Parameter estimation in memory-assisted noisy quantum interferometry

Szańkowski, Piotr; Trippenbach, Marek; Chwedeńczuk, Jan

doi:10.1103/physreva.90.063619

Cited by 19 publications

(43 citation statements)

References 50 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We stress thatF Q is actually the object utilized in more phenomenological approaches to quantum metrology, where the master equation is postulated to describe some specific kinds of noise, rather than microscopically derived so that the contributions due to the dependence of the rates on ω 0 are not accounted for. On the other hand, let us mention that in [35] the role of the dependence of the emission and absorption rates on the free system frequency for a qubit system coupled to a Gaussian classical noise has been investigated. Figure 5(c) summarizes the effects of the two contributions described above.…”

Section: Different Contributions To the Qfimentioning

confidence: 99%

Fundamental limits to frequency estimation: a comprehensive microscopic perspective

Haase¹,

Smirne²,

Kołodyński³

et al. 2018

New J. Phys.

View full text Add to dashboard Cite

We consider a metrology scenario in which qubit-like probes are used to sense an external field that affects their energy splitting in a linear fashion. Following the frequency estimation approach in which one optimizes the state and sensing time of the probes to maximize the sensitivity, we provide a systematic study of the attainable precision under the impact of noise originating from independent bosonic baths. Specifically, we invoke an explicit microscopic derivation of the probe dynamics using the spin-boson model with weak coupling of arbitrary geometry. We clarify how the secular approximation leads to a phase-covariant (PC) dynamics, where the noise terms commute with the field Hamiltonian, while the inclusion of non-secular contributions breaks the PC. Moreover, unless one restricts to a particular (i.e., Ohmic) spectral density of the bath modes, the noise terms may contain relevant information about the frequency to be estimated. Thus, by considering general evolutions of a single probe, we study regimes in which these two effects have a non-negligible impact on the achievable precision. We then consider baths of Ohmic spectral density yet fully accounting for the lack of PC, in order to characterize the ultimate attainable scaling of precision when N probes are used in parallel. Crucially, we show that beyond the semigroup (Lindbladian) regime the Zeno limit imposing the 1/N 3/2 scaling of the mean squared error, recently derived assuming PC, generalises to any dynamics of the probes, unless the latter are coupled to the baths in the direction perfectly transversal to the frequency encoding-when a novel scaling of 1/N 7/4 arises. As our microscopic approach covers all classes of dissipative dynamics, from semigroup to non-Markovian ones (each of them potentially non-phase-covariant), it provides an exhaustive picture, in which all the different asymptotic scalings of precision naturally emerge.

show abstract

Section: Different Contributions To the Qfimentioning

confidence: 99%

Fundamental limits to frequency estimation: a comprehensive microscopic perspective

Haase¹,

Smirne²,

Kołodyński³

et al. 2018

New J. Phys.

View full text Add to dashboard Cite

show abstract

“…When n is large enough, e.g.,n=20 (see the figure), there is a sharp improvement in precision as the success probability approaches the critical value. In the asymptotic limit,  ¥ n , it gives rise to a critical behavior that interpolates between the ultimate precision limit, equation (25), and the precision for finite values ofS, equation (26). Figure 4 shows the scaling of the uncertainty with the amount of resources, n, for low levels of noise = r 95% and for different values of the abstention probabilityS.…”

Section: Finite Nmentioning

confidence: 99%

“…The pre-factorr takes into account the scaling of the variance of the state equation (24) as compared to the pure-state case. The first equality of equation (26) uses the fact that only abstention on blocks about the typical spinj 0 is affordable for finite S. This also fixes the value ofS to be approximately s j 0 . The simple expression on the right of equation (26) is not an exact bound, but does provide a good approximation for moderate values ofS (see figure 3).…”

Section: Multiple-copiesmentioning

confidence: 99%

Probabilistic metrology or how some measurement outcomes render ultra-precise estimates

et al. 2016

View full text Add to dashboard Cite

We show on theoretical grounds that, even in the presence of noise, probabilistic measurement strategies (which have a certain probability of failure or abstention) can provide, upon a heralded successful outcome, estimates with a precision that exceeds the deterministic bounds for the average precision. This establishes a new ultimate bound on the phase estimation precision of particular measurement outcomes (or sequence of outcomes). For probe systems subject to local dephasing, we quantify such precision limit as a function of the probability of failure that can be tolerated. Our results show that the possibility of abstaining can set back the detrimental effects of noise. New J. Phys. 18 (2016) 103049 J Calsamiglia et al m m 2 . Solving equation (E.1) for c p m J 2 and summing over m we obtain 15 New J. Phys. 18 (2016) 103049 J Calsamiglia et al 1 . E . 2 J J m J J m m J m J m J , 2Now, for our strategy all j but the maximum one, j=J, are filtered out, and no further filtering is required within the block J, i.e. we have = f 1 m J , for all + J 2 1values of m. Then s J =1 and

show abstract

“…We restricted our calculations only to pure states and assumed that the interactions are fully suppressed during the interferometric sequence. We did not take into account the impact of decoherence [36][37][38]. In any realistic application, the above theory should be extended to include those effects.…”

Section: Discussionmentioning

confidence: 99%

“…On the other hand, such a state is Gaussian, meaning that it is characterized by the two lowest correlation functions. Not surprisingly, in such a case the sensitivity, which depends on these two moments (38), is as powerful as the estimation from the full probability (31). To summarize, at ϕ = π the simple estimation protocol from the average population imbalance is optimal, i.e., it saturates the ultimate bound of the QFI.…”

Section: Estimation From the Population Imbalancementioning

confidence: 99%

Atom interferometer in a double-well potential

Gietka

Chwedeńczuk

2014

Phys. Rev. A

View full text Add to dashboard Cite

We present a detailed study of an atom interferometer which can be realized in a double-well potential. We assume that the interferometric phase is imprinted in the presence of coherent tunneling between the wells. We calculate the ultimate bounds for the estimation sensitivity and show how they relate to the precision of the Mach-Zehnder interferometer. The interferometer presented here allows for sub shot-noise sensitivity when fed with the spin-squeezed states with reduced either the relative population imbalance or the relative phase. We also calculate the precision of the estimation from the population imbalance and show that it overcomes the shot-noise level when the entangled squeezed-states are used at the input.

show abstract

Parameter estimation in memory-assisted noisy quantum interferometry

Cited by 19 publications

References 50 publications

Fundamental limits to frequency estimation: a comprehensive microscopic perspective

Fundamental limits to frequency estimation: a comprehensive microscopic perspective

Probabilistic metrology or how some measurement outcomes render ultra-precise estimates

Atom interferometer in a double-well potential

Contact Info

Product

Resources

About