Abstract
Continuous-variable codes are an expedient solution for quantum information processing and quantum communication involving optical networks. Here we characterize the squeezed comb, a finite superposition of equidistant squeezed coherent states on a line, and its properties as a continuous-variable encoding choice for a logical qubit. The squeezed comb is a realistic approximation to the ideal code proposed by Gottesman, Kitaev, and Preskill [Phys. Rev. A 64, 012310 (2001)], which is fully protected against errors caused by the paradigmatic types of quantum noise in continuous-variable systems: damping and diffusion. This is no longer the case for the code space of finite squeezed combs, and noise robustness depends crucially on the encoding parameters. We analyze finite squeezed comb states in phase space, highlighting their complicated interference features and characterizing their dynamics when exposed to amplitude damping and Gaussian diffusion noise processes. We find that squeezed comb state are more suitable and less error-prone when exposed to damping, which speaks against standard error correction strategies that employ linear amplification to convert damping into easier-to-describe isotropic diffusion noise.
Highlights
Classical and quantum information is stored and accessed in discrete units, i.e., bits and qubits [1], respectively, but the actual physical encoding can be embedded in continuous, infinite-dimensional systems
We find that squeezed comb states are more suitable and less error prone when exposed to damping, which speaks against standard error-correction strategies that employ linear amplification to convert damping into easier-to-describe isotropic diffusion noise
We study a realistic GKP encoding with finite resources based on squeezed comb states: finite superpositions of teeth, i.e., equidistant, distinct wave packets with a finite amount of squeezing
Summary
Classical and quantum information is stored and accessed in discrete units, i.e., bits and qubits [1], respectively, but the actual physical encoding can be embedded in continuous, infinite-dimensional systems. We study a realistic GKP encoding with finite resources based on squeezed comb states: finite superpositions of teeth, i.e., equidistant, distinct wave packets with a finite amount of squeezing. We characterize these states with the help of the Wigner-Weyl phase-space representation [16,17], and we assess the impact of standard noise channels on the code space and on code errors. The amplitude damping channel describing pure loss of energy quanta to a zero-temperature bath, and the isotropic Gaussian noise channel describing pure diffusion resulting from a pure loss channel and the equivalent amount of linear amplification Both cases can be treated analytically in phase space.
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