We show that quantification of the performance of quantum-enhanced measurement schemes based on the concept of quantum Fisher information yields asymptotically equivalent results as the rigorous Bayesian approach, provided generic uncorrelated noise
is present in the setup. At the same time, we show that for the problem of decoherence-free phase estimation this equivalence breaks down and the achievable estimation uncertainty calculated within the Bayesian approach is by a $pi$ factor larger than that predicted by the QFI even in the large prior knowledge (small parameter fluctuation) regime, where QFI is conventionally regarded as a reliable figure of merit. We conjecture that the analogous discrepancy is present in arbitrary decoherence-free unitary parameter estimation scheme and propose a general formula for the asymptotically achievable precision limit. We also discuss protocols utilizing states with indefinite number of particles and show that within the Bayesian approach it is legitimate to replace the number of particles with the mean number of particles in the formulas for the asymptotic precision, which as a consequence provides another argument that proposals based on the properties of the QFI of indefinite particle number states leading to sub-Heisenberg precisions are not practically feasible.
We analyze the role of entanglement among probes and with external ancillas in quantum metrology. In the absence of noise, it is known that unentangled sequential strategies can achieve the same Heisenberg scaling of entangled strategies and that ext
ernal ancillas are useless. This changes in the presence of noise: here we prove that entangled strategies can have higher precision than unentangled ones and that the addition of passive external ancillas can also increase the precision. We analyze some specific noise models and use the results to conjecture a general hierarchy for quantum metrology strategies in the presence of noise.
Non-classical states of light find applications in enhancing the performance of optical interferometric experiments, with notable example of gravitational wave-detectors. Still, the presence of decoherence hinders significantly the performance of qua
ntum-enhanced protocols. In this review, we summarize the developments of quantum metrology with particular focus on optical interferometry and derive fundamental bounds on achievable quantum-enhanced precision in optical interferometry taking into account the most relevant decoherence processes including: phase diffusion, losses and imperfect interferometric visibility. We introduce all the necessary tools of quantum optics as well as quantum estimation theory required to derive the bounds. We also discuss the practical attainability of the bounds derived and stress in particular that the techniques of quantum-enhanced interferometry which are being implemented in modern gravitational wave detectors are close to the optimal ones.
We advocate a Bayesian approach to optimal quantum frequency estimation - an important issue for future quantum enhanced atomic clock operation. The approach provides a clear insight into the interplay between decoherence and the extent of the prior
knowledge in determining the optimal interrogation times and optimal estimation strategies. We propose a general framework capable of describing local oscillator noise as well as additional collective atomic dephasing effects. For a Gaussian noise the average Bayesian cost can be expressed using the quantum Fisher information and thus we establish a direct link between the two, often competing, approaches to quantum estimation theory
The fundamental quantum interferometry bound limits the sensitivity of an interferometer for a given total rate of photons and for a given decoherence rate inside the measurement device.We theoretically show that the recently reported quantum-noise l
imited sensitivity of the squeezed-light-enhanced gravitational-wave detector GEO600 is exceedingly close to this bound, given the present amount of optical loss. Furthermore, our result proves that the employed combination of a bright coherent state and a squeezed vacuum state is generally the optimum practical approach for phase estimation with high precision on absolute scales. Based on our analysis we conclude that neither the application of Fock states nor N00N states or any other sophisticated nonclassical quantum states would have yielded an appreciably higher quantum-noise limited sensitivity.
We demonstrate that the optimal states in lossy quantum interferometry may be efficiently simulated using low rank matrix product states. We argue that this should be expected in all realistic quantum metrological protocols with uncorrelated noise an
d is related to the elusive nature of the Heisenberg precision scaling in presence of decoherence.
We provide efficient and intuitive tools for deriving bounds on achievable precision in quantum enhanced metrology based on the geometry of quantum channels and semi-definite programming. We show that when decoherence is taken into account, the maxim
al possible quantum enhancement amounts generically to a constant factor rather than quadratic improvement. We apply these tools to derive bounds for models of decoherence relevant for metrological applications including: dephasing,depolarization, spontaneous emission and photon loss.
We discuss the role of an external phase reference in quantum interferometry. We point out inconsistencies in the literature with regard to the use of the quantum Fisher information (QFI) in phase estimation interferometric schemes. We discuss the in
terferometric schemes with and without an external phase reference and show a proper way to use QFI in both situations.
We report experimental generation of a noisy entangled four-photon state that exhibits a separation between the secure key contents and distillable entanglement, a hallmark feature of the recently established quantum theory of private states. The pri
vacy analysis, based on the full tomographic reconstruction of the prepared state, is utilized in a proof-of-principle key generation. The inferiority of distillation-based strategies to extract the key is exposed by an implementation of an entanglement distillation protocol for the produced state.
We find the optimal scheme for quantum phase estimation in the presence of loss when no a priori knowledge on the estimated phase is available. We prove analytically an explicit lower bound on estimation uncertainty, which shows that, as a function o
f number of probes, quantum precision enhancement amounts at most to a constant factor improvement over classical strategies
