Quantum Tomography
This is the draft version of a review paper which is going to appear in "Advances in Imaging and Electron Physics"
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arXiv subjects
Matteo G. A. Paris
Publications and source records attributed to Matteo G. A. Paris.
Evolution of twin-beam in active optical media
We study the evolution of twin-beam propagating inside active media that may be used to establish a continuous variable entangled channel between two distant users. In particular, we analyze how entanglement is degraded during propagation, and determine a threshold value for the interaction time, above which the state become separable, and thus useless for entanglement based manipulations. We explicitly calculate the fidelity for coherent state teleportation and show that it is larger than one half for the whole range of parameters preserving entanglemenent.
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Remote state preparation and teleportation in phase space
Continuous variable remote state preparation and teleportation are analyzed using Wigner functions in phase space. We suggest a remote squeezed state preparation scheme between two parties sharing an entangled twin beam, where homodyne detection on one beam is used as a conditional source of squeezing for the other beam. The scheme works also with noisy measurements, and provide squeezing if the homodyne quantum efficiency is larger than 50%. Phase space approach is shown to provide a convenient framework to describe teleportation as a generalized conditional measurement, and to evaluate relevant degrading effects, such the finite amount of entanglement, the losses along the line, and the nonunit quantum efficiency at the sender location.
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Teleportation improvement by inconclusive photon subtraction
Inconclusive photon subtraction (IPS) is a conditional measurement scheme to force nonlinear evolution of a given state. In IPS the input state is mixed with the vacuum in a beam splitter and then the reflected beam is revealed by ON/OFF photodetection. When the detector clicks we have the (inconclusive) photon subtracted state. We show that IPS on both channels of an entangled twin-beam of radiation improves the fidelity of coherent state teleportation if the energy of the incoming twin-beam is below a certain threshold, which depends on the beam splitter transmissivity and the quantum efficiency of photodetectors. We show that the energy threshold diverges when the transmissivity and the efficiency approach unit and compare our results with that of previous works on {\em conclusive} photon subtraction.
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Local observables for entanglement witnesses
We present an explicit construction of entanglement witnesses for depolarized states in arbitrary finite dimension. For infinite dimension we generalize the construction to twin-beams perturbed by Gaussian noises in the phase and in the amplitude of the field. We show that entanglement detection for all these families of states requires only three local measurements. The explicit form of the corresponding set of local observables (quorom) needed for entanglement witness is derived.
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Quantum state engineering assisted by entanglement
We suggest a general scheme for quantum state engineering based on conditional measurements carried out on entangled twin-beam of radiation. Realistic detection schemes such as {\sc on/off} photodetection, homodyne detection and joint measurement of two-mode quadratures are analyzed in details. Imperfections of the apparatuses, such as nonunit quantum efficiency and finite resolution, are taken into account. We show that conditional {\sc on/off} photodetection provides a reliable scheme to verify nonclassicality, whereas conditional homodyning represents a tunable and robust source of squeezed light. We also describe optical teleportation as a conditional measurement, and evaluate the degrading effects of finite amount of entanglement, decoherence due to losses, and nonunit quantum efficiency.
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Improved discrimination of unitaries by entangled probes
We consider the problem of discriminating among a set of unitaries by means of measurements performed on the state undergoing the transformation. We show that use of entangled probes improves the discrimination in the two following cases: i) for a set of unitaries that are the UIR of a group and, ii) for any pair of transformations provided that multiple uses of the channel are allowed.
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Optimized quantum nondemolition measurement of a field quadrature
We suggest an interferometric scheme assisted by squeezing and linear feedback to realize the whole class of field-quadrature quantum nondemolition measurements, from Von Neumann projective measurement to fully non-destructive non-informative one. In our setup, the signal under investigation is mixed with a squeezed probe in an interferometer and, at the output, one of the two modes is revealed through homodyne detection. The second beam is then amplitude-modulated according to the outcome of the measurement, and finally squeezed according to the transmittivity of the interferometer. Using strongly squeezed or anti-squeezed probes respectively, one achieves either a projective measurement, i.e. homodyne statistics arbitrarily close to the intrinsic quadrature distribution of the signal, and conditional outputs approaching the corresponding eigenstates, or fully non-destructive one, characterized by an almost uniform homodyne statistics, and by an output state arbitrarily close to the input signal. By varying the squeezing between these two extremes, or simply by tuning the internal phase-shift of the interferometer, the whole set of intermediate cases can also be obtained. In particular, an optimal quantum nondemolition measurement of quadrature can be achieved, which minimizes the information gain versus state disturbance trade-off.
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Quantum tomography as a tool for the characterization of optical devices
We describe a novel tool for the quantum characterization of optical devices. The experimental setup involves a stable reference state that undergoes an unknown quantum transformation and is then revealed by balanced homodyne detection. Through tomographic analysis on the homodyne data we are able to characterize the signal and to estimate parameters of the interaction, such as the loss of an optical component, or the gain of an amplifier. We present experimental results for coherent signals, with application to the estimation of losses introduced by simple optical components, and show how these results can be extended to the characterization of more general optical devices.
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Using entanglement improves precision of quantum measurements
We show how entanglement can be used to improve the estimation of an unknown transformation. Using entanglement is always of benefit, in improving either the precision or the stability of the measurement. Examples relevant for applications are illustrated, for either qubits and continuous variables
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Nearly ideal binary communication in squeezed channels
We analyze the effect of squeezing the channel in binary communication based on Gaussian states. We show that for coding on pure states, squeezing increases the detection probability at fixed size of the strategy, actually saturating the optimal bound already for moderate signal energy. Using Neyman-Pearson lemma for fuzzy hypothesis testing we are able to analyze also the case of mixed states, and to find the optimal amount of squeezing that can be effectively employed. It results that optimally squeezed channels are robust against signal-mixing, and largely improve the strategy power by comparison with coherent ones.
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Optimal quantum estimation of the coupling between two bosonic modes
We address the problem of the optimal quantum estimation of the coupling parameter of a bilinear interaction, such as the transmittivity of a beam splitter or the internal phase-shift of an interferometer. The optimal measurement scheme exhibits Heisenberg scaling of the measurement precision versus the total energy.
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A robust verification of the quantum nature of light
We present a conditional experiment involving a parametric amplifier and an avalanche photodetector to generate highly nonclassical states of the radiation field. The nonclassicality is robust against amplifier gain, detector efficiency and dark counts. At the output all the generalized Wigner functions have negative values, and this is exploited in order to reveal the nonclassicality through quantum homodyne tomography.
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Optical qubit using linear elements
A conditional scheme to prepare optical superposition of the vacuum and one-photon states using linear elements (beam splitters and phase-shifters) and avalanche photodetectors is suggested.
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Quorum of observables for universal quantum estimation
Any method for estimating the ensemble average of arbitrary operator (observables or not, including the density matrix) relates the quantity of interest to a complete set of observables, i.e. a quorum}. This corresponds to an expansion on an irreducible set of operators in the Liouville space. We give two general characterizations of these sets. All the known unbiased reconstruction techniques, i.e. ``quantum tomographies'', can be described in this framework. New operatorial resolutions are given that can be used to implement novel reconstruction schemes.
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Parameters estimation in quantum optics
We address several estimation problems in quantum optics by means of the maximum-likelihood principle. We consider Gaussian state estimation and the determination of the coupling parameters of quadratic Hamiltonians. Moreover, we analyze different schemes of phase-shift estimation. Finally, the absolute estimation of the quantum efficiency of both linear and avalanche photodetectors is studied. In all the considered applications, the Gaussian bound on statistical errors is attained with a few thousand data.
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Adaptive Quantum Homodyne Tomography
An adaptive optimization technique to improve precision of quantum homodyne tomography is presented. The method is based on the existence of so-called null functions, which have zero average for arbitrary state of radiation. Addition of null functions to the tomographic kernels does not affect their mean values, but changes statistical errors, which can then be reduced by an optimization method that "adapts" kernels to homodyne data. Applications to tomography of the density matrix and other relevant field-observables are studied in detail.
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Entanglement and visibility at the output of a Mach-Zehnder interferometer
We study the entanglement between the two beams exiting a Mach-Zehnder interferometer fed by a couple of squeezed-coherent states with arbitrary squeezing parameter. The quantum correlations at the output are function of the internal phase-shift of the interferometer, with the output state ranging from a totally disentangled state to a state whose degree of entanglement is an increasing function of the input squeezing parameter. A couple of squeezed vacuum at the input leads to maximum entangled state at the output. The fringes visibilities resulting from measuring the coincidence counting rate or the squared difference photocurrent are evaluated and compared each other. Homodyne-like detection turns out to be preferable in almost all situations, with the exception of the very low signals regime.
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