Maximal and total skew information for a two-qubit system using nonlinear interaction models

Maximal and total skew information is studied. For symmetric pure states of two-qubit, they are closely related to the linear entropy, the concurrence, and the spin squeezing parameter. For a two-qubit system implemented in three nonlinear interaction models with an external field, we give the exact state vectors and the expectation value （Sz） at any time t. Based on （Sz）2, we give the maximal and the total skew information and a condition in which the maximal and the total skew information can reach 1 and 2, respectively.

Maximal and total skew information of three-qubit system obtained using nonlinear interaction models

Both the maximal and the total skew information have been studied. For a three-qubit system implemented in three nonlinear interaction models, we give the exact state vector at any time t. Beused on this, we give the maximal and the total skew information. It is found that they have the same form and their evolution periods are dependent on the energy difference between the ground state and the second excited state in these models. The maximal skew information is always in the （Sx, Sv） plane. We give the condition for the occurrence of IGHZ}sy, in which they can reach the extreme values of 9/4 and 15/4, respectively. In three different decoherence channels, two kinds of information and the concurrence are calculated. We find that the phenomenon of the concurrence of sudden death occurs, but the above two kinds of information do not die suddenly. In the phase-damping channel, the two kinds of information will not be lost completely.

Tighter sum uncertainty relations via(α,β,γ)weighted Wigner–Yanase–Dyson skew information

We establish tighter uncertainty relations for arbitrary finite observables via(α,β,γ)weighted Wigner–Yanase–Dyson((α,β,γ)WWYD)skew information.The results are also applicable to the(α,γ)weighted Wigner–Yanase–Dyson((α,γ)WWYD)skew information and the weighted Wigner–Yanase–Dyson(WWYD)skew information.We also present tighter lower bounds for quantum channels and unitary channels via(α,β,γ)modified weighted Wigner–Yanase–Dyson((α,β,γ)MWWYD)skew information.Detailed examples are provided to illustrate the tightness of our uncertainty relations.

Geometry of skew information-based quantum coherence

We study the skew information-based coherence of quantum states and derive explicit formulas for Werner states and isotropic states in a set of autotensors of mutually unbiased bases(MUBs).We also give surfaces of skew information-based coherence for Bell-diagonal states and a special class of X states in both computational basis and in MUBs.Moreover,we depict the surfaces of the skew information-based coherence for Bell-diagonal states under various types of local nondissipative quantum channels.The results show similar as well as different features compared with relative entropy of coherence and l1 norm of coherence.

Quantifying nonclassicality of multimode bosonic fields via skew information

We quantify the nonclassicality of multimode bosonic field states by adopting an information-theoretic approach involving the Wigner-Yanase skew information.The fundamental properties of the quantifier such as convexity,superadditivity,monotonicity,and conservation relations are revealed.The quantifier is illustrated by a variety of typical examples,and applications to the quantification of nonclassical correlations are discussed.Various extensions are indicated.

Skew Information for a Single Cooper Pair Box Interacting with a Single Cavity Field

The dynamics of the skew information (SI) is investigated for a single Cooper Pair Box (CPB) interacting with a single cavity field. By suitably choosing the system parameters and precisely controlling the dynamics, novel connection is found between the SI and entanglement generation. It is shown that SI can be increased and reach its maximum value either by increasing the number of photons inside the cavity or considering the far off-resonant case.The number of oscillations of SI is increased by decreasing this ratio between the Josephson junction capacity and the gate capacity. This leads to significant improvement of the travelling time between the maximum and minimum values.

Uncertainty relations based on Wigner-Yanase skew information

In this paper,we use certain norm inequalities to obtain new uncertain relations based on the Wigner-Yanase skew information.First for an arbitrary finite number of observables we derive an uncertainty relation outperforming previous lower bounds.We then propose new weighted uncertainty relations for two noncompatible observables.Two separable criteria via skew information are also obtained.

Uncertainty relation of successive measurements based on Wigner-Yanase skew information

Wigner-Yanase skew information could quantify the quantum uncertainty of the observables that are not commuting with a conserved quantity.We present the uncertainty principle for two successive projective measurements in terms of Wigner-Yanase skew information based on a single quantum system.It could capture the incompatibility of the observables,i.e.the lower bound can be nontrivial for the observables that are incompatible with the state of the quanaim system.Furthermore,the lower bound is also constrained by the quantum Fisher information.In addition,we find the complementarity relation between the uncertainties of the observable which operated on the quantum state and the other observable that performed on the post-measured quantum state and the uncertainties formed by the non-degenerate quantum observables performed on the quantum state,respectively.

Uncertainty relations based on skew information with quantum memory

Uncertainty principle is one of the most fascinating features of the quantum world. It asserts a fundamental limit on the precision with which certain pairs of physical properties of a particle, such as position and momentum, can not be si- multaneously known. The uncertainty principle has attracted considerable attention since the innovation of quantum me- chanics and has been investigated in terms of various types of uncertainty inequalities： in terms of the noise and dis- turbance, according to successive measurements, as informa- tional recourses in entropic terms, by means of majorization technique and based on sum of variances and standard devia- tions.

Fisher Information of Wavefunctions： Classical and Quantum

A parametric quantum mechanical wavefunction naturally induces parametric probability distributions by taking absolute square, and we can consider its classical Fisher information. On the other hand, it also induces parametric rank-one projections which may be viewed as density operators, and we can talk about its quantum Fisher information. Among many versions of quantum Fisher information, there are two prominent ones. The first, defined via a quantum score function, was introduced by Helstrom in 1967 and is well known. The second, defined via the square root of the density operator, has its origin in the skew information introduced by Wigner and Yanase in 1963 and remains relatively unnoticed. This study is devoted to investigating the relationships between the classical Fisher information and these two versions of quantum Fisher information for wavefunctions. It is shown that the two versions of quantum Fisher information differ by a factor 2 and that they dominate the classical Fisher information. The non-coincidence of these two versions of quantum Fisher information may be interpreted as a manifestation of quantum discord. We further calculate the difference between the Helstrom quantum Fisher information and the classical Fisher information, and show that it is precisely the instantaneous phase fluctuation of the wavefunctions.

Uncertainty Principles on Clifford Modules

In this paper,we derive the optimal Cauchy–Schwarz inequalities on a class of Hilbert and Krein modules over a Clifford algebra,which heavily depend on the Clifford algebraic structure.The obtained inequalities further lead to very general uncertainty inequalities on these modules.Some new phenomena arise,due to the non-commutative nature,the Clifford-valued inner products and the Krein geometry.Taking into account applications,special attention is given to the Dirac operator and the Howe dual pair Pin(m)×osp(1|2).Moreover,it is surprisingly to find that the recent highly nontrivial uncertainty relation for triple observables is indeed a direct consequence of our Cauchy–Schwarz inequality.This new observation leads to refined uncertainty relations in terms of the Wigner–Yanase–Dyson skew information for mixed states and other generalizations.These show that the obtained uncertainty inequalities on Clifford modules can be considered as new uncertainty relations for multiple observables.

Uncertainty Relations for Coherence

Quantum mechanical uncertainty relations are fundamental consequences of the incompatible nature of noncommuting observables.In terms of the coherence measure based on the Wigner-Yanase skew information,we establish several uncertainty relations for coherence with respect to von Neumann measurements,mutually unbiased bases(MUBs),and general symmetric informationally complete positive operator valued measurements(SIC-POVMs),respectively.Since coherence is intimately connected with quantum uncertainties,the obtained uncertainty relations are of intrinsically quantum nature,in contrast to the conventional uncertainty relations expressed in terms of variance,which are of hybrid nature(mixing both classical and quantum uncertainties).From a dual viewpoint,we also derive some uncertainty relations for coherence of quantum states with respect to a fixed measurement.In particular,it is shown that if the density operators representing the quantum states do not commute,then there is no measurement(reference basis)such that the coherence of these states can be simultaneously small.