arXiv subjects
Publications and source records attributed to Junde Wu.
In this paper, we introduce a mixed form of ambiguous and unambiguous quantum state discriminations, and show that the mixed form has higher success probability than the unambiguous quantum state discriminations.
In order to study quantum measurement theory, sequential product defined for any two quantum effects is introduced. Physically motivated conditions ask the sequential product to be continuous with respect to the strong operator topology. In this paper, we study the continuity problems of the sequential product with respect to the other important topologies, as norm topology, weak operator topology, order topology, interval topology, etc.
The ESR model has been recently proposed in several papers to offer a possible solution of the problems raising from the nonobjectivity of physical properties in quantum mechanics (QM) (mainly the objectification problem of the quantum theory of measurement). This solution is obtained by embodying the mathematical formalism of QM into a broader mathematical framework and reinterpreting quantum probabilities as conditional on detection rather than absolute. We provide a new and more general formulation of the ESR model and discuss time evolution according to it, pointing out in particular that both linear and nonlinear evolution may occur, depending on the physical environment.
In this paper, we characterize the saturation of four universal inequalities in quantum information theory, including a variant version of strong subadditivity inequality for von Neumann entropy, the coherent information inequality, the Holevo quantity and average entropy inequalities. These results shed new light on quantum information inequalities.
Fidelity is a fundamental and ubiquitous concept in quantum information theory. Fuchs-van de Graaf's inequalities deal with bounding fidelity from above and below. In this paper, we give a lower bound on the quantum fidelity between two states in terms of their trace-norm distance and their max-relative entropy.
We prove uncertainty relations that quantitatively express the impossibility of jointly sharp preparation of pre- and post-selected quantum states for measuring incompatible observables during the weak measurement. By defining a suitable operator whose average in the pre-selected quantum state gives the weak value, we show that one can have new uncertainty relations for variances of two such operators corresponding to two non-commuting observables. These generalize the recent stronger uncertainty relations that give non-trivial lower bounds for the sum of variances of two observables which fully capture the concept of incompatible observables. Furthermore, we show that weak values for two non-commuting projection operators obey a complementarity relation. Specifically, we show that for a pre-selected state if we measure a projector corresponding to an observable $A$ weakly followed by the strong measurement of another observable $B$ (for the post-selection) and, for the same pre-selected state we measure a projector corresponding to an observable $B$ weakly followed by the strong measurement of the observable $A$ (for the post-selection), then the product of these two weak values is always less than one. This shows that even though individually they are complex and can be large, their product is always bounded.
A series of detailed quantitative results is established for the family of demi-distributions which is a large extension of the family of usual distributions.
In quantum information and communication one looks for the non-classical features like interference and quantum correlations to harness the true power of composite systems. We show how the concept akin to interference is, in fact, intertwined in a quantitative manner to entanglement and quantum correlation. In particular, we prove that the difference in the squared visibility for a density operator before and after a complete measurement, averaged over all unitary evolutions, is directly related to the quantum correlation measure based on the measurement disturbance. For pure and mixed bipartite states the unitary average of the squared visibility is related to entanglement measure. This may constitute direct detection of entanglement and quantum correlations with quantum interference setups. Furthermore, we prove that for a fixed purity of the subsystem state, there is a complementarity relation between the linear entanglement of formation and the measurement disturbance. This brings out a quantitative difference between two kinds of quantum correlations.
We show that the weak value of any observable in pre- and post-selected states can be expressed as the sum of the average of the observable in the pre-selected state and an anomalous part. We argue that at a fundamental level the anomalous nature of the weak values arises due to the interference between the post-selected state and another quantum state which is orthogonal to the pre-selected state. This provides a necessary and sufficient condition for the anomalous nature of the weak value of a quantum observable. Furthermore, we prove that for two non-commuting observables the product of their anomalous parts cannot be arbitrarily large.
In this paper, a lower bound of quantum conditional mutual information is obtained by employing the Peierls-Bogoliubov inequality and Golden Thompson inequality. Comparison with the bounds obtained by other researchers indicates that our result is independent of any measurements. It may give some new insights over squashed entanglement and perturbations of Markov chain states.
Fidelity is a fundamental and ubiquitous concept in quantum information theory. Fuchs-van de Graaf's inequalities deal with bounding fidelity from above and below. In this paper, we give a lower bound on the quantum fidelity between two states in terms of their Bures distance.
In this Letter, two counterexamples show that the superadditivity inequality of relative entropy is not true even for the full-ranked quantum states. Thus, an inequality of quantum channels and complementary channels is not also true. Finally, a conjecture of weak superadditivity inequality is presented.
N-site-lattice Hamiltonians H are introduced and perceived as a set of systematic discrete approximants of a certain PT-symmetric square-well-potential model with the real spectrum and with a non-Hermiticity which is localized near the boundaries of the interval. Its strength is controlled by one, two or three parameters. The problem of the explicit construction of a nontrivial metric which makes the theory unitary is then addressed. It is proposed and demonstrated that due to the not too complicated tridiagonal-matrix form of our input Hamiltonians the computation of the metric is straightforward and that its matrix elements prove obtainable, non-numerically, in elementary polynomial forms.
Let $\cH_A\ot \cH_B$ be a bipartite system and $ρ_{AB}$ a quantum state on $\cH_A\ot \cH_B$, $ρ_A = \Ptr{B}{ρ_{AB}}$, $ρ_B = \Ptr{A}{ρ_{AB}}$. Then each quantum operation $Φ_B$ on the quantum system $\cH_B$ can induce a quantum ensemble $\set{(p_μ,ρ_{A,μ})}$ on quantum system $\cH_A$. In this paper, we show that the Holevo quantity $χ\set{(p_μ,ρ_{A,μ})}$ of the quantum ensemble $\set{(p_μ,ρ_{A,μ})}$ can be upper bounded by both subsystem entropies. By using the result, we answer partly a conjecture of Fannes, de Melo, Roga and Życzkowski.
In this paper, two conjectures which were proposed in [Phys. Rev. A \textbf{82}, 052122(2010)] on the correlations in a bipartite state $ρ^{AB}$ are studied. If the mutual information $I\Pa{ρ^{AB}}$ between two quantum systems $A$ and $B$ before any measurement is considered as the total amount of correlations in the state $ρ^{AB}$, then it can be separated into two parts: classical correlations and quantum correlations. The so-called classical correlations $C\Pa{ρ^{AB}}$ in the state $ρ^{AB}$, defined by the maximizing mutual information between two quantum systems $A$ and $B$ after von Neumann measurements on system $B$, we show that it is upper bounded by the von Neumann entropies of both subsystems $A$ and $B$, this answered the conjecture on the classical correlation. If the quantum correlations $Q\Pa{ρ^{AB}}$ in the state $ρ^{AB}$ is defined by $Q\Pa{ρ^{AB}}= I\Pa{ρ^{AB}} - C\Pa{ρ^{AB}}$, we show also that it is upper bounded by the von Neumann entropy of subsystem $B$. It is also obtained that $Q\Pa{ρ^{AB}}$ is upper bounded by the von Neumann entropy of subsystem $A$ for a class of states.
In this note, we survey some elementary theorems and proofs concerning dynamical matrices theory. Some mathematical concepts and results involved in quantum information theory are reviewed. A little new result on the matrix representation of quantum operation are obtained. And best separable approximation for quantum operations is presented.
In the paper, the dynamical additivity of bi-stochastic quantum operations is characterized and the strong dynamical additivity is obtained under some restrictions.
For a given quantum state $ρ$ and two quantum operations $Φ$ and $Ψ$, the information encoded in the quantum state $ρ$ is quantified by its von Neumann entropy $§(ρ)$. By the famous Choi-Jamiołkowski isomorphism, the quantum operation $Φ$ can be transformed into a bipartite state, the von Neumann entropy $§^{\mathrm{map}}(Φ)$ of the bipartite state describes the decoherence induced by $Φ$. In this Letter, we characterize not only the pairs $(Φ, ρ)$ which satisfy $§(Φ(ρ))=§(ρ)$, but also the pairs $(Φ, Ψ)$ which satisfy $§^{\mathrm{map}}(Φ\circΨ) = §^{\mathrm{map}}(Ψ)$.