Arbitrary Bipartite State Research Articles

Private quantum decoupling and secure disposal of information

Given a bipartite system, correlations between its subsystems can be understood as the information that each one carries about the other. In order to give a model-independent description of secure information disposal, we propose the paradigm of private quantum decoupling, corresponding to locally reducing correlations in a given bipartite quantum state without transferring them to the environment. In this framework, the concept of private local randomness naturally arises as a resource, and total correlations are divided into eliminable and ineliminable ones. We prove upper and lower bounds on the quantity of ineliminable correlations present in an arbitrary bipartite state, and show that, in tripartite pure states, ineliminable correlations satisfy a monogamy constraint, making apparent their quantum nature. A relation with entanglement theory is provided by showing that ineliminable correlations constitute an entanglement parameter. In the limit of infinitely many copies of the initial state provided, we compute the regularized ineliminable correlations to be measured by the coherent information, which is thus equipped with a new operational interpretation. In particular, our results imply that two subsystems can be privately decoupled if their joint state is separable.

All Entangled States are Useful for Channel Discrimination

We prove that every entangled state is useful as a resource for the problem of minimum-error channel discrimination. More specifically, given a single copy of an arbitrary bipartite entangled state, it holds that there is an instance of a quantum channel discrimination task for which this state allows for a correct discrimination with strictly higher probability than every separable state.

Economic and Deterministic Quantum Teleportation of Arbitrary Bipartite Pure and Mixed State with Shared Cluster Entanglement

We present a novel protocol for teleportation of arbitrary bipartite pure and mixed state with shared cluster entanglement in this paper. By employing Bell-state measurement on the teleported state and the shared cluster state twice, a sender could transmit the arbitrary bipartite state to a distant receiver. We show the good feature of the cluster state channel, with which it can realize the deterministic teleportation rather than probabilistic one. Moreover, since we require less particles to be shared and need no auxiliary qubit in our protocol, it is more efficient and applicable than the previous schemes.

Teleportation of Multi-ionic GHZ States and ArbitraryBipartite Ionic State via Linear Optics

We present a scheme for teleportation of multi-ionic GHZ statesand arbitrary bipartite ionic state only by single-qubit measurementsvia linear optical elements. In our scheme, we avoid the difficulty of jointmeasurement and synchronizing the arrival time of the two scatteredphotons, which are faced by previous schemes. So our scheme can be realizedeasily within current experimental technology.

Concurrence revisited

Concurrence is a widely used entanglement measure of bipartite mixed states. We propose to consider the concurrence as being defined by a quadratic form on the space of self-adjoint operators. The square root of this form determines the values of the concurrence on the pure states, while the values on the mixed states are obtained as the largest convex extension, the convex roof. This viewpoint admits a generalization. Namely, the space of self-adjoint operators and the convex cone of positive semidefinite operators contained therein can be replaced by an arbitrary real vector space containing a convex cone. Then the concurrence is determined on the extreme rays of the cone by the square root of a quadratic form, and on the rest of the cone by the convex roof. We compute this generalized concurrence in the case when the cone is a second order cone. This enables us to compute the concurrence of arbitrary bipartite mixed states of rank 2. As an application, we compute the concurrences of the density matrices of all graphs with two edges or with three edges forming a triangle. We also consider the problem of maximizing the concurrence on the set of mixed states having a fixed spectrum.

Swap action in a solid-state controllable anisotropic Heisenberg model

Correct swap action can be realized via the control of the anisotropic Heisenberg interaction in solid-state quantum systems. The conditions of performing a swap are derived by the dynamics of arbitrary bipartite pure state. It is found that swap errors can be eliminated in the presence of symmetric anisotropy. In realistic quantum computers with unavoidable fluctuations, the gate fidelity of swap action is estimated. The scheme of quantum computation via the anisotropic Heisenberg interaction is implemented in a one-dimensional quantum dots. The slanting and static magnetic field can be used to adjust the anisotropy.

Improving the teleportation of entangled coherent states

We consider the scheme proposed by Wang [Phys. Rev. A 64, 022302 (2001)] for teleporting bipartite entangled states using beam splitters and phase shifters. It is shown that the proposed scheme can be altered slightly so as to obtain an almost perfect teleportation for an appreciable mean number of photons. For mean number of photons equal to 2, the minimum of average fidelity which is the minimum of sum of the product of probability for occurrence of any case and the corresponding fidelity for an arbitrary bipartite entangled state is less than unity by a quantity of the order of ${10}^{\ensuremath{-}4}$.

Steering, Entanglement, Nonlocality, and the Einstein-Podolsky-Rosen Paradox

The concept of steering was introduced by Schrödinger in 1935 as a generalization of the Einstein-Podolsky-Rosen paradox for arbitrary pure bipartite entangled states and arbitrary measurements by one party. Until now, it has never been rigorously defined, so it has not been known (for example) what mixed states are steerable (that is, can be used to exhibit steering). We provide an operational definition, from which we prove (by considering Werner states and isotropic states) that steerable states are a strict subset of the entangled states, and a strict superset of the states that can exhibit Bell nonlocality. For arbitrary bipartite Gaussian states we derive a linear matrix inequality that decides the question of steerability via Gaussian measurements, and we relate this to the original Einstein-Podolsky-Rosen paradox.

Distinguishing bipartite states by local operations and classical communication

We present a general method for distinguishing bipartite states by local operations and classical communication. It unifies several available methods together. This method is applicable for arbitrary bipartite states, i.e., it works not only for entangled states but also for separable states. We also study the local distinguishability for maximally entangled states which are in an arbitrary basis.

Classical simulation of traceless binary observables on any bipartite quantum state

We present a protocol to simulate the quantum correlations of an arbitrary bipartite state, when the parties perform a measurement according to two traceless binary observables. We show that ${\mathrm{log}}_{2}(d)$ bits of classical communication is enough on average, where $d$ is the dimension of both systems. To obtain this result, we use the sampling approach for simulating the quantum correlations.

Macroscopic Entanglement by Entanglement Swapping

We present a scheme for entangling two micromechanical oscillators. The scheme exploits the quantum effects of radiation pressure and it is based on a novel application of entanglement swapping, where standard optical measurements are used to generate purely mechanical entanglement. The scheme is presented by first solving the general problem of entanglement swapping between arbitrary bipartite Gaussian states, for which simple input-output formulas are provided.

Rfunction related to entanglement of formation

By investigating the convex property of the function R, appeared in computing the entanglement of formation for isotropic states in Phys. Rev. Lett. 85, 2625 (2000), and a tight lower bound of entanglement of formation for arbitrary bipartite mixed states in Phys. Rev. Lett. 95, 210501 (2005), we show analytically that the very nice results in these papers are valid not only for dimensions 2 and 3 but any dimensions.

A note on equivalence of bipartite states under local unitary transformations

The equivalence of arbitrary dimensional bipartite states under local unitary transformations (LUT) is studied. A set of invariants and ancillary invariants under LUT is presented. We show that two states are equivalent under LUT if and only if they have the same values for all of these invariants.

Entanglement of Formation of Bipartite Quantum States

We give an explicit tight lower bound for the entanglement of formation for arbitrary bipartite mixed states by using the convex hull construction of a certain function. This is achieved by revealing a novel connection among the entanglement of formation, the well-known Peres-Horodecki, and realignment criteria. The bound gives a quite simple and efficiently computable way to evaluate quantitatively the degree of entanglement for any bipartite quantum state.

Robust semidefinite programming approach to the separability problem

We express the optimization of entanglement witnesses for arbitrary bipartite states in terms of a class of convex optimization problems known as robust semidefinite programs (RSDPs). We propose, using well known properties of RSDPs, several sufficient tests for separability of mixed states. Our results are then generalized to multipartite density operators.

Teleportation and entanglement distillation in the presence of correlation among bipartite mixed states

The teleportation channel associated with an arbitrary bipartite state denotes the map that represents the change suffered by a teleported state when the bipartite state is used instead of the ideal maximally entangled state for teleportation. This work presents and proves an explicit expression of the teleportation channel for teleportation using Weyl's projective unitary representation of $(Z/dZ{)}^{2n}$ for integers $d>~2,$ $n>~1,$ which has been known for $n=1.$ This formula allows any correlation among the n bipartite mixed states, and an application shows the existence of reliable schemes for distillation of entanglement from a sequence of mixed states with correlation.

Entanglement cost under positive-partial-transpose-preserving operations.

We study the entanglement cost under quantum operations preserving the positivity of the partial transpose (PPT operations). We demonstrate that this cost is directly related to the logarithmic negativity, thereby providing the operational interpretation for this entanglement measure. As examples we discuss general Werner states and arbitrary bipartite Gaussian states. Then we prove that for the antisymmetric Werner state PPT cost and PPT entanglement of distillation coincide. This is the first example of a truly mixed state for which entanglement manipulation is asymptotically reversible, which points towards a unique entanglement measure under PPT operations.