Generalized parity measurements

Radu Ionicioiu; Anca E. Popescu; William J. Munro; Timothy P. Spiller

doi:10.1103/PhysRevA.78.052326

Generalized parity measurements

Radu Ionicioiu^*, Anca E. Popescu, William J. Munro, Timothy P. Spiller

^*Corresponding author for this work

Physics

Research output: Contribution to journal › Article › peer-review

Abstract

Measurements play an important role in quantum computing (QC), either by providing the nonlinearity required for two-qubit gates (linear optics QC), or by implementing a quantum algorithm using single-qubit measurements on a highly entangled initial state (cluster state QC). Parity measurements can be used as building blocks for preparing arbitrary stabilizer states, and, together with one-qubit gates, are universal for quantum computing. Here we generalize parity gates by using a higher-dimensional (qudit) ancilla. This enables us to go beyond the stabilizer or graph state formalism and prepare other types of multiparticle entangled states. The generalized parity module introduced here can prepare in one shot, heralded by the outcome of the ancilla, a large class of entangled states, including Greenberger-Home-Zeilinger states GHZn, Wn, Dicke states Dn,k, and, more generally, certain sums of Dicke states, like Gn states used in secret sharing. For Wn states it provides an exponential gain compared to linear-optics-based methods.

Original language	English
Article number	052326
Journal	Physical Review A
Volume	78
Issue number	5
DOIs	https://doi.org/10.1103/PhysRevA.78.052326
Publication status	Published - 14 Nov 2008

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title = "Generalized parity measurements",

abstract = "Measurements play an important role in quantum computing (QC), either by providing the nonlinearity required for two-qubit gates (linear optics QC), or by implementing a quantum algorithm using single-qubit measurements on a highly entangled initial state (cluster state QC). Parity measurements can be used as building blocks for preparing arbitrary stabilizer states, and, together with one-qubit gates, are universal for quantum computing. Here we generalize parity gates by using a higher-dimensional (qudit) ancilla. This enables us to go beyond the stabilizer or graph state formalism and prepare other types of multiparticle entangled states. The generalized parity module introduced here can prepare in one shot, heralded by the outcome of the ancilla, a large class of entangled states, including Greenberger-Home-Zeilinger states GHZn, Wn, Dicke states Dn,k, and, more generally, certain sums of Dicke states, like Gn states used in secret sharing. For Wn states it provides an exponential gain compared to linear-optics-based methods.",

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AU - Ionicioiu, Radu

AU - Popescu, Anca E.

AU - Munro, William J.

AU - Spiller, Timothy P.

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Y1 - 2008/11/14

N2 - Measurements play an important role in quantum computing (QC), either by providing the nonlinearity required for two-qubit gates (linear optics QC), or by implementing a quantum algorithm using single-qubit measurements on a highly entangled initial state (cluster state QC). Parity measurements can be used as building blocks for preparing arbitrary stabilizer states, and, together with one-qubit gates, are universal for quantum computing. Here we generalize parity gates by using a higher-dimensional (qudit) ancilla. This enables us to go beyond the stabilizer or graph state formalism and prepare other types of multiparticle entangled states. The generalized parity module introduced here can prepare in one shot, heralded by the outcome of the ancilla, a large class of entangled states, including Greenberger-Home-Zeilinger states GHZn, Wn, Dicke states Dn,k, and, more generally, certain sums of Dicke states, like Gn states used in secret sharing. For Wn states it provides an exponential gain compared to linear-optics-based methods.

AB - Measurements play an important role in quantum computing (QC), either by providing the nonlinearity required for two-qubit gates (linear optics QC), or by implementing a quantum algorithm using single-qubit measurements on a highly entangled initial state (cluster state QC). Parity measurements can be used as building blocks for preparing arbitrary stabilizer states, and, together with one-qubit gates, are universal for quantum computing. Here we generalize parity gates by using a higher-dimensional (qudit) ancilla. This enables us to go beyond the stabilizer or graph state formalism and prepare other types of multiparticle entangled states. The generalized parity module introduced here can prepare in one shot, heralded by the outcome of the ancilla, a large class of entangled states, including Greenberger-Home-Zeilinger states GHZn, Wn, Dicke states Dn,k, and, more generally, certain sums of Dicke states, like Gn states used in secret sharing. For Wn states it provides an exponential gain compared to linear-optics-based methods.

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Generalized parity measurements

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