreover, our results in this paper will provide a reference for general monogamy and polygamy relations in multipartite higher dimensional quantum systems.…”

“…In this section we reconsider the problem of quantum for GW states considered in Ref. [32,38] using Rényi entropy. A two-player game G = (A, B, X, Y, π, v) is played between a referee and two isolated players, Alice and Bob, who communicate only with the referee and not between themselves.…”

“…In Ref. [32,38], the authors presented bounds on the difference between multiplayer quantum games and classical games using the monogamy of Tsallis-q entropy and squashed entanglement, respectively.…”

“…In Ref. [32], the authors assume Alice has a d-dimensional system A. She can share quantum or classical correlation with an arbitrary number of players B 1 , B 2 , ..., B n , simultaneously.…”

Monotonicity Under Local Operations: Linear Entropic Formulas

“…This fact has motivated the study and construction of monotonic formulas, or monotones, in both classical and quantum information theory [4,5]. For example, entanglement measures have to be monotonic under local operations and classical communication [6,7]. Entropic monotones-monotones that can be expressed in terms of entropy-are especially useful because of its central role in information theory [8][9][10][11].…”