Continuous-variable quantum probes for structured environments

Bina, Matteo; Grasselli, Federico; Paris, Matteo G. A.

doi:10.1103/physreva.97.012125

Cited by 55 publications

(52 citation statements)

References 58 publications

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“…[51]), or even structured environments (e.g., see Ref. [52]) to be studied in the near future. = iA â †2 e iθs −â 2 e −iθs + 2iA β cosh re −iθs − β * sinh r â + β sinh r − β * e iθs cosh r â † + iA(β * 2 e iθs − β 2 e −iθs ), where β = |β| e iθb , and assuming that r 0, it can easily be shown that when A = (2n th + 1) sinh 2r 2n 2 th + 2n th + 1 , |β| = |α| A(2n th + 1)…”

Section: Discussionmentioning

confidence: 99%

Optimal Gaussian measurements for phase estimation in single-mode Gaussian metrology

Lee

Rockstuhl

et al. 2019

npj Quantum Inf

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The central issue in quantum parameter estimation is to find out the optimal measurement setup that leads to the ultimate lower bound of an estimation error. We address here a question of whether a Gaussian measurement scheme can achieve the ultimate bound for phase estimation in single-mode Gaussian metrology that exploits single-mode Gaussian probe states in a Gaussian environment. We identify three types of optimal Gaussian measurement setups yielding the maximal Fisher information depending on displacement, squeezing, and thermalization of the probe state. We show that the homodyne measurement attains the ultimate bound for both displaced thermal probe states and squeezed vacuum probe states, whereas for the other single-mode Gaussian probe states, the optimized Gaussian measurement cannot be the optimal setup, although they are sometimes nearly optimal. We then demonstrate that the measurement on the basis of the product quadrature operatorŝ XP +PX, i.e., a non-Gaussian measurement, is required to be fully optimal.

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Section: Discussionmentioning

confidence: 99%

Optimal Gaussian measurements for phase estimation in single-mode Gaussian metrology

Lee

Rockstuhl

et al. 2019

npj Quantum Inf

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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 the last decade, technological advances in control and manipulation of quantum systems have made quantum probes available to the characterization of a large set of physical platforms. In turn, a radically new approach to probe complex quantum systems emerged, and it is based on the quantification and optimization of the information that can be extracted by an immersed quantum probe, as opposed to a classical one [ 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 ]. Quantum probes offer two main advantages: on one hand, they often provide enhanced precision, due to the inherent sensitivity of quantum system to environment-induced decoherence.…”

Section: Introductionmentioning

confidence: 99%

Quantum Probes for Ohmic Environments at Thermal Equilibrium

Sehdaran

Bina²,

Benedetti³

et al. 2019

Entropy

Self Cite

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It is often the case that the environment of a quantum system may be described as a bath of oscillators with an ohmic density of states. In turn, the precise characterization of these classes of environments is a crucial tool to engineer decoherence or to tailor quantum information protocols. Recently, the use of quantum probes in characterizing ohmic environments at zero-temperature has been discussed, showing that a single qubit provides precise estimation of the cutoff frequency. On the other hand, thermal noise often spoil quantum probing schemes, and for this reason we here extend the analysis to a complex system at thermal equilibrium. In particular, we discuss the interplay between thermal fluctuations and time evolution in determining the precision attainable by quantum probes. Our results show that the presence of thermal fluctuations degrades the precision for low values of the cutoff frequency, i.e., values of the order ω c ≲ T (in natural units). For larger values of ω c , decoherence is mostly due to the structure of environment, rather than thermal fluctuations, such that quantum probing by a single qubit is still an effective estimation procedure.

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Continuous-variable quantum probes for structured environments

Cited by 55 publications

References 58 publications

Optimal Gaussian measurements for phase estimation in single-mode Gaussian metrology

Optimal Gaussian measurements for phase estimation in single-mode Gaussian metrology

Non-orthogonal bases for quantum metrology

Quantum Probes for Ohmic Environments at Thermal Equilibrium

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