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Quantum Information and Measurement (QIM)

Breeding Grid States from Schrödinger Cat States

Daniel J. Weigand, Barbara M. Terhal

Published Jan 1, 2017• 0 citations
Publisher

Abstract

Grid states can encode a qubit into a bosonic mode or be used for sensing. We propose protocols that prepare grid states using Schrödinger cat states, linear optics and homodyne detection without post-selection.
DOI
10.1364/qim.2017.qf6b.5

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Superpositions of macroscopically distinct quantum states, introduced in Schrödinger’s famous Gedankenexperiment, are an epitome of quantum “strangeness” and a natural tool for determining the validity limits of quantum physics. The optical incarnation of Schrödinger’s cat — the superposition of two opposite-amplitude coherent states — is also the backbone of quantum information processing in the continuous-variable domain. Here we implement two protocols for producing and amplifying optical Schrödinger’s cats. In the first protocol we remotely prepare a high-efficiency Schrödinger cat state by applying the remote state preparation to a N00N state prepared between two parties that are separated by a lossy medium. The second protocol consists in bringing the initial states into interference on a beamsplitter and a subsequent heralding quadrature measurement in one of the output channels. The latter technique enables implementation in an iterative manner, in principle allowing creation of Schrödinger’s cat states of arbitrarily high amplitude.
We propose a linear-optical scheme that allows encoding grid-state quantum bits (qubits) into a bosonic mode using cat state and postselection as sources of non-Gaussianity in the encoding. As a linear-optical realization of the quantum-walk encoding scheme in [Lin , ], we employ the cat state as a quantum coin that enables encoding approximate Gottesman-Kitaev-Preskill qubits through quantum walk of a squeezed vacuum state in phase space. We show that the conditional phase-space displacement necessary for the encoding can be realized through a Mach-Zehnder interferometer (MZI) assisted with ancillary cat-state input under appropriate parameter regimes. By analyzing the fidelity of the MZI-based displacement operation, we identify the region of parameter space over which the proposed linear-optical scheme can generate grid-state qubits with high fidelity. With adequate parameter setting, our proposal should be accessible to current optical and superconducting-circuit platforms in preparing grid-state qubits for bosonic modes in the, respectively, optical and microwave domains.