Typicality of Heisenberg scaling precision in multimode quantum metrology

Gramegna, Giovanni; Triggiani, Danilo; Facchi, Paolo; Narducci, Frank A.; Tamma, Vincenzo

doi:10.1103/physrevresearch.3.013152

Cited by 15 publications

(24 citation statements)

References 41 publications

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“…Interestingly, this latter case is similar to the single squeezed vacuum and single-homodyne scenario found in the literature [29,30]: in fact, the second term in (14) represents a generalisation of the single-homodyne Fisher information…”

Section: Heisenberg Scaling Of the Fisher Informationsupporting

confidence: 77%

“…This allows for estimation protocols not requiring a preparatory stage nor a prior coarse estimation of the parameter, as opposed to the single-channel homodyne protocols in Refs. [29,30]. We also show that two independent contributions on the precision arise from our analysis: one originated from the presence of displaced photons in addition to squeezed photons, and the other from the squeezing of the probe.…”

mentioning

confidence: 52%

“…where C = |Σ| Σ −1 is the cofactor matrix of Σ and Tr[•] denotes the trace. In the following we will discuss in detail expression (9) in the asymptotic limit of large N , showing which condition must be met in order for this set-up to reach Heisenberg-scaling precision in the estimation of ϕ, and compare differences and advantages with respect to the Heisenberg-scaling single-homodyne schemes [29,30]. We conclude this section by remarking that, in the case of a single channel, M = 1, the last term in the right-hand side of (9) vanishes, and thus the only relevant terms are the first two, containing the derivative of the mean μ and of the determinant of Σ, which reduces to the variance of a single-homodyne measurement.…”

Section: Set-upmentioning

confidence: 99%

“…Replacing in (30) and ( 33) the definition of A = Σ − I/2, it is straightforward to obtain Eqs. (10).…”

Section: Appendix B: Fisher Informationmentioning

confidence: 99%

“…Thus, differently from the schemes in Refs. [29,30], it is then possible to employ this set-up to retrieve information on the parameter through measurements of the average value (i.e. the displacement) of the signal observed with homodyne detection, as well as through the modulation of the noise.…”

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confidence: 99%

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Non-adaptive Heisenberg-limited metrology with multi-channel homodyne measurements

2022

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We show a protocol achieving the ultimate Heisenberg-scaling sensitivity in the estimation of a parameter encoded in a generic linear network, without employing any auxiliary networks, and without the need of any prior information on the parameter nor on the network structure. As a result, this protocol does not require a prior coarse estimation of the parameter, nor an adaptation of the network. The scheme we analyse consists of a single-mode squeezed state and homodyne detectors in each of the M output channels of the network encoding the parameter, making it feasible for experimental applications.

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Section: Heisenberg Scaling Of the Fisher Informationsupporting

confidence: 77%

mentioning

confidence: 52%

Section: Set-upmentioning

confidence: 99%

“…Replacing in (30) and ( 33) the definition of A = Σ − I/2, it is straightforward to obtain Eqs. (10).…”

Section: Appendix B: Fisher Informationmentioning

confidence: 99%

mentioning

confidence: 99%

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Non-adaptive Heisenberg-limited metrology with multi-channel homodyne measurements

2022

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Heisenberg scaling precision in multi-mode distributed quantum metrology

et al. 2021

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We consider the estimation of an arbitrary parameter φ, such as the temperature or a magnetic field, affecting in a distributed manner the components of an arbitrary linear optical passive network, such as an integrated chip. We demonstrate that Heisenberg scaling precision (i.e. of the order of 1/N, where N is the number of probe photons) can be achieved without any iterative adaptation of the interferometer hardware and by using only a simple, single, squeezed light source and well-established homodyne measurements techniques. Furthermore, no constraint on the possible values of the parameter is needed but only a preliminary shot-noise estimation (i.e. with a precision of N ) easily achievable without any quantum resources. Indeed, such a classical knowledge of the parameter is enough to prepare a single, suitable optical stage either at the input or the output of the network to monitor with Heisenberg-limited precision any variation of the parameter to the order of 1 / N without the need to iteratively modify such a stage.

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Gaussian phase sensitivity of boson-sampling-inspired strategies

Valido

García-Ripoll

2021

Phys. Rev. A

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In this paper we study the phase sensitivity of generic linear interferometric schemes using Gaussian resources and measurements. Our formalism is based on the Fisher information. This allows us to separate the contributions of the measurement scheme, the experimental imperfections, and auxiliary systems. We demonstrate the strength of this formalism using a broad class of multimode Gaussian states that includes well-known results from single-and two-mode metrology scenarios. Using this, we prove that input coherent states or squeezing improve upon the nonclassical states proposed in preceding boson-sampling-inspired phase-estimation schemes. We also develop a polychromatic interferometric protocol, demonstrating an enhanced sensitivity with respect to two-mode squeezed-vacuum states, for which the ideal homodyne detection is formally shown to be optimal.

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Typicality of Heisenberg scaling precision in multimode quantum metrology

Cited by 15 publications

References 41 publications

Non-adaptive Heisenberg-limited metrology with multi-channel homodyne measurements

Non-adaptive Heisenberg-limited metrology with multi-channel homodyne measurements

Heisenberg scaling precision in multi-mode distributed quantum metrology

Gaussian phase sensitivity of boson-sampling-inspired strategies

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