arXiv subjects

Matteo G. A. Paris

Publications and source records attributed to Matteo G. A. Paris.

At least 235 records · Page 13Linked to original sources

arXiv2012

About the probability distribution of a quantity with given mean and variance

Supplement 1 to GUM (GUM-S1) recommends the use of maximum entropy principle (MaxEnt) in determining the probability distribution of a quantity having specified properties, e.g., specified central moments. When we only know the mean value and the variance of a variable, GUM-S1 prescribes a Gaussian probability distribution for that variable. When further information is available, in the form of a finite interval in which the variable is known to lie, we indicate how the distribution for the variable in this case can be obtained. A Gaussian distribution should only be used in this case when the standard deviation is small compared to the range of variation (the length of the interval). In general, when the interval is finite, the parameters of the distribution should be evaluated numerically, as suggested by I. Lira, Metrologia, 46 L27 (2009). Here we note that the knowledge of the range of variation is equivalent to a bias of the distribution toward a flat distribution in that range, and the principle of minimum Kullback entropy (mKE) should be used in the derivation of the probability distribution rather than the MaxEnt, thus leading to an exponential distribution with non Gaussian features. Furthermore, up to evaluating the distribution negentropy, we quantify the deviation of mKE distributions from MaxEnt ones and, thus, we rigorously justify the use of GUM-S1 recommendation also if we have further information on the range of variation of a quantity, namely, provided that its standard uncertainty is sufficiently small compared to the range.

physics.data-an↗

arXiv2012

Optical interferometry in the presence of large phase diffusion

Phase diffusion represents a crucial obstacle towards the implementation of high precision interferometric measurements and phase shift based communication channels. Here we present a nearly optimal interferometric scheme based on homodyne detection and coherent signals for the detection of a phase shift in the presence of large phase diffusion. In our scheme the ultimate bound to interferometric sensitivity is achieved already for a small number of measurements, of the order of hundreds, without using nonclassical light.

quant-ph↗

arXiv2011

Reply on "Comment on 'Role of initial entanglement and non-Gaussianity in the decoherence of photon-number entangled states evolving in a noisy channel' "

In a recent work (Allegra et al, Phys. Rev. Lett. 105, 100503, 2010) we addressed the evolution of photon-number entangled states in noisy Gaussian channels. Upon exploiting several non equivalent separability criteria we found evidence that entanglement of Gaussian PNES survives longer, and thus we drew a conjecture about the generality of this result. In their Comment to our work, Lee et al. use an additional entanglement criterion (NDPT) which allows them to show some counterexamples to our conjecture, i.e., nonGaussian states whose entanglement survives longer. In this reply, we argue that although there are no flaws or central errors in our original Letter, the conjecture is not maintanable in a strict sense if one includes the NDPT criterion. Nevertheless, for the examples of non Gaussian states proposed in the Comment, which violate the conjecture, the residual entanglement is extremely low. Therefore it remains an open question whether these, as well as other kinds of states, could represent a useful resource in quantum communication protocols.

quant-ph↗

arXiv2011

Fidelity matters: the birth of entanglement in the interference of Gaussian states

We address the interaction of two Gaussian states interferring at a beam splitter and analyze the correlations exhibited by the resulting bipartite system. We demonstrate that nonlocal correlations (entanglement) arise if and only if the fidelity between the two input Gaussian states falls under a threshold value depending only on their purities and on the transmissivity of the beam splitter. Our result clarifies the role of squeezing as a prerequisite for entanglement and provide a tool to optimize the generation of entanglement by passive devices.

quant-ph↗

arXiv2011

Experimental investigation of initial system-environment correlations via trace distance evolution

The trace distance between two states of an open quantum system quantifies their distinguishability, and for a fixed environmental state can increase above its initial value only in the presence of initial system-environment correlations. We provide for the first time experimental evidence of such a behavior. In our all-optical apparatus we exploit spontaneous parametric down conversion as a source of polarization entangled states, and a spatial light modulator to introduce in a general fashion correlations between the polarization and the momentum degrees of freedom, which act as environment.

quant-ph↗

arXiv2011

Quantifying non-Markovianity of continuous variable Gaussian dynamical maps

We introduce a non-Markovianity measure for continuous variable open quantum systems based on the idea put forward in H.-P. Breuer et al., Phys. Rev. Lett.\textbf{103}, 210401 (2009), i.e., by quantifying the flow of information from the environment back to the open system. Instead of the trace distance we use here the fidelity to assess distinguishability of quantum states. We employ our measure to evaluate non-Markovianity of two paradigmatic Gaussian channels: the purely damping channel and the quantum Brownian motion channel with Ohmic environment. We consider different classes of Gaussian states and look for pairs of states maximizing the backflow of information. For coherent states we find simple analytical solutions, whereas for squeezed states we provide both exact numerical and approximate analytical solutions in the weak coupling limit.

quant-ph↗

arXiv2011

Qubit thermometry for micromechanical resonators

We address estimation of temperature for a micromechanical oscillator lying arbitrarily close to its quantum ground state. Motivated by recent experiments, we assume that the oscillator is coupled to a probe qubit via Jaynes-Cummings interaction and that the estimation of its effective temperature is achieved via quantum limited measurements on the qubit. We first consider the ideal unitary evolution in a noiseless environment and then take into account the noise due to non dissipative decoherence. We exploit local quantum estimation theory to assess and optimize the precision of estimation procedures based on the measurement of qubit population, and to compare their performances with the ultimate limit posed by quantum mechanics. In particular, we evaluate the Fisher information (FI) for population measurement, maximize its value over the possible qubit preparations and interaction times, and compare its behavior with that of the quantum Fisher information (QFI). We found that the FI for population measurement is equal to the QFI, i.e., population measurement is optimal, for a suitable initial preparation of the qubit and a predictable interaction time. The same configuration also corresponds to the maximum of the QFI itself. Our results indicate that the achievement of the ultimate bound to precision allowed by quantum mechanics is in the capabilities of the current technology.

quant-ph↗

arXiv2011

Finite-time quantum-to-classical transition for a Schroedinger-cat state

The transition from quantum to classical, in the case of a quantum harmonic oscillator, is typically identified with the transition from a quantum superposition of macroscopically distinguishable states, such as the Schrödinger cat state, into the corresponding statistical mixture. This transition is commonly characterized by the asymptotic loss of the interference term in the Wigner representation of the cat state. In this paper we show that the quantum to classical transition has different dynamical features depending on the measure for nonclassicality used. Measures based on an operatorial definition have well defined physical meaning and allow a deeper understanding of the quantum to classical transition. Our analysis shows that, for most nonclassicality measures, the Schrödinger cat dies after a finite time. Moreover, our results challenge the prevailing idea that more macroscopic states are more susceptible to decoherence in the sense that the transition from quantum to classical occurs faster. Since nonclassicality is prerequisite for entanglement generation our results also bridge the gap between decoherence, which appears to be only asymptotic, and entanglement, which may show a sudden death. In fact, whereas the loss of coherences still remains asymptotic, we have shown that the transition from quantum to classical can indeed occur at a finite time.

quant-ph↗

arXiv2011

Optimal detection of losses by thermal probes

We consider the discrimination of lossy bosonic channels and focus to the case when one of the values for the loss parameter is zero, i.e., we address the detection of a possible loss against the alternative hypothesis of an ideal lossless channel. This discrimination is performed by inputting one-mode or two-mode squeezed thermal states with fixed total energy. By optimizing over this class of states, we find that the optimal inputs are pure, thus corresponding to single- and two-mode squeezed vacuum states. In particular, we show that for any value of the damping rate smaller than a critical value there is a threshold on the energy that makes the two-mode squeezed vacuum state more convenient than the corresponding single-mode state, whereas for damping larger than this critical value two-mode squeezed vacua are always better. We then consider the discrimination in realistic conditions, where it is unlikely to have pure squeezing. Thus by fixing both input energy and squeezing, we show that two-mode squeezed thermal states are always better than their single- mode counterpart when all the thermal photons are directed into the dissipative channel. Besides, this result also holds approximately for unbalanced distribution of the thermal photons. Finally, we also investigate the role of correlations in the improvement of detection. For fixed input squeezing (single-mode or two-mode), we find that the reduction of the quantum Chernoff bound is a monotone function of the two-mode entanglement as well as the quantum mutual information and the quantum discord. We thus verify that employing squeezing in the form of correlations (quantum or classical) is always a resource for loss detection whenever squeezed thermal states are taken as input.

quant-ph↗

arXiv2011

Two proposals for testing quantum contextuality of continuous-variable states

We investigate the violation of non-contextuality by a class of continuous variable states, including variations of entangled coherent states (ECS's) and a two-mode continuous superposition of coherent states. We generalise the Kochen-Specker (KS) inequality discussed in A. Cabello, Phys. Rev. Lett. {\bf 101}, 210401 (2008) by using effective bidimensional observables implemented through physical operations acting on continuous variable states, in a way similar to an approach to the falsification of Bell-CHSH inequalities put forward recently. We test for state-independent violation of KS inequalities under variable degrees of state entanglement and mixedness. We then demonstrate theoretically the violation of a KS inequality for any two-mode state by using pseudo-spin observables and a generalized quasi-probability function.

quant-ph↗

arXiv2011

Balancing efficiencies by squeezing in realistic eight-port homodyne detection

We address measurements of covariant phase observables (CPOs) by means of realistic eight-port homodyne detectors. We do not assume equal quantum efficiencies for the four photodetectors and investigate the conditions under which the measurement of a CPO may be achieved. We show that balancing the efficiencies using an additional beam splitter allows us to achieve a CPO at the price of reducing the overall effective efficiency, and prove that it is never a smearing of the ideal CPO achievable with unit quantum efficiency. An alternative strategy based on employing a squeezed vacuum as a parameter field is also suggested, which allows one to increase the overall efficiency in comparison to the passive case using only a moderate amount of squeezing. Both methods are suitable for implementantion with current technology.

quant-ph↗

arXiv2011

Geometry of perturbed Gaussian states and quantum estimation

We address the nonGaussianity (nG) of states obtained by weakly perturbing a Gaussian state and investigate the relationships with quantum estimation. For classical perturbations, i.e. perturbations to eigenvalues, we found that nG of the perturbed state may be written as the quantum Fisher information (QFI) distance minus a term depending on the infinitesimal energy change, i.e. it provides a lower bound to statistical distinguishability. Upon moving on isoenergetic surfaces in a neighbourhood of a Gaussian state, nG thus coincides with a proper distance in the Hilbert space and exactly quantifies the statistical distinguishability of the perturbations. On the other hand, for perturbations leaving the covariance matrix unperturbed we show that nG provides an upper bound to the QFI. Our results show that the geometry of nonGaussian states in the neighbourhood of a Gaussian state is definitely not trivial and cannot be subsumed by a differential structure. Nevertheless, the analysis of perturbations to a Gaussian state reveals that nG may be a resource for quantum estimation. The nG of specific families of perturbed Gaussian states is analyzed in some details with the aim of finding the maximally non Gaussian state obtainable from a given Gaussian one.

quant-ph↗

arXiv2011

Optical phase estimation in the presence of phase-diffusion

The measurement problem for the optical phase has been traditionally attacked for noiseless schemes or in the presence of amplitude or detection noise. Here we address estimation of phase in the presence of phase diffusion and evaluate the ultimate quantum limits to precision for phase-shifted Gaussian states. We look for the optimal detection scheme and derive approximate scaling laws for the quantum Fisher information and the optimal squeezing fraction in terms of the overall total energy and the amount of noise. We also found that homodyne detection is a nearly optimal detection scheme in the limit of very small and large noise.

quant-ph↗

arXiv2010

Optimal unambiguous comparison of two unknown squeezed vacua

We propose a scheme for unambiguous state comparison (USC) of two unknown squeezed vacuum states of an electromagnetic field. Our setup is based on linear optical elements and photon-number detectors, and achieves optimal USC in an ideal case of unit quantum efficiency. In realistic conditions, i.e., for non-unit quantum efficiency of photodetectors, we evaluate the probability of getting an ambiguous result as well as the reliability of the scheme, thus showing its robustness in comparison to previous proposals.

quant-ph↗

arXiv2010

Quantifying non-Gaussianity for quantum information

We address the quantification of non-Gaussianity of states and operations in continuous-variable systems and its use in quantum information. We start by illustrating in details the properties and the relationships of two recently proposed measures of non-Gaussianity based on the Hilbert-Schmidt (HS) distance and the quantum relative entropy (QRE) between the state under examination and a reference Gaussian state. We then evaluate the non-Gaussianities of several families of non-Gaussian quantum states and show that the two measures have the same basic properties and also share the same qualitative behaviour on most of the examples taken into account. However, we also show that they introduce a different relation of order, i.e. they are not strictly monotone each other. We exploit the non-Gaussianity measures for states in order to introduce a measure of non-Gaussianity for quantum operations, to assess Gaussification and de-Gaussification protocols, and to investigate in details the role played by non-Gaussianity in entanglement distillation protocols. Besides, we exploit the QRE-based non-Gaussianity measure to provide new insight on the extremality of Gaussian states for some entropic quantities such as conditional entropy, mutual information and the Holevo bound. We also deal with parameter estimation and present a theorem connecting the QRE nonG to the quantum Fisher information. Finally, since evaluation of the QRE nonG measure requires the knowledge of the full density matrix, we derive some {\em experimentally friendly} lower bounds to nonG for some class of states and by considering the possibility to perform on the states only certain efficient or inefficient measurements.

quant-ph↗

arXiv2010

Non-Gaussianity of quantum states: an experimental test on single-photon added coherent states

Non Gaussian states and processes are useful resources in quantum information with continuous variables. An experimentally accessible criterion has been proposed to measure the degree of non Gaussianity of quantum states, based on the conditional entropy of the state with a Gaussian reference. Here we adopt such criterion to characterise an important class of non classical states, single-photon added coherent states. Our studies demonstrate the reliability and sensitivity of this measure, and use it to quantify how detrimental is the role of experimental imperfections in our realisation.

quant-ph↗

arXiv2010

Programmable entanglement oscillations in a non Markovian channel

We suggest and demonstrate an all-optical experimental setup to observe and engineer entanglement oscillations of a pair of polarization qubits in a non-Markovian channel. We generate entangled photon pairs by spontaneous parametric downconversion (SPDC), and then insert a programmable spatial light modulator in order to impose a polarization dependent phase-shift on the spatial domain of the SPDC output and to create an effective non-Markovian environment. Modulation of the enviroment spectrum is obtained by inserting a spatial grating on the signal arm. In our experiment, programmable oscillations of entanglement are achieved, with the maximally revived state that violates Bell's inequality by 17 standard deviations.

quant-ph↗

arXiv2010

The role of initial entanglement and nonGaussianity in the decoherence of photon number entangled states evolving in a noisy channel

We address the degradation of continuous variable (CV) entanglement in a noisy channel focusing on the set of photon-number entangled states. We exploit several separability criteria and compare the resulting separation times with the value of non-Gaussianity at any time, thus showing that in the low-temperature regime: i) non-Gaussianity is a bound for the relative entropy of entanglement and ii) Simon' criterion provides a reliable estimate of the separation time also for nonGaussian states. We provide several evidences supporting the conjecture that Gaussian entanglement is the most robust against noise, i.e. it survives longer than nonGaussian one, and that this may be a general feature for CV systems in Markovian channels.

quant-ph↗