arXiv subjects

Francesco Albarelli

Publications and source records attributed to Francesco Albarelli.

49 records · Page 3Linked to original sources

arXiv2020

A perspective on multiparameter quantum metrology: from theoretical tools to applications in quantum imaging

The interest in a system often resides in the interplay among different parameters governing its evolution. It is thus often required to access many of them at once for a complete description. Assessing how quantum enhancement in such multiparameter estimation can be achieved depends on understanding the many subtleties that come into play: establishing solid foundations is key to delivering future technology for this task. In this article we discuss the state of the art of quantum multiparameter estimation, with a particular emphasis on its theoretical tools, on application to imaging problems, and on the possible avenues towards the next developments.

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arXiv2020

Quantum frequency estimation with conditional states of continuously monitored independent dephasing channels

We discuss the problem of estimating a frequency via N-qubit probes undergoing independent dephasing channels that can be continuously monitored via homodyne or photo-detection. We derive the corresponding analytical solutions for the conditional states, for generic initial states and for arbitrary efficiency of the continuous monitoring. For the detection strategies considered, we show that: i) in the case of perfect continuous detection, the quantum Fisher information (QFI) of the conditional states is equal to the one obtained in the noiseless dynamics; ii) for smaller detection efficiencies, the QFI of the conditional state is equal to the QFI of a state undergoing the (unconditional) dephasing dynamics, but with an effectively reduced noise parameter.

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arXiv2020

Time-local optimal control for parameter estimation in the Gaussian regime

Information about a classical parameter encoded in a quantum state can only decrease if the state undergoes a non-unitary evolution, arising from the interaction with an environment. However, instantaneous control unitaries may be used to mitigate the decrease of information caused by an open dynamics. A possible, locally optimal (in time) choice for such controls is the one that maximises the time-derivative of the quantum Fisher information (QFI) associated with a parameter encoded in an initial state. In this study, we focus on a single bosonic mode subject to a Markovian, thermal master equation, and determine analytically the optimal time-local control of the QFI for its initial squeezing angle (optical phase) and strength. We show that a single initial control operation is already optimal for such cases and quantitatively investigate situations where the optimal control is applied after the open dynamical evolution has begun.

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arXiv2019

Evaluating the Holevo Cramér-Rao bound for multi-parameter quantum metrology

Only with the simultaneous estimation of multiple parameters are the quantum aspects of metrology fully revealed. This is due to the incompatibility of observables. The fundamental bound for multi-parameter quantum estimation is the Holevo Cramér-Rao bound (HCRB) whose evaluation has so far remained elusive. For finite-dimensional systems we recast its evaluation as a semidefinite program, with reduced size for rank-deficient states. We use this result to study phase and loss estimation in optical interferometry and three-dimensional magnetometry with noisy multi-qubit systems. For the former, we show that, in some regimes, it is possible to attain the HCRB with the optimal (single-copy) measurement for phase estimation. For the latter, we show a non-trivial interplay between the HCRB and incompatibility, and provide numerical evidence that projective single-copy measurements attain the HCRB in the noiseless two-qubit case.

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arXiv2019

Quantum state engineering by non-deterministic noiseless linear amplification

We address quantum state engineering of single- and two-mode states by means of non-deterministic noiseless linear amplifiers (NLAs) acting on Gaussian states. In particular, we show that NLAs provide an effective scheme to generate highly non-Gaussian and non-classical states. Additionally, we show that the amplification of a two-mode squeezed vacuum state (twin-beam) may highly increase entanglement.

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arXiv2019

Characterizing non-deterministic noiseless linear amplifiers at the quantum limit

We address the characterization of the gain parameter of a non-deterministic noiseless linear amplifier (NLA) and compare the performances of different estimation strategies using tools from quantum estimation theory. At first, we show that, contrary to naive expectations, post-selecting only the amplified states does not offer the most accurate estimate. We then focus on minimal implementations of a NLA, i.e. those obtained by coupling the input state to a two-level system, and show that the maximal amount of information about the gain of the NLA is obtained by measuring the whole composite system. The quantum Fisher information (QFI) of this best-case scenario is analysed in some details, and compared to the QFI of the post-selected states, both for successful and unsuccessful amplification. Eventually, we show that full extraction of the available information is achieved when the non-deterministic process is implemented by a Lüders instrument. We also analyse the precision attainable by probing NLAs by single-mode pure states and measuring the field or the number of quanta, and discuss in some details the specific cases of squeezed vacuum and coherent states.

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arXiv2018

Resource theory of quantum non-Gaussianity and Wigner negativity

We develop a resource theory for continuous-variable systems grounded on operations routinely available within current quantum technologies. In particular, the set of free operations is convex and includes quadratic transformations and conditional coarse-grained measurements. The present theory lends itself to quantify both quantum non-Gaussianity and Wigner negativity as resources, depending on the choice of the free-state set --- i.e., the convex hull of Gaussian states or the states with positive Wigner function, respectively. After showing that the theory admits no maximally resourceful state, we define a computable resource monotone --- the Wigner logarithmic negativity. We use the latter to assess the resource content of experimentally relevant states --- e.g., photon-added, photon-subtracted, cubic-phase, and cat states --- and to find optimal working points of some resource concentration protocols. We envisage applications of this framework to sub-universal and universal quantum information processing over continuous variables.

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arXiv2018

Restoring Heisenberg scaling in noisy quantum metrology by monitoring the environment

We study quantum frequency estimation for $N$ qubits subjected to independent Markovian noise, via strategies based on time-continuous monitoring of the environment. Both physical intuition and an extended convexity property of the quantum Fisher information (QFI) suggest that these strategies are more effective than the standard ones based on the measurement of the unconditional state after the noisy evolution. Here we focus on initial GHZ states and on parallel or transverse noise. For parallel noise, i.e. dephasing, we show that perfectly efficient time-continuous photo-detection allows to recover the unitary (noiseless) QFI, and thus to obtain a Heisenberg scaling for every value of the monitoring time. For finite detection efficiency, one falls back to the noisy standard quantum limit scaling, but with a constant enhancement due to an effective reduced dephasing. Also in the transverse noise case we obtain that the Heisenberg scaling is recovered for perfectly efficient detectors, and we find that both homodyne and photo-detection based strategies are optimal. For finite detectors efficiency, our numerical simulations show that, as expected, an enhancement can be observed, but we cannot give any conclusive statement regarding the scaling. We finally describe in detail the stable and compact numerical algorithm that we have developed in order to evaluate the precision of such time-continuous estimation strategies, and that may find application in other quantum metrology schemes.

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arXiv2018

Locally optimal control of continuous variable entanglement

We consider a system of two bosonic modes each subject to the dynamics induced by a thermal Markovian environment and we identify instantaneous, local symplectic controls that minimise the loss of entanglement in the Gaussian regime. By minimising the decrease of the logarithmic negativity at every instant in time, it will be shown that a non-trivial, finite amount of local squeezing helps to counter the effect of decoherence during the evolution. We also determine optimal control routines in the more restrictive scenario where the control operations are applied on only one of the two modes. We find that applying an instantaneous control only at the beginning of the dynamics, i.e. preparing an appropriate initial state, is the optimal strategy for states with symmetric correlations and when the dynamics is the same on both modes. More generally, even in asymmetric cases, the delayed decay of entanglement resulting from the optimal preparation of the initial state with no further action turns out to be always very close to the optimised control where multiple operations are applied during the evolution. Our study extends directly to mono-symmetric systems of any number of modes, i.e. to systems that are invariant under any local permutation of the modes within any one partition, as they are locally equivalent to two-mode systems.

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arXiv2017

Ultimate limits for quantum magnetometry via time-continuous measurements

We address the estimation of the magnetic field B acting on an ensemble of atoms with total spin J subjected to collective transverse noise. By preparing an initial spin coherent state, for any measurement performed after the evolution, the mean-square error of the estimate is known to scale as $1/J$, i.e. no quantum enhancement is obtained. Here, we consider the possibility of continuously monitoring the atomic environment, and conclusively show that strategies based on time-continuous non-demolition measurements followed by a final strong measurement may achieve Heisenberg-limited scaling $1/{J^2}$ and also a monitoring-enhanced scaling in terms of the interrogation time. We also find that time-continuous schemes are robust against detection losses, as we prove that the quantum enhancement can be recovered also for finite measurement efficiency. Finally, we analytically prove the optimality of our strategy.

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arXiv2017

Generation of Coherence via Gaussian Measurements

We address measurement-based generation of quantum coherence in continuous variable systems. We consider Gaussian measurements performed on Gaussian states and focus on two scenarios. In the first one, we assume an initially correlated bipartite state shared by two parties and study how correlations may be exploited to remotely create quantum coherence via measurement back-action. In particular, we focus on conditional states with zero first moments, so as to address coherence due to properties of the covariance matrix. We consider different classes of bipartite states with incoherent marginals and show that the larger the measurement squeezing, the larger the conditional coherence. Homodyne detection is thus the optimal Gaussian measurement to remotely generate coherence. We also show that for squeezed thermal states there exists a threshold value for the generated coherence which separates entangled and separable states at a fixed energy. Finally, we briefly discuss the tripartite case and the relationship between tripartite correlations and the conditional two-mode coherence. In the second scenario, we address the steady state coherence of a system interacting with an environment which is continuously monitored. In particular, we discuss the dynamics of an optical parametric oscillator in order to investigate how the coherence of a Gaussian state may be increased by means of time-continuous Gaussian measurement on the interacting environment.

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arXiv2016

Quantum backflow effect and nonclassicality

The quantum backflow effect is a counterintuitive behavior of the probability current of a free particle, which may be negative even for states with vanishing negative momentum component. Here we address the notion of nonclassicality arising from the backflow effect, i.e. from the negativity of the probability current, and analyze its relationships with the notion of nonclassicality based on the negativity of the Wigner function. Our results suggest that backflow is linked to a different, and in fact more restrictive, notion of nonclassicality, the negativity of the Wigner function being only a necessary prerequisite for its occurrence. This hierarchical structure may be confirmed by looking at the addition of thermal noise, which more easily destroys the negativity of the probability current than the negativity of the Wigner function itself.

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arXiv2016

Enhanced estimation of loss in the presence of Kerr nonlinearity

We address the characterization of dissipative bosonic channels and show that estimation of the loss rate by Gaussian probes (coherent or squeezed) is improved in the presence of Kerr nonlinearity. In particular, enhancement of precision may be substantial for short interaction time, i.e. for media of moderate size, e.g. biological samples. We analyze in detail the behaviour of the quantum Fisher information (QFI), and determine the values of nonlinearity maximizing the QFI as a function of the interaction time and of the parameters of the input signal. We also discuss the precision achievable by photon counting and quadrature measurement and present additional results for truncated, few-photon, probe signals. Finally, we discuss the origin of the precision enhancement, showing that it cannot be linked quantitatively to the non-Gaussianity of the interacting probe signal.

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