Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

AIP conference proceedings

Criteria for the Implementation of Projective Measurements in Quantum Optics

Philippe Raynal

Published Jan 1, 2004• 0 citations
Publisher

Abstract

We present a set of criteria to decide whether a given projection measurement can be, in principle, exactly implemented by quantum optical means when only quadratic interaction Hamiltonians are available. These criteria hence apply to any implementation that is based on a linear Bogoliubov transformation of the optical modes, i.e., an arbitrary combination of linear optical elements (multi‐port interferometers), multi‐mode squeezers, and phase‐space displacements. The derivation can be adapted to different detection methods, including photon counting and homodyne detection. Our criteria enable one to obtain easily No‐Go theorems for the exact distinguishability of orthogonal quantum states using linear Bogoliubov transformations, auxiliary photons, and conditional dynamics.

DOI
10.1063/1.1834390

Related papers

Simple criteria for the implementation of projective measurements with linear optics

Peter van Loock, Norbert Lütkenhaus

We derive a set of criteria to decide whether a given projection measurement can be, in principle, exactly implemented solely by means of linear optics. The derivation can be adapted to various detection methods, including photon counting and homodyne detection. These criteria enable one to obtain no-go theorems easily for the exact distinguishability of orthogonal quantum states with linear optics, including the use of auxiliary photons and conditional dynamics.

arXiv:quant-ph/0304057•Physical Review A•Jan 9, 2004•39 citations

Implementation of projective measurements with linear optics and continuous photon counting

Masahiro Takeoka, Masahide Sasaki, Peter van Loock +1 more

We investigate the possibility of implementing a given projection measurement using linear optics and arbitrarily fast feedforward based on the continuous detection of photons. In particular, we systematically derive the so-called Dolinar scheme that achieves the minimum-error discrimination of binary coherent states. Moreover, we show that the Dolinar-type approach can also be applied to projection measurements in the regime of photonic-qubit signals. Our results demonstrate that for implementing a projection measurement with linear optics, in principle, unit success probability may be approached even without the use of expensive entangled auxiliary states, as they are needed in all known (near-)deterministic linear-optics proposals.

arXiv:quant-ph/0410133•Physical Review A•Feb 23, 2005•60 citations

Projective measurements via linear optics and photon detectors

Masahiro Takeoka

The possibility of implementing a given photonic projective measurement with linear optics and photon detectors is discussed. This problem can be viewed as a single-shot discrimination of orthogonal pure quantum states. It is particularly shown that any two orthogonal states can be perfectly discriminated using only linear optics, photon counting, coherent ancillary states, and feedforward. This means that one can construct any binary projective measurement with these means, but without any nonclassical ancillary state. The statement holds in the asymptotic limit of a large number of these physical resources. To extend this result, we also address the problem of discriminating a simple set of three orthogonal states.

Optics and Spectroscopy•Jul 1, 2007•2 citations

SINGLE-PHOTON DETECTION AND RECONSTRUCTION (TOMOGRAPHY) OF OPTICAL-FIELD STATES

Masahiro Takeoka

The possibility of implementing a given photonic projective measurement with linear optics and photon detectors is discussed. This problem can be viewed as a single-shot discrimination of orthogonal pure quantum states. It is particularly shown that any two orthogonal states can be perfectly discriminated using only linear optics, photon counting, coherent ancillary states, and feedforward. This means that one can construct any binary projective measurement with these means, but without any nonclassical ancillary state . The state- ment holds in the asymptotic limit of a large number of these physical resources. To extend this result, we also address the problem of discriminating a simple set of three orthogonal states.

•Jan 1, 2007•0 citations

Quantum computation with continuous variables: requirement of nonlinearity for photon counting

Stephen D. Bartlett, Barry C. Sanders

Summary form only given. We show that universal continuous-variable (CV) quantum computation can be obtained using linear optics (phase-space displacements and squeezing), homodyne measurement with classical feed-forward, and a realization of the photon counting projective value measurements (PVM). We describe the PVM for current (ideal) photodetectors, and demonstrate that such detectors cannot be used to implement the photon counting PVM with linear optics alone. Specifically, proposals to implement photon counting using arrays of beamsplitters to distribute the photons across several modes is insufficient for universal CV quantum computation. The photon counting PVM carries with it an implicit nonlinearity, and we discuss how it can be implemented in a CV system using a Kerr interaction (or another nonlinear Hamiltonian) and homodyne measurement. The resource requirements of this measurement scheme compared with using linear optics and current photodetectors are outlined.

Quantum Electronics and Laser Science Conference•Jun 25, 2003•0 citations

Optimum unambiguous discrimination between linearly independent nonorthogonal quantum states and its optical realization

Yuqing Sun, Mark S. Hillery, János A. Bergou

Unambiguously distinguishing between nonorthogonal but linearly independent quantum states is a challenging problem in quantum information processing. In principle, the problem can be solved by mapping the set of nonorthogonal quantum states onto a set of orthogonal ones, which then can be distinguished without error. Such nonunitary transformations can be performed conditionally on quantum systems; a unitary transformation is carried out on a larger system of which the system of interest is a subsytem, a measurement is performed, and if the proper result is obtained the desired nonunitary transformation has been performed on the subsystem. We show how to construct generalized interferometers (multiports), which when combined with measurements on some of the output ports, implement nonunitary transformations of this type. The input states are single-photon states in which the photon is divided among several modes. A number of explicit examples of distinguishing among three nonorthogonal states are discussed, and the networks that optimally distinguish among these states are presented.

arXiv:quant-ph/0012131•Physical Review A•Jul 1, 2001•80 citations
We present a set of criteria to decide whether a given projection measurement can be, in principle, exactly implemented by quantum optical means when only quadratic interaction Hamiltonians are available. These criteria hence apply to any implementation that is based on a linear Bogoliubov transformation of the optical modes, i.e., an arbitrary combination of linear optical elements (multi‐port interferometers), multi‐mode squeezers, and phase‐space displacements. The derivation can be adapted to different detection methods, including photon counting and homodyne detection. Our criteria enable one to obtain easily No‐Go theorems for the exact distinguishability of orthogonal quantum states using linear Bogoliubov transformations, auxiliary photons, and conditional dynamics.
We investigate the possibility of implementing a given projection measurement using linear optics and arbitrarily fast feedforward based on the continuous detection of photons. In particular, we systematically derive the so-called Dolinar scheme that achieves the minimum-error discrimination of binary coherent states. Moreover, we show that the Dolinar-type approach can also be applied to projection measurements in the regime of photonic-qubit signals. Our results demonstrate that for implementing a projection measurement with linear optics, in principle, unit success probability may be approached even without the use of expensive entangled auxiliary states, as they are needed in all known (near-)deterministic linear-optics proposals.
The possibility of implementing a given photonic projective measurement with linear optics and photon detectors is discussed. This problem can be viewed as a single-shot discrimination of orthogonal pure quantum states. It is particularly shown that any two orthogonal states can be perfectly discriminated using only linear optics, photon counting, coherent ancillary states, and feedforward. This means that one can construct any binary projective measurement with these means, but without any nonclassical ancillary state. The statement holds in the asymptotic limit of a large number of these physical resources. To extend this result, we also address the problem of discriminating a simple set of three orthogonal states.
The possibility of implementing a given photonic projective measurement with linear optics and photon detectors is discussed. This problem can be viewed as a single-shot discrimination of orthogonal pure quantum states. It is particularly shown that any two orthogonal states can be perfectly discriminated using only linear optics, photon counting, coherent ancillary states, and feedforward. This means that one can construct any binary projective measurement with these means, but without any nonclassical ancillary state . The state- ment holds in the asymptotic limit of a large number of these physical resources. To extend this result, we also address the problem of discriminating a simple set of three orthogonal states.
Summary form only given. We show that universal continuous-variable (CV) quantum computation can be obtained using linear optics (phase-space displacements and squeezing), homodyne measurement with classical feed-forward, and a realization of the photon counting projective value measurements (PVM). We describe the PVM for current (ideal) photodetectors, and demonstrate that such detectors cannot be used to implement the photon counting PVM with linear optics alone. Specifically, proposals to implement photon counting using arrays of beamsplitters to distribute the photons across several modes is insufficient for universal CV quantum computation. The photon counting PVM carries with it an implicit nonlinearity, and we discuss how it can be implemented in a CV system using a Kerr interaction (or another nonlinear Hamiltonian) and homodyne measurement. The resource requirements of this measurement scheme compared with using linear optics and current photodetectors are outlined.
Unambiguously distinguishing between nonorthogonal but linearly independent quantum states is a challenging problem in quantum information processing. In principle, the problem can be solved by mapping the set of nonorthogonal quantum states onto a set of orthogonal ones, which then can be distinguished without error. Such nonunitary transformations can be performed conditionally on quantum systems; a unitary transformation is carried out on a larger system of which the system of interest is a subsytem, a measurement is performed, and if the proper result is obtained the desired nonunitary transformation has been performed on the subsystem. We show how to construct generalized interferometers (multiports), which when combined with measurements on some of the output ports, implement nonunitary transformations of this type. The input states are single-photon states in which the photon is divided among several modes. A number of explicit examples of distinguishing among three nonorthogonal states are discussed, and the networks that optimally distinguish among these states are presented.