Theoretical Foundations of Quantum Information Processing and Communication

Brüning, Erwin; Petruccione, Francesco

doi:10.1007/978-3-642-02871-7

Cited by 4 publications

(2 citation statements)

References 25 publications

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“…Moreover, stemming from the microscopic picture, it allows to take into account the effect of the dissipative dynamics being dependent on the parameter being sensed-which we demonstrate to significantly improve the attainable sensing precision at a single-probe level. Last but not least, it gives a clear interpretation of the phase-covariance assumption [38][39][40], which forces the noise terms to commute with the parameter-encoding Hamiltonian, as it is then naturally guaranteed by the secular approximation within which one discards fast oscillating terms in the master equation [41]. Hence, by considering the model yielding non-secular dynamics induced by the baths with Ohmic spectral densities, we are able to explicitly show that it is the Zeno limit (see [42,43]) that dictates the asymptotic precision scaling also when the phase-covariance (PC) is broken.…”

Section: Introductionmentioning

confidence: 94%

“…Importantly, all the dynamics for which such limitation was proven are characterized by the fact that the action of the noise commutes with the unitary encoding of the parameter. In other terms, the dynamics of the probes, besides being independent and identical, is PC [38][39][40], which means that at any time t the quantum channel L w ( ) t 0 can be decomposed into the unitary encoding term and a noise term, and these two commute. More precisely, the dynamics of a two-level system is said to be PC, if for any rotation by an angle…”

Section: Realistic Bounds On Precision In the Presence Of Local Noisementioning

confidence: 99%

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Fundamental limits to frequency estimation: a comprehensive microscopic perspective

Haase¹,

Smirne²,

Kołodyński³

et al. 2018

New J. Phys.

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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.

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Section: Introductionmentioning

confidence: 94%

Section: Realistic Bounds On Precision In the Presence Of Local Noisementioning

confidence: 99%

Fundamental limits to frequency estimation: a comprehensive microscopic perspective

Haase¹,

Smirne²,

Kołodyński³

et al. 2018

New J. Phys.

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A Qutrit Switch for Quantum Networks

Wiśniewska

Sawerwain

2017

Computer Networks

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Ultimate Precision Limits for Noisy Frequency Estimation

et al. 2016

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Quantum metrology protocols allow to surpass precision limits typical to classical statistics. However, in recent years, no-go theorems have been formulated, which state that typical forms of uncorrelated noise can constrain the quantum enhancement to a constant factor, and thus bound the error to the standard asymptotic scaling. In particular, that is the case of time-homogeneous (Lindbladian) dephasing and, more generally, all semigroup dynamics that include phase covariant terms, which commute with the system Hamiltonian. We show that the standard scaling can be surpassed when the dynamics is no longer ruled by a semigroup and becomes time-inhomogeneous. In this case, the ultimate precision is determined by the system short-time behaviour, which when exhibiting the natural Zeno regime leads to a non-standard asymptotic resolution. In particular, we demonstrate that the relevant noise feature dictating the precision is the violation of the semigroup property at short timescales, while non-Markovianity does not play any specific role.Introduction.-Parameter estimation, ranging from the precise determination of atomic transition frequencies to external magnetic field strengths, is a central task in modern physics [1][2][3][4][5][6][7]. Quantum probes made up of N entangled particles can attain the so-called Heisenberg limit (HL), where the estimation mean squared error (MSE) scales as ∼ 1/N 2 , as compared with the standard quantum limit (SQL) ∼ 1/N of classical statistics [8].Heisenberg resolution relies on the unitarity of the time evolution. In realistic situations, however, quantum probes decohere as a result of the unavoidable interaction with the surrounding environment [9]. Such interactions can have a dramatic effect on estimation precision-even infinitesimally small uncorrelated dephasing noise, modelled as a semigroup (time-homogeneous-Lindbladian) evolution [10], forces the MSE to eventually follow the SQL [11]. This result was proven to be an instance of the quantum Cramér-Rao bound (QCRB) [12] for generic Lindbladian dephasing and thus holds even when using optimized entangled states and measurements [13][14][15][16]. The question then arises of what is the ultimate precision limit when the noisy time evolution is not governed by a dephasing dynamical semigroup [13][14][15][16][17][18][19][20][21][22][23][24][25][26]. The SQL has been shown to be surpassable in the presence of time-inhomogeneous (non-semigroup) dephasing noise [24], noise with a particular geometry [25] and correlated timehomogeneous dephasing [27], or when the noise geometry allows for error correction techniques [28].Here, we derive the ultimate lower bounds on the MSE for the noisy frequency estimation scenario depicted in Fig. 1 where probe systems are independently affected by the decoherence. In particular, we focus on uncorrelated phase-covariant noise, that is, noise-types commuting with the parameter-encoding Hamiltonian, as these underpin the asymptotic SQL-like precision in the semigroup case [16,25]. Yet, most importantl...

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Theoretical Foundations of Quantum Information Processing and Communication

Cited by 4 publications

References 25 publications

Fundamental limits to frequency estimation: a comprehensive microscopic perspective

Fundamental limits to frequency estimation: a comprehensive microscopic perspective

A Qutrit Switch for Quantum Networks

Ultimate Precision Limits for Noisy Frequency Estimation

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