Which verification qubits perform best for secure communication in noisy channel?

Abstract

In secure quantum communication protocols, a set of single qubits prepared using 2 or more mutually unbiased bases or a set of $n$-qubit ($n\geq2$) entangled states of a particular form are usually used to form a verification string which is subsequently used to detect traces of eavesdropping. The qubits that form a verification string are referred to as decoy qubits, and there exists a large set of different quantum states that can be used as decoy qubits. In the absence of noise, any choice of decoy qubits provides equivalent security. In this paper, we examine such equivalence for noisy environment (e.g., in amplitude damping, phase damping, collective dephasing and collective rotation noise channels) by comparing the decoy-qubit assisted schemes of secure quantum communication that use single qubit states as decoy qubits with the schemes that use entangled states as decoy qubits. Our study reveals that the single qubit assisted scheme perform better in some noisy environments, while some entangled qubits assisted schemes perform better in other noisy environments. Specifically, single qubits assisted schemes perform better in amplitude damping and phase damping noisy channels, whereas a few Bell-state-based decoy schemes are found to perform better in the presence of the collective noise. Thus, if the kind of noise present in a communication channel (i.e., the characteristics of the channel) is known or measured, then the present study can provide the best choice of decoy qubits required for implementation of schemes of secure quantum communication through that channel.