Converse bounds for quantum and private communication over Holevo–Werner channels

Abstract

Werner states have a host of interesting properties, which often serve to illuminate the unusual properties of quantum information. Starting from these states, one may define a family of quantum channels, known as the Holevo-Werner channels, which themselves afford several unusual properties. In this paper we use the teleportation covariance of these channels to upper bound their two-way assisted quantum and secret-key capacities. This bound may be expressed in terms of relative entropy distances, such as the relative entropy of entanglement, and also in terms of the squashed entanglement. Most interestingly, we show that the relative entropy bounds are strictly subadditive for a sub-class of the Holevo-Werner channels, so that their regularisation provides a tighter performance. These information-theoretic results are first found for point-to-point communication and then extended to repeater chains and quantum networks, under different types of routing strategies.

End-to-end capacities of a quantum communication network

“…For instance, our benchmarks may be used to evaluate performances in relay-assisted QKD protocols such as MDI-QKD and variants [56][57][58]. Related literature and other developments [59][60][61][62][63][64][65][66] are discussed in Supplementary Note 6.…”

“…Then, note that the tightest values of the upper bounds are achieved by extending the minimization to all network simulations σ(N ), i.e., by enforcing min C → min σ(N ) min C in Eqs. (62) and (66). Specifying Eqs.…”

Advances in quantum cryptography

“…In this way, we may achieve better long-distance scalings and further boost the rates by resorting to more complex routing strategies. The study of quantum repeaters and secure QKD networks is one of the hottest topics today [39][40][41][42][43][44][45][46][47][48].…”

Optimized correlation measures in holography

“…The squashed entanglement has been extensively studied in the context of quantum information [43][44][45][46][47][48][49][50], as it satisfies several abstract properties that make it arguably the most promising measure of purely quantum correlations between parties in mixed states. For example, if ρ AB is a pure state, then the only extensions of the state are tensor products ρ ABE ¼ ρ AB ⊗ ρ E , so which is easily interpreted: There cannot be more quantum correlations than total correlations.…”