Quantum Metrology in Open Systems: Dissipative Cramér-Rao Bound

The dynamics of spin squeezing of an ensemble of N separate spin-1/2 particles, each coupled to a zero-temperature non-Markovian reservoir have been investigated. We show that the initial spin squeezing could be prolonged for a long time by utilizing detuning modification. We further explore that the spin squeezing sudden death (SSSD) could be circumvented with the increasing of detuning. By comparison with the results in Markovian regime with detuning and those in non-Markovian regime without detuning, we conclude that the disappearance of SSSD and the robust preservation of spin squeezing should be attributed to the combination of detuning and non-Markovian effect. The present results may be of direct importance for quantum metrology in open systems.

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Phase sensitivity of an $\operatorname{SU}(1,1)$ interferometer via product detection

EPJ Quantum Technology ◽

10.1140/epjqt/s40507-021-00110-1 ◽

2021 ◽

Vol 8 (1) ◽

Author(s):

Qingle Wang ◽

Yami Fang ◽

Xiaoping Ma ◽

Dong Li

Keyword(s):

Coherent States ◽

The Other ◽

Phase Sensitivity ◽

Homodyne Detection ◽

Quantum Metrology ◽

Parametric Amplifiers ◽

Detection Scheme ◽

Beam Splitters ◽

Cramer Rao Bound

AbstractWe theoretically analyze the phase sensitivity of an $\operatorname{SU}(1,1)$ SU ( 1 , 1 ) interferometer with various input states by product detection in this paper. This interferometer consists of two parametric amplifiers that play the role of beam splitters in a traditional Mach–Zehnder interferometer. The product of the amplitude quadrature of one output mode and the momentum quadrature of the other output mode is measured via balanced homodyne detection. We show that product detection has the same phase sensitivity as parity detection for most cases, and it is even better in the case with two coherent states at the input ports. The phase sensitivity is also compared with the Heisenberg limit and the quantum Cramér–Rao bound of the $\operatorname{SU}(1,1)$ SU ( 1 , 1 ) interferometer. This detection scheme can be easily implemented with current homodyne technology, which makes it highly feasible. It can be widely applied in the field of quantum metrology.

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Nonlinear Quantum Metrology of Many-Body Open Systems

Physical Review Letters ◽

10.1103/physrevlett.119.010403 ◽

2017 ◽

Vol 119 (1) ◽

Cited By ~ 28

Author(s):

M. Beau ◽

A. del Campo

Keyword(s):

Open Systems ◽

Quantum Metrology ◽

Many Body ◽

Nonlinear Quantum

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Quantum enhanced metrology of Hamiltonian parameters beyond the Cramèr–Rao bound

International Journal of Quantum Information ◽

10.1142/s0219749920300016 ◽

2020 ◽

Vol 18 (03) ◽

pp. 2030001

Author(s):

Luigi Seveso ◽

Matteo G. A. Paris

Keyword(s):

Statistical Models ◽

Unknown Parameter ◽

Quantum Metrology ◽

Measuring Devices ◽

Starting Point ◽

Estimation Problems ◽

Recent Developments ◽

Cramer Rao Bound ◽

Hamiltonian Parameters ◽

Quantum Parameter Estimation

This is a tutorial aimed at illustrating some recent developments in quantum parameter estimation beyond the Cramèr–Rao bound, as well as their applications in quantum metrology. Our starting point is the observation that there are situations in classical and quantum metrology where the unknown parameter of interest, besides determining the state of the probe, is also influencing the operation of the measuring devices, e.g. the range of possible outcomes. In those cases, nonregular statistical models may appear, for which the Cramèr–Rao theorem does not hold. In turn, the achievable precision may exceed the Cramèr–Rao bound, opening new avenues for enhanced metrology. We focus on quantum estimation of Hamiltonian parameters and show that an achievable bound to precision (beyond the Cramèr–Rao) may be obtained in a closed form for the class of so-called controlled energy measurements. Examples of applications of the new bound to various estimation problems in quantum metrology are worked out in some details.

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Efficient qubit phase estimation using adaptive measurements

Quantum ◽

10.22331/q-2021-06-04-467 ◽

2021 ◽

Vol 5 ◽

pp. 467

Author(s):

Marco A. Rodríguez-García ◽

Isaac Pérez Castillo ◽

P. Barberis-Blostein

Keyword(s):

State Of The Art ◽

Phase Estimation ◽

Quantum Metrology ◽

Quantum Phases ◽

Likelihood Functions ◽

Current State ◽

Wide Range ◽

Adaptive Measurements ◽

Cramer Rao Bound ◽

Quantum Parameter Estimation

Estimating correctly the quantum phase of a physical system is a central problem in quantum parameter estimation theory due to its wide range of applications from quantum metrology to cryptography. Ideally, the optimal quantum estimator is given by the so-called quantum Cramér-Rao bound, so any measurement strategy aims to obtain estimations as close as possible to it. However, more often than not, the current state-of-the-art methods to estimate quantum phases fail to reach this bound as they rely on maximum likelihood estimators of non-identifiable likelihood functions. In this work we thoroughly review various schemes for estimating the phase of a qubit, identifying the underlying problem which prohibits these methods to reach the quantum Cramér-Rao bound, and propose a new adaptive scheme based on covariant measurements to circumvent this problem. Our findings are carefully checked by Monte Carlo simulations, showing that the method we propose is both mathematically and experimentally more realistic and more efficient than the methods currently available.

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