Xianqing Li-Jost

Entanglement of Formation for a Class of Quantum States

Abstract Entanglement of formation for a class of higher-dimensional quantum mixed states is studied in terms of a generalized formula of concurrence for N -dimensional quantum systems. As applications, the entanglement of formation for a class of 16×16 density matrices are calculated.

A class of special matrices and quantum entanglement

Abstract We present a kind of construction for a class of special matrices with at most two different eigenvalues, in terms of some interesting multiplicators which are very useful in calculating eigenvalue polynomials of these matrices. This class of matrices defines a special kind of quantum states — d-computable states. The entanglement of formation for a large class of quantum mixed states is explicitly presented.

A class of bound entangled states

We construct a set of PPT (positive partial transpose) states and show that these PPT states are not separable, thus present a class of bound entangled quantum states.

Identification of three-qubit entanglement

We present a way of identifying all kinds of entanglement for three-qubit pure states in terms of the expectation values of Pauli operators. The necessary and sufficient conditions to classify the fully separable, biseparable, and genuine entangled states are explicitly given. The approach can be generalized to multipartite high-dimensional cases. For three-qubit mixed states, we propose two kinds of inequalities in terms of the expectation values of complementary observables. One inequality has advantages in entanglement detection of the quantum state with positive partial transpositions, and the other is able to detect genuine entanglement. The results give an effective method for experimental entanglement identification.

Complete Entanglement Witness for Quantum Teleportation

We propose a set of linear quantum entanglement witnesses constituted by local quantum-mechanical observables with each two possible measurement outcomes. These witnesses detect all the entangled resources which give rise to a better fidelity than separable states in quantum teleportation and present both sufficient and necessary conditions in experimentally detecting the useful resources for quantum teleportation.

Weighted Uncertainty Relations.

Recently, Maccone and Pati have given two stronger uncertainty relations based on the sum of variances and one of them is nontrivial when the quantum state is not an eigenstate of the sum of the observables. We derive a family of weighted uncertainty relations to provide an optimal lower bound for all situations and remove the restriction on the quantum state. Generalization to multi-observable cases is also given and an optimal lower bound for the weighted sum of the variances is obtained in general quantum situation.

Time optimal quantum control of two-qubit systems †

We study the optimal quantum control of heteronuclear two-qubit systems described by a Hamiltonian containing both nonlocal internal drift and local control terms. We derive an explicit formula to compute the minimum time required to steer the system from an initial state to a specified final state. As applications the minimal time to implement Controlled-NOT gate, SWAP gate and Controlled-U gate is calculated in detail. The experimental realizations of these quantum gates are explicitly presented.

Local Unitary Equivalence of Arbitrary Dimensional Bipartite Quantum States

The nonlocal properties of arbitrary dimensional bipartite quantum systems are investigated. A complete set of invariants under local unitary transformations is presented. These invariants give rise to both sufficient and necessary conditions for the equivalence of quantum states under local unitary transformations: two density matrices are locally equivalent if and only if all these invariants have equal values.

Universal Inequalities for Eigenvalues of the Buckling Problem of Arbitrary Order

We investigate the eigenvalues of the buckling problem of arbitrary order on compact domains in Euclidean spaces and spheres. We obtain universal bounds for the kth eigenvalue in terms of the lower eigenvalues independently of the particular geometry of the domain.

Multi-observable Uncertainty Relations in Product Form of Variances.

We investigate the product form uncertainty relations of variances for n (n ≥ 3) quantum observables. In particular, tight uncertainty relations satisfied by three observables has been derived, which is shown to be better than the ones derived from the strengthened Heisenberg and the generalized Schrödinger uncertainty relations, and some existing uncertainty relation for three spin-half operators. Uncertainty relation of arbitrary number of observables is also derived. As an example, the uncertainty relation satisfied by the eight Gell-Mann matrices is presented.