Quantum Ring States

Abstract

Quantum ring states are non-Gaussian mixed states generated by uniformly modulating the phase of one arm of a bipartite Gaussian quantum resource and transmitting the modulated arm through a lossy thermal bosonic channel. For resources such as two-mode squeezed vacuum (TMSV) states and split coherent states, the continuous phase modulation produces classical states that are diagonal in the Fock basis and fully characterized by photon-number distributions involving hypergeometric functions. We precisely characterize how well states obtained with a finite m-ary phase-shift keying (PSK) modulation approximate quantum ring states. We also leverage bounds on hypergeometric functions to develop closed-form and surprisingly tight bounds for information-theoretic quantities involving quantum ring states, such as the von Neumann entropy and the associated Holevo information. We demonstrate the usefulness of quantum ring states by revisiting several canonical problems and deriving new results including: 1) closed-form achievable communication rates with PSK modulation for lossy thermal bosonic channels over a broad range of channel parameters; 2) improved achievable covert throughputs for one-way and round-trip lossy thermal bosonic channels.