arXiv subjects

Marco G. Genoni

Publications and source records attributed to Marco G. Genoni.

87 records · Page 5Linked to original sources

arXiv2011

Optimal quantum estimation of the coupling constant of Jaynes-Cummings interaction

We address the estimation of the coupling constant of the Jaynes-Cummings Hamiltonian for a coupled qubit-oscillator system. We evaluate the quantum Fisher Information (QFI) for the system undergone the Jaynes-Cummings evolution, considering that the probe initial state is prepared in a Fock state for the oscillator and in a generic pure state for the qubit; we obtain that the QFI is exactly equal to the number of excitations present in the probe state. We then focus on the two subsystems, namely the qubit and the oscillator alone, deriving the two QFIs of the two reduced states, and comparing them with the previous result. Next we focus on feasible measurements on the system, and we find out that if population measurement on the qubit and Fock number measurement on the oscillator are performed together, the Cramer-Rao bound is saturated, that is the corresponding Fisher Information (FI) is always equal to the QFI. We compare also the performances of these measurements performed alone, that is when one of the two subsystem is ignored. We show that, when the qubit is prepared in either the ground or the excited state, the local measurements are still optimal.

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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.

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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.

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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.

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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.

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arXiv2009

State mapping and discontinuous entanglement transfer in a multipartite open system

We describe the transfer of quantum information and correlations from an entangled tripartite bosonic system to three separate qubits through their local environments also in the presence of various dissipative effects. Optimal state mapping and entanglement transfer are shown in the framework of optical cavity quantum electrodynamics involving qubit-like radiation states and two-level atoms via the mediation of cavity modes. For an input GHZ state mixed with white noise we show the occurrence of sudden death and birth of entanglement that is discontinuously exchanged among the tripartite subsystems.

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arXiv2009

Non-Gaussian states by conditional measurements

We address realistic schemes for the generation of non-Gaussian states of light based on conditional intensity measurements performed on correlated bipartite states. We consider both quantum and classically correlated states and different kind of detection, comparing the resulting non Gaussianity parameters upon varying the input energy and the detection efficiency. We find that quantum correlations generally lead to higher non Gaussianity, at least in the low energy regime. An experimental implementation feasible with current technology is also suggested.

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arXiv2009

Enhancement of parameter estimation by Kerr interaction

We address quantum estimation of displacement and squeezing parameters by the class of probes made of Gaussian states undergoing Kerr interaction. If we fix the overall energy available to the probe, without posing any constraint on the available Gaussian squeezing, then Gaussian squeezing represents the optimal resource for parameter estimation. On the other hand, in the more realistic case where the amount of Gaussian squeezing is fixed, or even absent, then Kerr interaction turns out to be useful to improve estimation, especially for probe states with large amplitude. Our results indicate that precision achievable with current technology Gaussian squeezing may be attained and surpassed for realistic values of the Kerr coupling.

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arXiv2009

Quantifying the non-Gaussian character of a quantum state by quantum relative entropy

We introduce a novel measure to quantify the non-Gaussian character of a quantum state: the quantum relative entropy between the state under examination and a reference Gaussian state. We analyze in details the properties of our measure and illustrate its relationships with relevant quantities in quantum information as the Holevo bound and the conditional entropy; in particular a necessary condition for the Gaussian character of a quantum channel is also derived. The evolution of non-Gaussianity (nonG) is analyzedfor quantum states undergoing conditional Gaussification towards twin-beam and de-Gaussification driven by Kerr interaction. Our analysis allows to assess nonG as a resource for quantum information and, in turn, to evaluate the performances of Gaussification and de-Gaussification protocols.

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arXiv2008

Non-Gaussianity and purity in finite dimension

We address truncated states of continuous variable systems and analyze their statistical properties numerically by generating random states in finite-dimensional Hilbert spaces. In particular, we focus to the distribution of purity and non-Gaussianity for dimension up to d=21. We found that both quantities are distributed around typical values with variances that decrease for increasing dimension. Approximate formulas for typical purity and non-Gaussianity as a function of the dimension are derived.

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arXiv2008

Optimal estimation of entanglement

Entanglement does not correspond to any observable and its evaluation always corresponds to an estimation procedure where the amount of entanglement is inferred from the measurements of one or more proper observables. Here we address optimal estimation of entanglement in the framework of local quantum estimation theory and derive the optimal observable in terms of the symmetric logarithmic derivative. We evaluate the quantum Fisher information and, in turn, the ultimate bound to precision for several families of bipartite states, either for qubits or continuous variable systems, and for different measures of entanglement. We found that for discrete variables, entanglement may be efficiently estimated when it is large, whereas the estimation of weakly entangled states is an inherently inefficient procedure. For continuous variable Gaussian systems the effectiveness of entanglement estimation strongly depends on the chosen entanglement measure. Our analysis makes an important point of principle and may be relevant in the design of quantum information protocols based on the entanglement content of quantum states.

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arXiv2007

A measure of the non-Gaussian character of a quantum state

We address the issue of quantifying the non-Gaussian character of a bosonic quantum state and introduce a non-Gaussianity measure based on the Hilbert-Schmidt distance between the state under examination and a reference Gaussian state. We analyze in details the properties of the proposed measure and exploit it to evaluate the non-Gaussianity of some relevant single- and multi-mode quantum states. The evolution of non-Gaussianity is also analyzed for quantum states undergoing the processes of Gaussification by loss and de-Gaussification by photon-subtraction. The suggested measure is easily computable for any state of a bosonic system and allows to define a corresponding measure for the non-Gaussian character of a quantum operation.

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arXiv2006

Information/disturbance trade-off in single and sequential measurements on a qudit signal

We address the trade-off between information gain and state disturbance in measurement performed on qudit systems and devise a class of optimal measurement schemes that saturate the ultimate bound imposed by quantum mechanics to estimation and transmission fidelities. The schemes are minimal, i.e. they involve a single additional probe qudit, and optimal, i.e. they provide the maximum amount of information compatible with a given level of disturbance. The performances of optimal single-user schemes in extracting information by sequential measurements in a N -user transmission line are also investigated, and the optimality is analyzed by explicit evaluation of fidelities. We found that the estimation fidelity does not depend on the number of users, neither for single-measure inference nor for collective one, whereas the transmission fidelity decreases with N . The resulting trade-off is no longer optimal and degrades with increasing N . We found that optimality can be restored by an effective preparation of the probe states and present explicitly calculations for the 2-user case.

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arXiv2006

Information/disturbance trade-off in continuous variable Gaussian systems

We address the information/disturbance trade-off for state-measurements on continuous variable Gaussian systems and suggest minimal schemes for implementations. In our schemes, the symbols from a given alphabet are encoded in a set of Gaussian signals which are coupled to a probe excited in a known state. After the interaction the probe is measured, in order to infer the transmitted state, while the conditional state of the signal is left for the subsequent user. The schemes are minimal, {\em i.e.} involve a single additional probe, and allow for the nondemolitive transmission of a continuous real alphabet over a quantum channel. The trade-off between information gain and state disturbance is quantified by fidelities and, after optimization with respect to the measurement, analyzed in terms of the energy carried by the signal and the probe. We found that transmission fidelity only depends on the energy of the signal and the probe, whereas estimation fidelity also depends on the alphabet size and the measurement gain. Increasing the probe energy does not necessarily lead to a better trade-off, the most relevant parameter being the ratio between the alphabet size and the signal width, which in turn determine the allocation of the signal energy.

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arXiv2005

Optimal quantum repeaters for qubits and qudits

A class of optimal quantum repeaters for qubits is suggested. The schemes are minimal, i.e. involve a single additional probe qubit, and optimal, i.e. provide the maximum information adding the minimum amount of noise. Information gain and state disturbance are quantified by fidelities which, for our schemes, saturate the ultimate bound imposed by quantum mechanics for randomly distributed signals. Special classes of signals are also investigated, in order to improve the information-disturbance trade-off. Extension to higher dimensional signals (qudits) is straightforward.

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