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Interferometry as a binary decision problem

Matteo G. A. Paris

Published Jan 1, 1996• 16 citations
OpenAlex

Abstract

Binary decision theory has been applied to the general interferometric problem. Optimal detection scheme-according to the Neyman-Pearson criterion-has been considered for different phase-enhanced states of radiation field, and the corresponding bounds on minimum detectable phase shift has been evaluated. A general bound on interferometric precision has been also obtained in terms of photon number fluctuations of the signal mode carrying the phase information.

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We address the use of entanglement to improve the precision of generalized quantum interferometry, i.e., of binary measurements aimed to determine whether or not a perturbation has been applied by a given device. For the most relevant operations in quantum optics, we evaluate the optimal detection strategy and the ultimate bounds to the minimum detectable perturbation. Our results indicate that entanglement-assisted strategies improve the discrimination in comparison with conventional schemes. Possible implementations of entanglement-assisted schemes, in order to approach the performances of the optimal strategies, are also suggested.

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Optical interferometry in the presence of large phase diffusion

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Phase diffusion represents a crucial obstacle toward the implementation of high-precision interferometric measurements and phase-shift-based communication channels. Here we present a nearly optimal interferometric scheme based on homodyne detection and coherent signals for the detection of a phase shift in the presence of large phase diffusion. In our scheme the ultimate bound to interferometric sensitivity is achieved already for a small number of measurements, of the order of hundreds, without using nonclassical light.

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Masahiro Takeoka, Masahide Sasaki, Masashi Ban

A practically realizable detection scheme that corresponds to the optimal measurement strategy within the Neyman-Pearson approach is proposed. The pure state probe field is generally described by | /spl psi//sub 0/> = U/spl circ/|0>, where U/spl circ/ is the unitary operator that defines the quantum property of the probe field. The prepared probe field is incident into the black box in which the unitary perturbative operation U/spl circ//sub p/(g) sometimes occurs, where g is the small parameter, such as the small phase shift, to be detected. The output field (|/spl psi//sub 0/> or |/spl psi//sub 1/> = U/spl circ//sub p/(g) |/spl psi//sub 0/> ) is then measured by the positive operator-valued measure (POVM) which consists of the reverse process of the preparation of the probe field and the photodetection process that discriminates if the field includes zero or non-zero photons. This is an application of the Kennedy detection scheme which has been considered as the detector for a binary communications system. The detection probability of the scheme is given by P/sub d/ = 1-||/sup 2/ that is what expected from the mathematical optimization procedure of the Neyman-Pearson hypothesis testing. The scheme is easily applicable to various quantum states such as the coherent or the squeezed probe fields, and so on.

European Quantum Electronics Conference (EQEC)•Jan 1, 2003•0 citations

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Abstract In this work we address the optimization of two important quantum states in terms of interferometric phase sensitivity, given a constraint on the total average number of input photons, N ¯ We use the quantum Fisher information (QFI) as our main tool. We employ both the single- and two-parameter QFI in order to address detection schemes having, and respectively, not having access to an external phase reference. The first quantum state we consider is the coherent plus squeezed vacuum input and find the optimum coherent fraction that maximizes both the single- and two-parameter QFI. We also discuss detection schemes able to perform almost optimally. Finally, we consider the double squeezed vacuum input and determine the squeezed fraction between the inputs that maximizes the QFI. Similar to the previous input state, we also provide detection schemes able to perform optimally.

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Matteo G. A. Paris

We address the problem of determining whether or not a harmonic oscillator has been perturbed by an external force. Quantum detection and estimation theory has been used in devising optimum measurement schemes. Detection probability has been evaluated for different initial state preparations of oscillator. The corresponding lower bounds on minimum detectable perturbation intensity has been evaluated and a general bound for random phase perturbation has been also induced. 1

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Interferometric detection of optical phase shift using twin beams

Junxiang Zhang, Tiancai Zhang, Changde Xie +1 more

An interferometric detection scheme to measure optical phase shift with sensitivity beyond the shot noise limit is proposed. The theoretical calculation shows that using the quantum correlated twin beams produced from an optical parametric amplifier as the input fields of a Mach-Zehnder interferometer, the minimum detectable phase shift will exceed the shot noise limit N-1/2 and approach the Heisenberg limit N-1. The parametric dependences of the minimum detectable phase shift on the nonlinear interaction, input photon number, and detection efficiency are shown.

Acta Physica Sinica (Overseas Edition)•Jun 1, 1999•0 citations
Binary decision theory has been applied to the general interferometric problem. Optimal detection scheme-according to the Neyman-Pearson criterion-has been considered for different phase-enhanced states of radiation field, and the corresponding bounds on minimum detectable phase shift has been evaluated. A general bound on interferometric precision has been also obtained in terms of photon number fluctuations of the signal mode carrying the phase information.
We address the use of entanglement to improve the precision of generalized quantum interferometry, i.e., of binary measurements aimed to determine whether or not a perturbation has been applied by a given device. For the most relevant operations in quantum optics, we evaluate the optimal detection strategy and the ultimate bounds to the minimum detectable perturbation. Our results indicate that entanglement-assisted strategies improve the discrimination in comparison with conventional schemes. Possible implementations of entanglement-assisted schemes, in order to approach the performances of the optimal strategies, are also suggested.
Phase diffusion represents a crucial obstacle toward the implementation of high-precision interferometric measurements and phase-shift-based communication channels. Here we present a nearly optimal interferometric scheme based on homodyne detection and coherent signals for the detection of a phase shift in the presence of large phase diffusion. In our scheme the ultimate bound to interferometric sensitivity is achieved already for a small number of measurements, of the order of hundreds, without using nonclassical light.
A practically realizable detection scheme that corresponds to the optimal measurement strategy within the Neyman-Pearson approach is proposed. The pure state probe field is generally described by | /spl psi//sub 0/> = U/spl circ/|0>, where U/spl circ/ is the unitary operator that defines the quantum property of the probe field. The prepared probe field is incident into the black box in which the unitary perturbative operation U/spl circ//sub p/(g) sometimes occurs, where g is the small parameter, such as the small phase shift, to be detected. The output field (|/spl psi//sub 0/> or |/spl psi//sub 1/> = U/spl circ//sub p/(g) |/spl psi//sub 0/> ) is then measured by the positive operator-valued measure (POVM) which consists of the reverse process of the preparation of the probe field and the photodetection process that discriminates if the field includes zero or non-zero photons. This is an application of the Kennedy detection scheme which has been considered as the detector for a binary communications system. The detection probability of the scheme is given by P/sub d/ = 1-||/sup 2/ that is what expected from the mathematical optimization procedure of the Neyman-Pearson hypothesis testing. The scheme is easily applicable to various quantum states such as the coherent or the squeezed probe fields, and so on.
Abstract In this work we address the optimization of two important quantum states in terms of interferometric phase sensitivity, given a constraint on the total average number of input photons, N ¯ We use the quantum Fisher information (QFI) as our main tool. We employ both the single- and two-parameter QFI in order to address detection schemes having, and respectively, not having access to an external phase reference. The first quantum state we consider is the coherent plus squeezed vacuum input and find the optimum coherent fraction that maximizes both the single- and two-parameter QFI. We also discuss detection schemes able to perform almost optimally. Finally, we consider the double squeezed vacuum input and determine the squeezed fraction between the inputs that maximizes the QFI. Similar to the previous input state, we also provide detection schemes able to perform optimally.
An interferometric detection scheme to measure optical phase shift with sensitivity beyond the shot noise limit is proposed. The theoretical calculation shows that using the quantum correlated twin beams produced from an optical parametric amplifier as the input fields of a Mach-Zehnder interferometer, the minimum detectable phase shift will exceed the shot noise limit N-1/2 and approach the Heisenberg limit N-1. The parametric dependences of the minimum detectable phase shift on the nonlinear interaction, input photon number, and detection efficiency are shown.