Narrow Results

In this paper, we address quantum systems isospectral to the harmonic oscillator, as those found within the framework of supersymmetric quantum mechanics, as potential resources for continuous variable quantum information. These deformed oscillator potentials share the equally spaced energy levels of the shifted harmonic oscillator but differ significantly in that they are nonharmonic. Consequently, their ground states and thermal equilibrium states are no longer Gaussian and exhibit nonclassical properties. We quantify their non-Gaussianity and evaluate their nonclassicality using various measures, including quadrature squeezing, photon number squeezing, Wigner function negativity, and quadrature coherence scale. Additionally, we employ quantum estimation theory to identify optimal measurement strategies and establish ultimate precision bounds for inferring the deformation parameter. Our findings prove that quantum systems isospectral to the harmonic oscillator may represent promising platforms for quantum information with continuous variables. In turn, non-Gaussian and nonclassical stationary states may be obtained and these features persist at nonzero temperature.

We give a list of equivalent conditions for reversibility of the adjoint of a unital Schwarz map, with respect to a set of quantum states. A large class of such conditions is given by preservation of distinguishability measures: F-divergences, L₁-distance, quantum Chernoff and Hoeffding distances. Here we summarize and extend the known results. Moreover, we prove a number of conditions in terms of the properties of a quantum Radon–Nikodym derivative and factorization of states in the given set. Finally, we show that reversibility is equivalent to preservation of a large class of quantum Fisher informations and χ²-divergences.

This paper gives an overview about particular quasi-entropies, generalized quantum covariances, quantum Fisher informations, skew informations and their relations. The point is the dependence on operator monotone functions. It is proven that a skew information is the Hessian of a quasi-entropy. The skew information and some inequalities are extended to a von Neumann algebra setting.

In this contribution, we reformulated the bidirectional teleportation protocol suggested in Ref. 7, by means of Bloch vectors as well as the local operations are represented by using Pauli operators. Analytical and numerical calculations for the teleported state and Fisher information are introduced. It is shown that both quantities depend on the initial state settings of the teleported qubits and their triggers. The Fidelities and the Fisher information of the bidirectionally teleported states are maximized when the qubit and its trigger are polarized in the same direction. The minimum values are predicted if both initial qubits have different polarization or nonzero phase. The maximum values of the Fidelity and the quantum Fisher information are the same, but they are predicted at different polarization angles. We display that the multi-parameter form is much better than the single parameter form, where it satisfies the bounds of classical, entangled systems and the uncertainty principle.

We investigate spin squeezing (SS) and the quantum Fisher information (QFI) for the Jaynes–Cummings–Dicke (JCD) model in a two-component atomic Bose–Einstein condensate (BEC) inside an optical cavity. Analytical expressions for spin squeezing and the reciprocal of the quantum Fisher information per particle (RMQFI) are derived using the frozen spin approximation. It is shown that in the superradiant phase near the critical point, maximum squeezing and maximum quantum entanglement occur and thus the critical point emerges as a useful resource for precision measurements. In the presence of decoherence and particle loss, we show that gradually with time, even though the ability of squeezing and entanglement generation are weakened, yet significant amounts are still present which can be relevant to quantum information processing and precision spectroscopy.

The Quantum Fisher information (QFI) of a two charged qubits system that interacts locally with a dephasing channel is quantified with respect to the charged qubits’ and the channel’s parameters. The behavior of Fisher information displays different phenomena as; the sudden changes (increasing/decreasing); the gradual decay and freezing of the QFI. It is shown that the QFI of the dephasing parameter decays gradually and vanishes completely as one increases the initial energies of the qubits and their mutual energy. The possibility of estimating the charged qubits’ energies may be maximized at smaller values of the initial dephasing’s parameter. The estimation degree of the mutual information reaches its upper bounds by increasing the initial energies. It is depicted that, by controlling the qubits’ and the channel’s parameters, the QFI may be frozen. We expect that this result may be interesting in the context of quantum encoding and quantum cryptography.

We explore the changes of Quantum Fisher information (QFI) for an uniformly accelerating atom coupling to fluctuating massless scalar field with a perfectly reflecting boundary. We first deduce the master equation that the system obeys. For the unbounded case, the vacuum fluctuation and Unruh thermal bath can rapidly degrade the QFI. However, with a boundary, the degradation, preservation, fluctuation and enhancement of QFI are dependent on the evolution time, boundary and acceleration. In addition, the existing boundary can effectively shield QFI from the influence of the vacuum fluctuation and Unruh thermal effect. Especially, the QFI seems to be unaffected by the vacuum fluctuation and acceleration when the atom is very close to the boundary. The efficient control of the boundary and acceleration can provide the feasible scheme of improving the parameter estimation precision.

We study the quantum Fisher information (QFI) of a one-dimensional anisotropic XY chain in a transverse field with three-spin interaction. It is shown that the QFI, computed at a finite temperature, can be used to estimate the critical point (CP) of the quantum phase transition (QPT) at zero temperature. The accuracy of the obtained result depends on both the anisotropy parameter of the chain and the local observable used in the computation of QFI.

Temperature as an environmental parameter influences the evolution of an open quantum system. In detail, temperature lies in Lindblad operator of quantum master equation that the evolution of an open quantum system follows. Hence, one can implement a temperature estimation of thermal baths through a measurement of quantum Fisher information about temperature brought from quantum states. Such a method by calculating quantum Fisher information about a parameter to estimate its value avoids measuring the parameter directly and it does not change the value of the parameter due to making measurements. In this paper, we consider a model consisting of a XXZ spin-$\frac{1}{2}$ chain coupled locally to independent thermal baths with different temperature. Based on the model, we investigate optimal temperature estimation for thermal baths with respect to an open quantum system subjected to non-steady states. We first study optimal probe time for temperature estimation in the case of non-steady states and find that the optimal time shows different features for different types of system variables. It proves that in a certain duration there exists a tradeoff between the trial times and the attaining amount of Fisher information in each trial. In addition, we pay attention to an issue on optimal probe states. We demonstrate that in many cases the optimal states are not always the maximally entangled states and even maybe the separable states, which is related with the measuring time, system couplings.

The influence of time dependence on the model which consists of two qubits interacting with a two-mode electromagnetic field of the parametric amplifier type is investigated. The analytical solution of the wave function is obtained. The quantum Fisher information, entanglement and population inversion for a time-dependent system are analyzed. The photon statistics of a single-mode are quantified by the evolution of the Mandel parameter. Our results showed that there exists a positive relationship between the time-dependent parameter and entanglement. In other words, the time-dependent parameter due to the degree of entanglement is increased. Also, the quantum quantifier is strongly affected by the time-dependent coupling parameter in the absence and presence of the detuning parameter. This enables new parameters to control the degree of entanglement and quantum Fisher information, especially in quantum communication.

We address the quantum estimation of parameters encoded into the initial state of two modes of a Dirac field described by relatively accelerated parties. By using the quantum Fisher information (QFI), we investigate how the weak measurements performed before and after the accelerating observer, affect the optimal estimation of information encoded into the weight and phase parameters of the initial state shared between the parties. Studying the QFI, associated with weight parameter $𝜗$, we find that the acceleration at which the optimal estimation occurs may be controlled by weak measurements. Moreover, it is shown that the post-measurement plays the role of a quantum key for manifestation of the Unruh effect. On the other hand, investigating the phase estimation optimization and assuming that there is no control over the initial state, we show that the weak measurements may be utilized to match the optimal $𝜗$ to its predetermined value. Moreover, in addition to determination of a lower bound on the QFI with the local quantum uncertainty (LQU), we unveil an important upper bound on the precision of phase estimation in our relativistic scenario, given by the maximal steered coherence (MSC). We also obtain a compact expression of the MSC for general X states.

This paper attempts to give an overview about sufficiency in the setting of quantum statistics. The basic concepts are treated in parallel to the measure theoretic case. It turns out that several classical examples and results have a noncommutative analogue. Some of the results are presented without proof (but with exact references) and the presentation is intended to be self-contained. The main examples discussed in the paper are related to the Weyl algebra and to the exponential family of states. The characterization of sufficiency in terms of quantum Fisher information is a new result.

Motivated by the direct approach to quantum extensions of Fisher information in Chen and Luo [Front. Math. China2 (2007) 359], we introduce a further generalized version of Wigner–Yanase–Dyson information, and investigate its fundamental properties including positivity, convexity and super-additivity, etc. As an application, we present a generalized uncertainty relation.

The classical communication capacities of quantum Pauli channels with memory (correlation) are known to exhibit a transition effect. We revisit this phenomenon from the standpoint of the functionally analogous task of Pauli channel correlation identification. We treat the complete class of Pauli channels with correlation and determine the maximum quantum Fisher information achievable both with pure separable channel probe states and with maximally entangled bipartite probe states. A comparison of these Fisher informations reveals four distinct classes of Pauli channels and shows that only those channels that exceed a certain parametric threshold exhibit a transition effect. For those Pauli channels that exhibit this effect, the threshold at which it occurs has a simple analytic expression.

A generalization of the classical covariance for quantum mechanical observables has previously been presented by Gibilisco et al. Gibilisco and Isola has proved that the usual quantum covariance gives the sharpest inequalities for the determinants of covariance matrices. We introduce a new generalization of the classical covariance which gives better inequalities than the classical one, furthermore it has a direct geometric interpretation.

We address nearly pure quantum statistical models, i.e. situations where the information about a parameter is encoded in pure states weakly perturbed by the mixing with a parameter independent state, mimicking a weak source of noise. We show that the symmetric logarithmic derivative is left unchanged, and find an approximate analytic expression for the quantum Fisher information (QFI) which provides bounds on how much a weak source of noise may degrade the QFI.

Protecting the accelerated information coherence and suppressing of its decay due to the acceleration is achieved by using different noisy channels. The behavior of three different types of information; Fisher, nonlocal and local information of qubit–qutrit system is discussed. It is shown that, the estimation rate of the acceleration parameter is maximized if both subsystems are accelerated and interacted locally with their noise channels. However, if the largest subsystem is accelerated, then the estimation rate is minimized. The rate of change of the nonlocal information depends on which subsystem is accelerated. The results display that the local information is almost unaltered during the acceleration process, that is, the information is frozen. We show that the phase-flip channel represents the weak channel, where its suppressing of the decay due to the acceleration is smaller than the dephasing and depolarize of channels.

In this paper, we address the adiabatic technique for quantum estimation of the azimuthal orientation of a magnetic field. Exactly solving a model consisting of a two-qubit system, where one of which is driven by a static magnetic field while the other is coupled with the magnetic field rotating adiabatically, we obtain the analytical expression of the quantum Fisher information (QFI). We investigate how the two-qubit system can be used to probe the azimuthal direction of the field and analyze the roles of the intensities of the magnetic fields, Dzyaloshinskii–Moriya (DM) interaction, spin–spin coupling coefficient, and the polar orientation of the rotating field on the precision of the estimation. In particular, it is illustrated that the QFI trapping or saturation may occur if the qubit is subjected to a strong rotating field. Moreover, we discuss how the azimuthal direction of the rotating field can be estimated using only the qubit not affected by that field and investigate the conditions under which this strategy is more efficient than use of the qubit locally interacting with the adiabatically rotating field. Interestingly, in the one-qubit scenario, it was found that when the rotating field is weak, the best estimation is achieved by subjecting the probe to a static magnetic field.