Arbitrary Mixed States Research Articles

Robust multipartite thermal entanglement

Recently, Mintert et al (MKB) (2005 Phys. Rev. Lett. 95 260502) proposed generalizations of the Wootters concurrence for multipartite quantum systems, which can be evaluated efficiently for arbitrary mixed states. In this paper, we study in detail the origin of the robustness of multipartite thermal entanglement in N-qubit XY models with N = 2, 4 and 6 using the MKB concurrences. For N = 2, we establish the principle for the occurrence of robust bipartite thermal entanglement (Kamta and Starace 2002 Phys. Rev. Lett. 88 107901). We show explicitly that similar robust multipartite thermal entanglement can be found in the N = 4 case, and how this can be explained employing the same principle. It is then deduced that the six-qubit XY model also possesses robust multipartite thermal entanglement like the N = 2 case. More generally, our work spells out the characteristic properties for a given realistic model to have robust multipartite thermal entanglement like that in the two-qubit XY model.

Probabilistic Teleportation via Entanglement

With an arbitrary bi-particle entangled mixed state which is shared by Alice (the sender) and Bob (the receiver) acted as a quantum channel, at first, a teleportation protocol that Alice successfully transmits an unknown mixed state to Bob based on a positive operator-valued measurement (POVM) is presented. The upper bound of probability to teleport successfully an unknown mixed state is then investigated, and conclude that it completely depends on the entanglement degree of the bi-particle entangled mixed state as a resource.

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.

Navigation between quantum states by quantum mirrors

We introduce a technique that allows one to connect any two arbitrary (pure or mixed) superposition states of an $N$-state quantum system. The proposed solution to this inverse quantum mechanical problem is analytical, exact, and very compact. The technique uses standard and generalized quantum Householder reflections (QHRs), which require external pulses of precise areas and frequencies. We show that any two pure states can be linked by just a single generalized QHR. The transfer between any two mixed states with the same dynamic invariants (e.g., the same density matrix eigenvalues) requires in general $N$ QHRs. Moreover, we propose recipes for synthesis of arbitrary preselected mixed states using a combination of QHRs and incoherent processes (pure dephasing or spontaneous emission).

Teleportation with a mixed state of four qubits and the generalized singlet fraction

Recently, an explicit protocol ${\cal E}_0$ for faithfully teleporting arbitrary two-qubit states using genuine four-qubit entangled states was presented by us [Phys. Rev. Lett. {\bf 96}, 060502 (2006)]. Here, we show that ${\cal E}_0$ with an arbitrary four-qubit mixed state resource $\Xi$ is equivalent to a generalized depolarizing bichannel with probabilities given by the maximally entangled components of the resource. These are defined in terms of our four-qubit entangled states. We define the generalized singlet fraction ${\cal G}[\Xi]$, and illustrate its physical significance with several examples. We argue that in order to teleport arbitrary two-qubit states with average fidelity better than is classically possible, we have to demand that ${\cal G}[\Xi] > 1/2$. In addition, we conjecture that when ${\cal G}[\Xi] < 1/4$ then no entanglement can be teleported. It is shown that to determine the usefulness of $\Xi$ for ${\cal E}_0$, it is necessary to analyze ${\cal G}[\Xi]$.

State reconstruction of a qutrit by a minimal set of discrete measurements

We propose a simple and practical method for measuring the parameters of a fully or partially coherent superposition state of a qutrit quantum system. The method is based on the coupling of the qutrit to an excited state by two polarized laser fields and measurement of the fluorescence or ionization signal from the excited state for a discrete set of laser ellipticities and phases. We show that nine independent signals suffice to determine the parameters of an arbitrary unknown mixed qutrit state.

Dephasing representation of quantum fidelity for general pure and mixed states

A general semiclassical expression for quantum fidelity (Loschmidt echo) of arbitrary pure and mixed states is derived. It expresses fidelity as an interference sum of dephasing trajectories weighed by the Wigner function of the initial state, and does not require that the initial state be localized in position or momentum. This general dephasing representation is special in that, counterintuitively, all of fidelity decay is due to dephasing and none is due to the decay of classical overlaps. Surprising accuracy of the approximation is justified by invoking the shadowing theorem: twice--both for physical perturbations and for numerical errors. Beyond justifying the approximation, the shadowing theorem makes the dephasing representation practical: without shadowing it would be impossible to find numerically the precise trajectories needed in a semiclassical approximation. It is shown how the general expression reduces to the previously known special forms for localized states. The superiority of the general over the specialized forms is explained and supported by numerical tests for wave packets, nonlocal pure states, and for simple and random mixed states. The tests are done in nonuniversal regimes in mixed phase space where detailed features of fidelity are important. Although semiclassically motivated, the present approach is valid for abstract systems with a finite Hilbert basis provided that the discrete Wigner transform is used. This makes the method applicable, via a phase-space approach, to problems of quantum computation.

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.

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.

A Simple Scheme to Entangle Distant Qubits from a Mixed State via an Entanglement Mediator

A simple scheme to prepare an entanglement between two separated qubits from a given mixed state is proposed. A single qubit (entanglement mediator) is repeatedly made to interact locally and consecutively with the two qubits through rotating-wave couplings and is then measured. It is shown that we need to repeat this kind of process only three times to establish a maximally entangled state directly from an arbitrary initial mixed state, with no need to prepare the state of the qubits in advance or to rearrange the setup step by step. Furthermore, the maximum yield realizable with this scheme is compatible with the maximum entanglement, provided that the coupling constants are properly tuned.

Quantum information transfer from one system to another one

The topics of the paper are: a) Anti-linear maps governing EPR tasks in the absence of distinguished reference bases. b) Imperfect quantum teleportation and its composition rule. c) Quantum teleportation by distributed measurements. d) Remarks on EPR with an arbitrary mixed state, and triggered by a Luders measurement.

Optimal unambiguous filtering of a quantum state: An instance in mixed state discrimination

Deterministic discrimination of nonorthogonal states is forbidden by quantum measurement theory. However, if we do not want to succeed all the time, i.e., allow for inconclusive outcomes to occur, then unambiguous discrimination becomes possible with a certain probability of success. A variant of the problem is set discrimination: the states are grouped in sets and we want to determine to which particular set a given pure input state belongs. We consider here the simplest case, termed quantum state filtering, when the $N$ given nonorthogonal states ${\ensuremath{\mid}{\ensuremath{\psi}}_{1}⟩,\dots{},\ensuremath{\mid}{\ensuremath{\psi}}_{N}⟩}$ are divided into two sets and the first set consists of one state only while the second consists of all of the remaining states. We present the derivation of the optimal measurement strategy, in terms of a generalized measurement (positive-operator-valued measure), to distinguish $\ensuremath{\mid}{\ensuremath{\psi}}_{1}⟩$ from the set ${\ensuremath{\mid}{\ensuremath{\psi}}_{2}⟩,\dots{},\ensuremath{\mid}{\ensuremath{\psi}}_{N}⟩}$ and the corresponding optimal success and failure probabilities. The results, but not the complete derivation, were presented previously [Phys. Rev. Lett. 90, 25901 (2003)] as the emphasis there was on appplication of the results to probabilistic quantum algorithms. We also show that the problem is equivalent to the discrimination of a pure state and an arbitrary mixed state.

Synthesizing arbitrary two-photon polarization mixed states

Two methods for creating arbitrary two-photon polarization pure states are introduced. Based on these, four schemes for creating two-photon polarization mixed states are proposed and analyzed. The first two schemes can synthesize completely arbitrary two-qubit mixed states, i.e., control all 15 free parameters: Scheme I requires several sets of crystals, while Scheme II requires only a single set, but relies on decohering the pump beam. Additionally, we describe two further schemes which are much easier to implement. Although the total capability of these is still being studied, we show that they can synthesize all two-qubit Werner states, maximally entangled mixed states, Collins-Gisin states, and arbitrary Bell-diagonal states.

Superselection Sectors, Pure States, Bose and Fermi Distributions by Completely Positive Quantum-Motions

The connection of the operators V, building up the Kossakowski-Lindblad generator, with the asymptotic states of the corresponding completely positive quantum-maps is discussed. Maps leading to decoherence are constructed, the importance of zero-modes in the absolute value [Formula: see text] of V for the generation of pure states from arbitrary mixed states is illustrated. The universal rôle of equipartite states appears when unitary V are chosen. The 'damped oscillator model' is generalized to yield Bose and Fermi distributions as asymptotic states for systems described by a Hamiltonian and other constants of motion. Calculations are performed in finite dimensional Hilbert spaces.

An Efficient Scheme to Entangle Distant Qubits from an Arbitrary Mixed State(Quantum Field Theories : Fundamental Problems and Applications)

An Efficient Scheme to Entangle Distant Qubits from an Arbitrary Mixed State(Quantum Field Theories : Fundamental Problems and Applications)

Local invariants for multi-partite entangled states allowing for a simple entanglement criterion

We present local invariants of multi-partite pure or mixed states, which can be easily calculated and have a straight-forward physical meaning. As an application, we derive a new entanglement criterion for arbitrary mixed states of $n$ parties. The new criterion is weaker than the partial transposition criterion but offers advantages for the study of multipartite systems. A straightforward generalization of these invariants allows for the construction of a complete set of observable polynomial invariants.

Preparation of polarization-entangled mixed states of two photons

We propose a scheme for preparing arbitrary two-photons polarization-entangled mixed states via controlled location decoherence. The scheme uses only linear optical devices and single-mode optical fibers, and may be feasible in experiment within current optical technology.

Lower bounds on the entanglement of formation for general Gaussian states

We derive two lower bounds on entanglement of formation for arbitrary mixed Gaussian states by two distinct methods. To achieve the first one we use a local measurement procedure that symmetrizes a general Gaussian state and the fact that entanglement cannot increase under local operations and classical communications. The second one is obtained via a generalization to mixed states of an interesting result already known for pure states, which says that squeezed states are those that, for a fixed amount of entanglement, maximize Einstein-Podolsky-Rosen-like correlations.

Characterizing entanglement with global and marginal entropic measures

We qualify the entanglement of arbitrary mixed states of bipartite quantum systems by comparing global and marginal mixednesses quantified by different entropic measures. For systems of two qubits we discriminate the class of maximally entangled states with fixed marginal mixednesses, and determine an analytical upper bound relating the entanglement of formation to the marginal linear entropies. This result partially generalizes to mixed states the quantification of entanglement with marginal mixednesses holding for pure states. We identify a class of entangled states that, for fixed marginals, are globally more mixed than product states when measured by the linear entropy. Such states cannot be discriminated by the majorization criterion.

Quantum cloning of mixed states in symmetric subspaces

Quantum cloning machine for arbitrary mixed states in symmetric subspace is proposed. This quantum cloning machine can be used to copy part of the output state of another quantum cloning machine and is useful in quantum computation and quantum information. The shrinking factor of this quantum cloning achieves the well-known upper bound. When the input is identical pure states, two different fidelities of this cloning machine are optimal.