Optimal phase estimation and square root measurement

Sasaki, Masahide; Carlini, A.; Chefles, Anthony

doi:10.1088/0305-4470/34/35/327

Cited by 6 publications

(9 citation statements)

References 14 publications

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“…[13], but we rephrase it here in a slightly different and more practical way according to the results of Ref. [16]. For convenience of calculation we introduce a new basis {|v 0 , |v 1 } for which our great circle of feature states |f (φ) is the equator.…”

Section: B Template Matching By State Estimationmentioning

confidence: 99%

Quantum template matching

2001

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We consider the quantum analogue of the pattern matching problem, which consists of classifying a given unknown system according to certain predefined pattern classes. We address the problem of quantum template matching in which each pattern class Ci is represented by a known quantum stateĝi called a template state, and our task is to find a template which optimally matches a given unknown quantum statef . We set up a precise formulation of this problem in terms of the optimal strategy for an associated quantum Bayesian inference problem. We then investigate various examples of quantum template matching for qubit systems, considering the effect of allowing a finite number of copies of the input statef . We compare quantum optimal matching strategies and semiclassical strategies and demonstrate an entanglement assisted enhancement of performance in the general quantum optimal strategy.

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Section: B Template Matching By State Estimationmentioning

confidence: 99%

Quantum template matching

2001

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“…But this cannot happen since M (ĝ) is the optimal maximum-likelihood POVM. Therefore p(ĝ|g) must be maximum inĝ = g. For nonunimodular groups the previous argument does not apply, since the POVM given by (26) is no longer normalized. In fact, the operator ξ ′ does not satisfy the normalization constraints (10), since the DMC operators do not commute with the unitaries U h .…”

Section: Maximum Likelihood Measurementsmentioning

confidence: 98%

“…For example, if the group G is a discrete group of phase shifts, it has been proved in Refs. [25,26,27], that SRM minimize the probability of error in estimating the unknown state, and, equivalently, they maximize the likelihood, i.e. the probability of correct estimation.…”

Section: Maximum Likelihood Measurementsmentioning

confidence: 99%

Joint estimation of real squeezing and displacement

Chiribella

D’Ariano

Sacchi

2006

J. Phys. A: Math. Gen.

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We study the problem of joint estimation of real squeezing and amplitude of the radiation field, deriving the measurement that maximizes the probability density of detecting the true value of the unknown parameters. More generally, we provide a solution for the problem of estimating the unknown unitary action of a nonunimodular group in the maximum likelihood approach. Remarkably, in this case the optimal measurements do not coincide with the so called square-root measurements. In the case of squeezing and displacement we analyze in detail the sensitivity of estimation for coherent states and displaced squeezed states, deriving the asymptotic relation between the uncertainties in the joint estimation and the corresponding uncertainties in the optimal separate measurements of squeezing and displacement. A two-mode setup is also analyzed, showing how entanglement between optical modes can be used to approximate perfect estimation.

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“…He performs a single square root measurement on | θn . It is shown [16] that such a measurement is optimal to estimate a single parameter θ n , in the sense that a specific score be maximized as mentioned above. We derive POVMs as in Ref.…”

Section: Protocol Via Distillation Of Entanglementmentioning

confidence: 99%

“…[16,17] in order to estimate a single parameter, in the sense that a specific score is maximized. Such a score is something like that (Probability of a situation) × (Fidelity to an ideal situation).…”

Section: Introductionmentioning

confidence: 99%

Establishing a Private Shared Reference Frame via the Distillation of Entanglement

Nagata

2009

Int J Theor Phys

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We show how a collection of N ebits can be used to establish a private shared reference frame, in the sense that a relative orientation of the x and y axes with respect to a publicly-known z axis is unconditionally private to Alice and Bob. Our protocol relies on the distillation protocol of entanglement. The scheme is based on tensor product states of spin pairs. We implicitly assume a shared reference frame (which is not guaranteed to be private) at the beginning of the protocol. It turns out that the entanglement distillation protocol implies the construction of a private shared reference frame.

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Optimal phase estimation and square root measurement

Cited by 6 publications

References 14 publications

Quantum template matching

Quantum template matching

Joint estimation of real squeezing and displacement

Establishing a Private Shared Reference Frame via the Distillation of Entanglement

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