Private Quantum Channels and the Cost of Randomizing Quantum Information

TL;DR

This paper establishes that transmitting n qubits privately over an insecure quantum channel requires 2n bits of shared key, and provides bounds on the entropy needed for quantum state randomization, extending classical encryption concepts.

Contribution

It demonstrates the quantum analogue of the one-time pad, quantifies key requirements for private quantum communication, and bounds the entropy for quantum state randomization.

Findings

2n bits of key are necessary and sufficient for private transmission of n qubits

Established bounds on entropy needed for quantum state randomization

Extended classical encryption principles to quantum information

Abstract

We investigate how a classical private key can be used by two players, connected by an insecure one-way quantum channel, to perform private communication of quantum information. In particular we show that in order to transmit n qubits privately, 2n bits of shared private key are necessary and sufficient. This result may be viewed as the quantum analogue of the classical one-time pad encryption scheme. From the point of view of the eavesdropper, this encryption process can be seen as a randomization of the original state. We thus also obtain strict bounds on the amount of entropy necessary for randomizing n qubits.