Distributed implementation of standard oracle operators

TL;DR

This paper analyzes the capacities of distributed quantum oracle operators, showing their classical and entangling capacities depend on the function's range, and provides optimal protocols for their implementation and bidirectional communication.

Contribution

It characterizes the classical and entangling capacities of distributed standard oracle operators and introduces optimal protocols for their implementation and bidirectional communication.

Findings

Classical and entangling capacities are log2(n_f) bits/ebits for arbitrary functions.

Bidirectional capacity for permutation oracles is 2log2(M) bits.

Optimal distributed protocol for implementing any standard oracle operator.

Abstract

The standard oracle operator corresponding to a function f is a unitary operator that computes this function coherently, i.e. it maintains superpositions. This operator acts on a bipartite system, where the subsystems are the input and output registers. In distributed quantum computation, these subsystems may be spatially separated, in which case we will be interested in its classical and entangling capacities. For an arbitrary function f, we show that the unidirectional classical and entangling capacities of this operator are log_{2}(n_{f}) bits/ebits, where n_{f} is the number of different values this function can take. An optimal procedure for bidirectional classical communication with a standard oracle operator corresponding to a permutation on Z_{M} is given. The bidirectional classical capacity of such an operator is found to be 2log_{2}(M) bits. The proofs of these capacities are facilitated by an optimal distributed protocol for the implementation of an arbitrary standard oracle operator.