Communication over Quantum Channels with Parameter Estimation

Abstract

Communication over a random-parameter quantum channel when the decoder is required to reconstruct the parameter sequence is considered. We study scenarios that include either strictly-causal, causal, or non-causal channel side information (CSI) available at the encoder, and also when CSI is not available. This model is the quantum counterpart of the classical rate-and-state channel with state estimation at the decoder. Regularized formulas for the capacity-distortion regions are derived. In the special case of measurement channels, single-letter characterizations are derived for the strictly-causal and causal settings. Furthermore, in the more general case of entanglement-breaking channels, a single-letter characterization is derived when CSI is not available. As a consequence, we obtain regularized formulas for the capacity of random-parameter quantum channels with CSI, generalizing previous results by Boche et al.[5] on classical-quantum channels.

Classical State Masking over a Quantum Channel

“…In other words, the parameter S i chooses whether the ith input system is projected onto |ψ . This channel has also been considered in the dual model of parameter estimation (see [34,Example 4]).…”

“…where the supremum is over the conditional distributions p X|S and the collections of input states ϕ x A , such that given S = s, we have the state [33,34]). The classical capacity of a random-parameter quantum channel (N SA→B , S ∼ q(s)), with CSI at the encoder and without a masking requirement, is given by…”

“…Consider the region R Cl (N ) as defined in (13). To bound the alphabet size, we use the Fenchel-Eggleston-Carathéodory lemma [78] and similar arguments as in in [34]. First, observe that since Λ s E0 is a measurement on E 0 , we can restrict the dimension of this measurement to…”

The Quantum Multiple-Access Channel with Cribbing Encoders

“…Standard method-of-types concepts are defined as in [53,54]. We briefly introduce the notation and basic properties while the detailed definitions can be found in [54, Appendix A].…”

“…To bound the alphabet size of the random variables U , X 1 , and X 2 , we use the Fenchel-Eggleston-Carathéodory lemma [58] and similar arguments as in [23,54]. Let…”