Optical quantum communication complexity in the simultaneous message passing model

TL;DR

This paper introduces a framework for analyzing the physical resources, such as time and energy, in optical quantum communication protocols, highlighting differences from qubit-based measures and establishing fundamental tradeoff bounds.

Contribution

It develops a new resource-based framework for infinite-dimensional optical quantum protocols, focusing on physical quantities like time and energy rather than qubits.

Findings

Established lower bounds on the tradeoff between communication time and energy.

Defined physical resource measures specific to optical quantum communication.

Provided a theoretical foundation for resource analysis in infinite-dimensional quantum protocols.

Abstract

The communication cost of a classical protocol is typically measured in terms of the number of bits communicated for this determines the time required for communication during the protocol. Similarly, for quantum communication protocols, which use finite-dimensional quantum states, the communication cost is measured in terms of the number of qubits communicated. However, in quantum physics, one can also use infinite-dimensional states, like optical quantum states, for communication protocols. Communication cost measures based on counting the (equivalent) number of qubits transmitted during communication cannot be directly used to measure the cost of such protocols, which use infinite-dimensional states. Moreover, one cannot infer any physical property of infinite-dimensional protocols using such qubit based communication costs. In this paper, we provide a framework to understand the growth of physical resources in infinite-dimensional protocols. We focus on optical protocols for the sake of concreteness. The time required for communication and the energy expended during communication are identified as the important physical resources of such protocols. In an optical protocol, the time required for communication is determined by the number of time-bin modes that are transmitted from one party to another. The mean photon number of the messages sent determines the energy required during communication in the protocol. We prove a lower bound on the tradeoff between the growth of these two quantities with the growth of the problem size. We call such tradeoff relations optical quantum communication complexity relations.