Quantum non-Gaussianity and secure quantum communication

Jaehak Lee,Jiyong Park,Hyunchul Nha

doi:10.1038/s41534-019-0164-9

Jaehak Lee, Jiyong Park + Show 1 more

Open Access

https://doi.org/10.1038/s41534-019-0164-9

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Abstract

No-cloning theorem, a profound fundamental principle of quantum mechanics, also provides a crucial practical basis for secure quantum communication. The security of communication can be ultimately guaranteed if the output fidelity via the communication channel is above the no-cloning bound (NCB). In quantum communications using continuous-variable (CV) systems, Gaussian states, more specifically, coherent states have been widely studied as inputs, but less is known for non-Gaussian states. We aim at exploring quantum communication covering CV states comprehensively with distinct sets of unknown states properly defined. Our main results here are (i) to establish the NCB for a broad class of quantum non-Gaussian states, including Fock states, their superpositions, and Schrodinger-cat states and (ii) to examine the relation between NCB and quantum non-Gaussianity (QNG). We find that NCB typically decreases with QNG. Remarkably, this does not mean that QNG states are less demanding for secure communication. By extending our study to mixed-state inputs, we demonstrate that QNG specifically in terms of Wigner negativity requires more resources to achieve output fidelity above NCB in CV teleportation. The more non-Gaussian, the harder to achieve secure communication, which can have crucial implications for CV quantum communications.

Highlights

No-cloning theorem is one of the fundamental quantum principles providing a crucial practical basis for quantum communication—an eavesdropper cannot gain information without disturbing the quantum state carrying information
The no-cloning bound (NCB) varies with the set of input states and it is of crucial importance to identify it for different input states to address communication security relevant to various protocols
We show that non-Gaussian input states require more resources to achieve secure teleportation,[13,35,36] even though NCB

Summary

Introduction

No-cloning theorem is one of the fundamental quantum principles providing a crucial practical basis for quantum communication—an eavesdropper cannot gain information without disturbing the quantum state carrying information. Numerous works studied an approximate cloning scheme, making clones with imperfect quality[1,2,3,4] and rigorously established as a security benchmark the no-cloning bound (NCB), above which the output fidelity of two clones cannot reach.[4,5,6,7,8,9] If a receiver obtains an output state with fidelity higher than NCB, he can be assured of no better copy existing elsewhere and extract more information than Eve—an ultimate security of communication Such a connection was made between the optimal cloning and the security of quantum cryptographic protocols.[4,6,10,11,12]. It was recently proved that coherent states are the optimal input states achieving the ultimate classical capacity of bosonic Gaussian channels.[14,15] The NCB of coherent states was well studied with some extension to other Gaussian (squeezed) states.[7,8,16] On the other hand, quantum non-Gaussian (QNG) states have recently drawn much attention as an essential ingredient for quantum information processing, due to the limited capability of Gaussian states and operations in some crucial tasks, e.g., entanglement distillation,[17] quantum computation,[18] and error correction.[19]

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