Entanglement is not very useful for estimating multiple phases

Ballester, Manuel A.

doi:10.1103/physreva.70.032310

Cited by 54 publications

(65 citation statements)

References 8 publications

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“…(26) is expressed by the site-sum ( i ) of independent contributions of the output Fisher information in Eq. (11). Hence, by simultaneously maximizing the output Fisher information at each site, J (N ) trivially becomes maximum.…”

Section: S+a Imentioning

confidence: 99%

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N-body-extended channel estimation for low-noise parameters

Hotta

Karasawa

Ozawa

2006

J. Phys. A: Math. Gen.

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The notion of low-noise channels was recently proposed and analyzed in detail in order to describe noise-processes driven by environment [M. Hotta, T. Karasawa and M. Ozawa, Phys. Rev. A72, 052334 (2005) ]. An estimation theory of low-noise parameters of channels has also been developed. In this report, we address the low-noise parameter estimation problem for the N -body extension of low-noise channels. We perturbatively calculate the Fisher information of the output states in order to evaluate the lower-bound of the mean-square error of the parameter estimation. We show that the maximum of the Fisher information over all input states can be attained by a factorized input state in the leading order of the low-noise parameter. Thus, to achieve optimal estimation, it is not necessary for there to be entanglement of the N subsystems, as long as the true low-noise parameter is sufficiently small.

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Section: S+a Imentioning

confidence: 99%

“…The state |Ψ opt Ψ opt | maximizes the output Fisher information in Eq. (11). A factorized input state given by …”

Section: S+a Imentioning

confidence: 99%

N-body-extended channel estimation for low-noise parameters

Hotta

Karasawa

Ozawa

2006

J. Phys. A: Math. Gen.

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“…(28) can be applied, whereas a generalization to Abelian group parameters may follow. For multiple phase parameter estimation of unitary channels, Ballester [17,18] showed, ancilla-assisted enhancement actually takes place, whereas for commuting phase parameter estimation no enhancement occurs.…”

Section: One-parameter Unitary Channels Have No Enhancementmentioning

confidence: 99%

“…Recent progress has been reported on problems for special families of quantum channels, in particular, SU(2) channel [14], a generalized Pauli channel [15], a generalized amplitude-damping channel [16], U(N) channel and its Abelian subgroup channel [17,18]. A review by Fujiwara [19] is also available.…”

Section: Introductionmentioning

confidence: 99%

Ancilla-assisted enhancement of channel estimation for low-noise parameters

2005

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In order to make a unified treatment for estimation problems of a very small noise or a very weak signal in a quantum process, we introduce the notion of a low-noise quantum channel with one noise parameter. It is known in several examples that prior entanglement together with nonlocal output measurement improves the performance of the channel estimation. In this paper, we study this "ancilla-assisted enhancement" for estimation of the noise parameter in a general low-noise channel. For channels on two level systems we prove that the enhancement factor, the ratio of the Fisher information of the ancilla-assisted estimation to that of the original one, is always upper bounded by 3/2. Some conditions for the attainability are also given with illustrative examples.

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“…While the QCRB for a single parameter can generally be attained, this is not always true of the QCRB for multiple parameters [22,23]. Where multiple parameters are being estimated, it matters whether the generators of translation of the parameters commute or not, with implications for the optimal strategies of the parameter estimation procedures [24][25][26][27][28][29]. Even though multimode entanglement can be used to improve the estimation of multiple phase parameters beyond the classical SNL [13], this is not always the case.…”

Section: Introductionmentioning

confidence: 99%

Role of entanglement in calibrating optical quantum gyroscopes

2017

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We consider the calibration of an optical quantum gyroscope by modeling two Sagnac interferometers, mounted approximately at right angles to each other. Reliable operation requires that we know the angle between the interferometers with high precision, and we show that a procedure akin to multiposition testing in inertial navigation systems can be generalized to the case of quantum interferometry. We find that while entanglement is a key resource within an individual Sagnac interferometer, its presence between the interferometers is a far more complicated story. The optimum level of entanglement depends strongly on the sought parameter values, and small but significant improvements may be gained from choosing states with the optimal amount of entanglement between the interferometers.

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Entanglement is not very useful for estimating multiple phases

Cited by 54 publications

References 8 publications

N-body-extended channel estimation for low-noise parameters

N-body-extended channel estimation for low-noise parameters

Ancilla-assisted enhancement of channel estimation for low-noise parameters

Role of entanglement in calibrating optical quantum gyroscopes

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