Epistemic view of quantum states and communication complexity of quantum channels

TL;DR

This paper explores the classical simulation of quantum channels using hidden variable theories, establishing a link between quantum states as knowledge and the communication cost, with new bounds for single qubits.

Contribution

It introduces a class of hidden variable theories where quantum states are statistical knowledge, and derives a tighter upper bound on the classical communication needed for simulating single-qubit channels.

Findings

Communication complexity for single qubits is less than 1.28 bits.

Derived simulation cost equals mutual information between quantum and classical states.

Established a connection between hidden variable theories and classical simulation bounds.

Abstract

The communication complexity of a quantum channel is the minimal amount of classical communication required for classically simulating a process of state preparation, transmission through the channel and subsequent measurement. It establishes a limit on the power of quantum communication in terms of classical resources. We show that classical simulations employing a finite amount of communication can be derived from a special class of hidden variable theories where quantum states represent statistical knowledge about the classical state and not an element of reality. This special class has attracted strong interest very recently. The communication cost of each derived simulation is given by the mutual information between the quantum state and the classical state of the parent hidden variable theory. Finally, we find that the communication complexity for single qubits is smaller than 1.28 bits. The previous known upper bound was 1.85 bits.