Entangling measurements for multiparameter estimation with two qubits

Roccia, Emanuele; Gianani, Ilaria; Mancino, Luca; Sbroscia, Marco; Somma, Fabrizia; Genoni, Marco G.; Barbieri, Marco

doi:10.1088/2058-9565/aa9212

Cited by 53 publications

(53 citation statements)

References 63 publications

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“…On the other hand, this inequality proves how the dimension of the Hilbert space imposes a trade-off on the ultimately achievable estimation precision for the whole set of parameters; for example if one restricts to qubits one obtains that 0 ≤ Υ( λ , Π) ≤ 1. This problem has been extensively studied both in the context of estimation of unitary operations [60,61] and of estimation of phase and phase-diffusion [62][63][64]. It is important to remark that in cases where the econding of the parameters E λ is fixed and one can optimize over the possible input probe states 0 , such that λ = E λ ( 0 ), the results of the optimization for different figures of merit such as Υ( λ , Π) or Tr[W V] will in general give different results: different probe states will in fact yield different SLD-QFI matrices Q(λ), and while Υ( λ , Π) maximizes the joint optimal estimability at fixed Q(λ), the quantity Tr[W V] maximizes the overall (weighted) precision for the parameters λ.…”

Section: Scalar Quantum Cramér-rao Boundsmentioning

confidence: 99%

A perspective on multiparameter quantum metrology: From theoretical tools to applications in quantum imaging

et al. 2020

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The interest in a system often resides in the interplay among different parameters governing its evolution. It is thus often required to access many of them at once for a complete description. Assessing how quantum enhancement in such multiparameter estimation can be achieved depends on understanding the many subtleties that come into play: establishing solid foundations is key to delivering future technology for this task. In this article we discuss the state of the art of quantum multiparameter estimation, with a particular emphasis on its theoretical tools, on application to imaging problems, and on the possible avenues towards the next developments.

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Section: Scalar Quantum Cramér-rao Boundsmentioning

confidence: 99%

A perspective on multiparameter quantum metrology: From theoretical tools to applications in quantum imaging

et al. 2020

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“…Under certain regularity assumptions, the QFI matrix encodes the ultimate precision bounds on the estimation of unknown parameters encoded in a density matrix (know as quantum Cramer-Rao bounds), while the SLDs and their commutators determine whether such bounds may be saturated with physically realizable measurements [5,6]. The associated applications are plenty, including phase and frequency estimation [4,[7][8][9][10][11][12][13][14][15][16][17], estimation of noise parameters [18][19][20][21][22][23], joint estimation of unitary and/or noisy parameters [24][25][26][27][28][29][30][31], sub-wavelength resolution of optical sources [32][33][34][35][36][37][38], nano-scale thermometry [39][40][41][42][43][44][45], and estimation of Hamiltonian parameters in the presence of phase-transitions [46][47][48]. The most common approach for ...…”

Section: Introductionmentioning

confidence: 99%

Non-orthogonal bases for quantum metrology

Genoni¹,

Tufarelli²

2019

J. Phys. A: Math. Theor.

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Many quantum statistical models are most conveniently formulated in terms of non-orthonormal bases. This is the case, for example, when mixtures and superpositions of coherent states are involved. In these instances, we show that the analytical evaluation of the quantum Fisher information may be greatly simplified by bypassing both the diagonalization of the density matrix and the orthogonalization of the basis. The key ingredient in our method is the Gramian matrix (i.e. the matrix of scalar products between basis elements), which may be interpreted as a metric tensor for index contraction. As an application, we derive novel analytical results for several estimation problems involving noisy Schrödinger cat states.

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“…In order to better study the trade-o in simultaneous estimation of quantum parameters, the following gure of merit has been introduced and studied in detail [9,13,34,35]:…”

Section: Multi-parameter Quantum Estimation Theorymentioning

confidence: 99%

“…In order to violate this inequality one is then left with two possible options: either consider non-separable (entangling) measurements, as suggested above and investigated in [34], or to consider states de ned in a larger Hilbert space [7], as, for instance, correlated two-qubit probes that we will consider in the following.…”

Section: Multi-parameter Quantum Estimation Theorymentioning

confidence: 99%

Monitoring dispersive samples with single photons: the role of frequency correlations

Roccia¹,

Genoni²,

Mancino³

et al. 2017

Quantum Measurements and Quantum Metrology

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Abstract:The physics that governs quantum monitoring may involve other degrees of freedom than the ones initialised and controlled for probing. In this context we address the simultaneous estimation of phase and dephasing characterizing a dispersive medium, and we explore the role of frequency correlations within a photon pair generated via parametric down-conversion, when used as a probe for the medium. We derive the ultimate quantum limits on the estimation of the two parameters, by calculating the corresponding quantum Cramér-Rao bound; we then consider a feasible estimation scheme, based on the measurement of Stokes operators, and address its absolute performances in terms of the correlation parameters, and, more fundamentally, of the role played by correlations in the simultaneous achievability of the quantum Cramér-Rao bounds for each of the two parameters.Quantum light provides a gentler touch when observing fragile samples [1][2][3]. While typically all the information needed can be e ciently collected through a single parameter [4,5], there are instances in which two parameters or more are necessary to capture the physical process under study [6][7][8]. Such parameters might not be associated to compatible observables, hence trade-o may appear in attempts at simultaneously measuring them at the ultimate quantum precision, especially when restrictions are imposed on the resources or, in other words, to the available Hilbert space [7,[9][10][11][12][13][14][15] These trade-o can be interpreted, and often circumvented, by understanding the estimation process under the geometrical standpoint by identifying the physical carrier of information with their state vectors [13]; however, quantum probes only partly approximate such geometric entities, since these typically describe one degree of freedom at the time. The interaction with the sample might actually depend on other degrees of freedom, on which we might have limited control. A relevant example is given by dispersion e ects in phase estimation: if the phase under observation depends on the optical frequency of a photonic probe, the adoption of broad bandwidths would result in dephasing [13,[17][18][19]. An e cient way to tackle this is a joint estimation of the mean phase together with the characteristic width of the dephasing.Single photons from down-conversion are often employed as building blocks of quantum light probes [20][21][22][23][24]. These are produced in pairs that, under standard conditions, share frequency entanglement as a consequence of energy conservation in the generation process [25][26][27][28][29][30][31][32][33] . In this article we calculate what impact such frequency correlation might have on the joint estimation of phase and dephasing in dispersive elements. Our study found that di erences arise if one considers correlated and anticorrelated photon pairs, particularly showing how anticorrelated photons result as more interesting resources to be employed in such noisy phase estimation problem.The manuscript is organized as follows...

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Entangling measurements for multiparameter estimation with two qubits

Cited by 53 publications

References 63 publications

A perspective on multiparameter quantum metrology: From theoretical tools to applications in quantum imaging

A perspective on multiparameter quantum metrology: From theoretical tools to applications in quantum imaging

Non-orthogonal bases for quantum metrology

Monitoring dispersive samples with single photons: the role of frequency correlations

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