Entropy Bound for the Classical Capacity of a Quantum Channel Assisted by Classical Feedback

Abstract

We prove that the classical capacity of an arbitrary quantum channel assisted by a free classical feedback channel is bounded from above by the maximum average output entropy of the quantum channel. As a consequence of this bound, we conclude that a classical feedback channel does not improve the classical capacity of a quantum erasure channel, and by taking into account energy constraints, we conclude the same for a pure-loss bosonic channel. The method for establishing the aforementioned entropy bound involves identifying an information measure having two key properties: 1) it does not increase under a one-way local operations and classical communication channel from the receiver to the sender and 2) a quantum channel from sender to receiver cannot increase the information measure by more than the maximum output entropy of the channel. This information measure can be understood as the sum of two terms, with one corresponding to classical correlation and the other to entanglement.

Capacity of Quantum Private Information Retrieval With Multiple Servers

“…At the end of the protocol, the receiver receives the classical message W . The paper [32] proved that the capacity of this problem when the sender and the receiver have their local quantum registers, respectively. More specifically, the paper [32] also considered the energy constraint E that for a given Hamiltonian H on the input system of N , the input states ρ 1 , .…”

“…Our proof comes from the fact that the multi-round QPIR protocol can be considered as a case of the Classical-Quantum (CQ) channel coding with classical feedback [32]. In the CQ channel coding with classical feedback, the sender encodes a classical message W as a quantum state and sends the state over a fixed channel N .…”

“…The CQ channel capacity is characterized by the following proposition. 32,Theorem 4]). Let N be a quantum channel, r be the number of communication rounds, m be the size of the message set, H be the Hamiltonian on the input system of N , E be the energy constraint, and ε be the error probability.…”

Capacity of Quantum Private Information Retrieval with Multiple Servers

“…Remark V.1. The statement of Proposition V.1 is slightly different from the statement of [29,Theorem 4]. First, whereas [29,Theorem 4] considers an energy constraint on the quantum channel, Proposition V.1 assumes that there is no energy constraint.…”

“…First, whereas [29,Theorem 4] considers an energy constraint on the quantum channel, Proposition V.1 assumes that there is no energy constraint. Second, whereas [29,Theorem 4] is for the repetitive uses of a fixed quantum channel N , Proposition V.1 considers each use of the identity quantum channels over A (1) , . .…”