Heisenberg scaling precision in the estimation of functions of parameters in linear optical networks

Triggiani, Danilo; Facchi, Paolo; Tamma, Vincenzo

doi:10.1103/physreva.104.062603

Cited by 15 publications

(15 citation statements)

References 39 publications

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“…In other words, within certain non-restrictive regularity conditions and for linear networks with a large enough number of channels, the value of the pre-factor becomes essentially unaffected by the choice of the non-optimised auxiliary network. This important feature can be exploited for experimental applications, for example, employing the arbitrary non-optimised stage to manipulate the information encoded into the probe regarding the structure of a linear network with multiple unknown parameters, ultimately allowing the choice of functions of such parameters to be estimated at the Heisenberg scaling sensitivity [ 46 ].…”

Section: Quantum Estimation Based On Single-homodyne Measurementsmentioning

confidence: 99%

Estimation with Heisenberg-Scaling Sensitivity of a Single Parameter Distributed in an Arbitrary Linear Optical Network

Triggiani

Tamma

2022

Sensors

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Quantum sensing and quantum metrology propose schemes for the estimation of physical properties, such as lengths, time intervals, and temperatures, achieving enhanced levels of precision beyond the possibilities of classical strategies. However, such an enhanced sensitivity usually comes at a price: the use of probes in highly fragile states, the need to adaptively optimise the estimation schemes to the value of the unknown property we want to estimate, and the limited working range, are some examples of challenges which prevent quantum sensing protocols to be practical for applications. This work reviews two feasible estimation schemes which address these challenges, employing easily realisable resources, i.e., squeezed light, and achieve the desired quantum enhancement of the precision, namely the Heisenberg-scaling sensitivity. In more detail, it is here shown how to overcome, in the estimation of any parameter affecting in a distributed manner multiple components of an arbitrary M-channel linear optical network, the need to iteratively optimise the network. In particular, we show that this is possible with a single-step adaptation of the network based only on a prior knowledge of the parameter achievable through a “classical” shot-noise limited estimation strategy. Furthermore, homodyne measurements with only one detector allow us to achieve Heisenberg-limited estimation of the parameter. We further demonstrate that one can avoid the use of any auxiliary network at the price of simultaneously employing multiple detectors.

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Section: Quantum Estimation Based On Single-homodyne Measurementsmentioning

confidence: 99%

Estimation with Heisenberg-Scaling Sensitivity of a Single Parameter Distributed in an Arbitrary Linear Optical Network

Triggiani

Tamma

2022

Sensors

Self Cite

View full text Add to dashboard Cite

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“…[41] Moreover, they have been extensively studied both theoretically and experimentally in the context of quantum speed limit, [42,43] Lee-Yang zeros, [44,45] and quantum multiparameter parameter estimation. [16,[46][47][48][49][50][51][52][53][54] The ultimate precision limit in parameter estimation is given by the quantum Cramér-Rao bound. This limit is known as the standard quantum limit (SQL)…”

Section: Introductionmentioning

confidence: 99%

“…[ 41 ] Moreover, they have been extensively studied both theoretically and experimentally in the context of quantum speed limit, [ 42,43 ] Lee‐Yang zeros, [ 44,45 ] and quantum multiparameter parameter estimation. [ 16,46–54 ] The ultimate precision limit in parameter estimation is given by the quantum Cramér‐Rao bound. This limit is known as the standard quantum limit (SQL)

\sqrt {n}

, However, by using

n

‐qubit quantum entangled states, it is possible to attain a higher precision limit known as the Heisenberg limit

n

.…”

Section: Introductionmentioning

confidence: 99%

Quantum Parameter Estimation With Graph States In SU(N) Dynamics

Tao,

Huang,

Tan

2024

Adv Quantum Tech

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In quantum metrology, achieving optimal simultaneous multiparameter estimation is of great significance but remains highly challenging. The research approach involving evolution on dynamics provides a framework to investigate simultaneous multiparameter estimation within graph states. For single‐parameter estimation, it is observed that the precision limit exceeds the Heisenberg limit in higher‐dimensional spin systems. For multiparameter estimation, two scenarios are considered: one with commutative Hamiltonian operators and another with non‐commutative Hamiltonian operators. The results demonstrate that the global estimation precision exceeds the local estimation precision. Under the conditions of parameter limit, the precision of parameter estimation for simultaneously estimating each parameter is equal to that of single‐parameter estimation. Furthermore, a precision‐enhancement scheme has been identified that depends on the dynamics of . The smaller the value of in the dynamic evolution, the higher the precision of the parameter estimation. Finally, it is demonstrated that graph states serve as optimal states in quantum metrology. A set of optimal measurement bases is also identified, and it is illustrated that the precision limit of multiparameter estimation can attain the quantum Cramér‐Rao bound.

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“…On the other hand, the FI value can be increased by optimizing the parameters affecting the visibility and the width of the HOM interference dip. Despite the experimental demonstration of nanometer path length (few-attosecond timing) precision [12,21] and a recent theoretical study on the tailoring of the spectral properties [22,23] of photon pairs to achieve precision beyond the value reported in the laboratory condition, the width of the HOM interference dip governed by the bandwidth of the pair photons remained the limiting factor for optimal measurement precision [12,13,24,25] in HOM interferometer based dynamic (realtime) or fast sensing applications. As such, ultra-broadband photon sources have long been hailed as a vital prerequisite for ultraprecise HOM interferometry.…”

Section: Introductionmentioning

confidence: 99%

Near‐Video Frame Rate Quantum Sensing Using Hong–Ou–Mandel Interferometry

Singh,

Kumar,

Sharma

et al. 2023

Adv Quantum Tech

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Hong–Ou–Mandel (HOM) interference, bunching of two indistinguishable photons on a balanced beam‐splitter, has emerged as a promising tool for quantum sensing. There is a need for wide spectral‐bandwidth photon pairs (for high‐resolution sensing) with high brightness (for fast sensing). Here, the generation of photon‐pairs with flexible spectral‐bandwidth even using single‐frequency, continuous‐wave diode laser enabling high‐precision, real‐time sensing is showed. Using 1‐mm‐long periodically‐poled KTP crystal, degenerate, photon‐pairs with spectral‐bandwidth of 163.42±1.68 nm are produced resulting in a HOM‐dip width of 4.01±0.04 m to measure a displacement of 60 nm, and sufficiently high brightness to enable the measurement of vibrations with amplitude of 205 ± 0.75 nm and frequency of 8 Hz. Fisher‐information (FI) and maximum likelihood estimation enables optical delay measurements as small as 4.97 nm with precision (Cramér–Rao bound) and accuracy of 0.89 and 0.54 nm, respectively, therefore showing HOM sensing capability for real‐time, precision‐augmented, in‐field quantum sensing applications.

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Heisenberg scaling precision in the estimation of functions of parameters in linear optical networks

Cited by 15 publications

References 39 publications

Estimation with Heisenberg-Scaling Sensitivity of a Single Parameter Distributed in an Arbitrary Linear Optical Network

Estimation with Heisenberg-Scaling Sensitivity of a Single Parameter Distributed in an Arbitrary Linear Optical Network

Quantum Parameter Estimation With Graph States In SU(N) Dynamics

Near‐Video Frame Rate Quantum Sensing Using Hong–Ou–Mandel Interferometry

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