Narrow Results

We employ techniques from quantum estimation theory (QET) to estimate the Lorentz violation parameters in the (1+3)-dimensional flat spacetime. We obtain and discuss the expression of the quantum Fisher information (QFI) in terms of the Lorentz violation parameter ${\sigma }_0$ and the momentum $k$ of the created particles. We show that the maximum QFI is achieved for a specific momentum $k_{\mathrm{\text{max}}}$. We also find that the optimal precision of estimation of the Lorentz violation parameter is obtained near the Planck scale.

The fundamental quantum information processing task of estimating the phase of a qubit is considered. Following quantum measurement, the estimation efficiency is evaluated by the classical Fisher information which determines the best performance limiting any estimator and achievable by the maximum likelihood estimator. The estimation process is analyzed in the presence of decoherence represented by essential quantum noises that can affect the qubit and belonging to the broad class of unital quantum noises. Such a class especially contains the bit-flip, the phase-flip, the depolarizing noises, or the whole family of Pauli noises. As the level of noise is increased, we report the possibility of non-standard behaviors where the estimation efficiency does not necessarily deteriorate uniformly, but can experience non-monotonic variations. Regimes are found where higher noise levels prove more favorable to estimation. Such behaviors are related to stochastic resonance effects in signal estimation, shown here feasible for the first time with unital quantum noises. The results provide enhanced appreciation of quantum noise or decoherence, manifesting that it is not always detrimental for quantum information processing.

This paper further explores the recent scheme of switched quantum channels with indefinite causal order applied to the reference metrological task of quantum phase estimation in the presence of noise. We especially extend the explorations, previously reported with depolarizing noise and thermal noise, to the class of Pauli noises, important to the qubit and not previously addressed. Nonstandard capabilities, not accessible with standard quantum phase estimation, are exhibited and analyzed, with significant properties that are specific to the Pauli noises, while other properties are found in common with the depolarizing noise or the thermal noise. The results show that the presence and the type of quantum noise are both crucial to the determination of the nonstandard capabilities from the switched channel with indefinite causal order, with a constructive action of noise reminiscent of stochastic resonance phenomena. The study contributes to a more comprehensive and systematic characterization of the roles and specificities of quantum noise in the operation of the novel devices of switched quantum channels with indefinite causal order.

The maximum likelihood strategy for the estimation of group parameters allows one to derive in a general fashion optimal measurements, optimal signal states, and their relations with other information theoretical quantities. These results provide deep insight into the general structure underlying optimal quantum estimation strategies. The entanglement between representation spaces and multiplicity spaces of the group action appears to be the unique kind of entanglement which is really useful for the optimal estimation of group parameters.

Several quantities of interest in quantum information, including entanglement and purity, are nonlinear functions of the density matrix and cannot, even in principle, correspond to proper quantum observables. Any method aimed to determine the value of these quantities should resort to indirect measurements and thus corresponds to a parameter estimation problem whose solution, i.e. the determination of the most precise estimator, unavoidably involves an optimization procedure. We review local quantum estimation theory and present explicit formulas for the symmetric logarithmic derivative and the quantum Fisher information of relevant families of quantum states. Estimability of a parameter is defined in terms of the quantum signal-to-noise ratio and the number of measurements needed to achieve a given relative error. The connections between the optmization procedure and the geometry of quantum statistical models are discussed. Our analysis allows to quantify quantum noise in the measurements of non observable quantities and provides a tools for the characterization of signals and devices in quantum technology.

We address the estimation of phase-shifts for qubit systems in the presence of noise. Different sources of noise are considered including bit flip, bit-phase flip and phase flip. We derive the ultimate quantum limits to precision of estimation by evaluating the analytical expressions of the quantum Fisher information and assess performances of feasible measurements by evaluating the Fisher information for realistic spin-like measurements. We also propose an experimental scheme to test our results.

We address the estimation of purity for a quantum oscillator initially prepared in a displaced thermal state and probed by a suitably prepared qubit interacting with the oscillator via Jaynes–Cummings Hamiltonian without the rotating-wave approximation. We evaluate the quantum Fisher information (QFI) and show that optimal estimation of purity can be achieved by measuring the population of the qubit after a properly chosen interaction time. We also address the estimation of purity at fixed total energy and show that the corresponding precision is independent of the presence of a coherent amplitude.

We address potential deviations of radiation field from the bosonic behavior and employ local quantum estimation theory to evaluate the ultimate bounds to precision in the estimation of these deviations using quantum-limited measurements on optical signals. We consider different classes of boson deformations and found that intensity measurement on coherent or thermal states would be suitable for their detection making, at least in principle, tests of boson deformation feasible with current quantum optical technology. On the other hand, we found that the quantum signal-to-noise ratio (QSNR) is vanishing with the deformation itself for all the considered classes of deformations and probe signals, thus making any estimation procedure of photon deformation inherently inefficient. A partial way out is provided by the polynomial dependence of the QSNR on the average number of photons, which suggests that, in principle, it would be possible to detect deformation by intensity measurements on high-energy thermal states.

For parameter estimation from an $N$-component composite quantum system, it is known that a separable preparation leads to a mean-squared estimation error scaling as $1/N$ while an entangled preparation can in some conditions afford a smaller error with $1/N^2$ scaling. This quantum superefficiency is however very fragile to noise or decoherence, and typically disappears with any small amount of random noise asymptotically at large $N$. To complement this asymptotic characterization, here we characterize how the estimation efficiency evolves as a function of the size $N$ of the entangled system and its degree of entanglement. We address a generic situation of qubit phase estimation, also meaningful for frequency estimation. Decoherence is represented by the broad class of noises commuting with the phase rotation, which includes depolarizing, phase-flip and thermal quantum noises. In these general conditions, explicit expressions are derived for the quantum Fisher information quantifying the ultimate achievable efficiency for estimation. We confront at any size $N$ the efficiency of the optimal separable preparation to that of an entangled preparation with arbitrary degree of entanglement. We exhibit the $1/N^2$ superefficiency with no noise, and prove its asymptotic disappearance at large $N$ for any nonvanishing noise configuration. For maximizing the estimation efficiency, we characterize the existence of an optimum $N_{\mathrm{\text{opt}}}$ of the size of the entangled system along with an optimal degree of entanglement. For nonunital noises, maximum efficiency is usually obtained at partial entanglement. Grouping the $N$ qubits into independent blocks formed of $N_{\mathrm{\text{opt}}}$ entangled qubits restores at large $N$ a nonvanishing efficiency that can improve over that of $N$ independent qubits optimally prepared. Also, one inactive qubit included in the entangled probe sometimes stands as the most efficient setting for estimation. The results further attest with new characterizations the subtlety of entanglement for quantum information in the presence of noise, showing that when entanglement is beneficial, maximum efficiency is not necessarily obtained by maximum entanglement but instead by a controlled degree and finite optimal amount of it.

We consider the problem of estimating the spatial separation between two mutually incoherent point light sources using the super-resolution imaging technique based on spatial mode demultiplexing (SPADE) with noisy detectors. We show that in the presence of noise, the resolution of the measurement is limited by the signal-to-noise ratio (SNR) and the minimum resolvable spatial separation has a characteristic dependence of $\sim {\mathrm{\text{SNR}}}^{-1∕2}$. Several detection techniques, including direct photon counting, as well as homodyne and heterodyne detection are considered.