Arbitrary Pure State Research Articles

Quantum entanglement in multiparticle systems of two-level atoms

We propose the necessary and sufficient condition for the presence of quantum entanglement in arbitrary symmetric pure states of two-level atomic systems. We introduce a parameter to quantify quantum entanglement in such systems. We express the inherent quantum fluctuations of a composite system of two-level atoms as a sum of the quantum fluctuations of the individual constituent atoms and their correlation terms. This helps to separate out and study solely the quantum correlations among the atoms and obtain the criterion for the presence of entanglement in such multiatomic systems.

Selected topics in dynamics and control of open quantum systems

This work reviews several topics in the non-equilibrium dynamics and control of open quantum systems, including the dynamics of the system and the environment in the weak coupling and low density regimes, incoherent control, production of universal Kraus maps and engineering of arbitrary pure and mixed quantum states.

Remote state preparation of spatial qubits

We study the quantum communication protocol of remote state preparation (RSP) for pure states of qubits encoded in single photons transmitted through a double slit, the so-called spatial qubits. Two measurement strategies that one can adopt to remotely prepare the states are discussed. The first strategy is the well-known spatial postselection, where a single-pixel detector measures the transverse position of the photon between the focal and the image plane of a lens. The second strategy, proposed by ourselves, is a generalized measurement divided into two steps: the implementation of a two-outcome positive operator-valued measurement (POVM) followed by the spatial postselection at the focal plane of the lens by a two-pixel detector in each output of the POVM. In both cases we analyze the effects of the finite spatial resolution of the detectors over three figures of merit of the protocol, namely, the probability of preparation, the fidelity, and purity of the remotely prepared states. It is shown that our strategy improves these figures compared with spatial postselection, at the expense of increasing the classical communication cost as well as the required experimental resources. In addition, we present a modified version of our strategy for RSP of spatial qudits which is able to prepare arbitrary pure states, unlike spatial postselection alone. We expect that our study may also be extended for RSP of the angular spectrum of a single-photon field as an alternative for quantum teleportation which requires very inefficient nonlinear interactions.

Observables can be tailored to change the entanglement of any pure state

We show that, for a finite-dimensional Hilbert space, there exist observables that induce a tensor product structure such that the entanglement properties of any pure state can be tailored. In particular, we provide an explicit, finite method for constructing observables in an unstructured $d$-dimensional system so that an arbitrary known pure state has any Schmidt decomposition with respect to an induced bipartite tensor product structure. In effect, this article demonstrates that, in a finite-dimensional Hilbert space, entanglement properties can always be shifted from the state to the observables and all pure states are equivalent as entanglement resources in the ideal case of complete control of observables.

AN EFFICIENT SEPARABILITY CRITERION FOR n-PARTITE ARBITRARILY DIMENSIONAL QUANTUM STATES

In this paper, we obtain an efficient separability criterion for bipartite quantum pure state systems, which is based on the two-order minors of the coefficient matrix corresponding to quantum state. Then, we generalize this criterion to multipartite arbitrarily dimensional pure states. Our criterion is directly built upon coefficient matrices, but not density matrices or observables, so it has the advantage of being computed easily. Indeed, to judge separability for an arbitrary n-partite pure state in a d-dimensional Hilbert space, it only needs at most O(d) times operations of multiplication and comparison. Our criterion can be extended to mixed states. Compared with Yu's criteria, our methods are faster, and can be applied to any quantum state.

Nonequilibrium cluster perturbation theory

The cluster perturbation theory (CPT) is one of the simplest but systematic quantum cluster approaches to lattice models of strongly correlated electrons with local interactions. By treating the inter-cluster potential, in addition to the interactions, as a perturbation, it is shown that the CPT can be reformulated as an all-order re-summation of diagrams within standard weak-coupling perturbation theory where vertex corrections are neglected. This reformulation is shown to allow for a straightforward generalization of the CPT to the general non-equilibrium case using contour-ordered Green's functions. Solving the resulting generalized CPT equation on the discretized Keldysh-Matsubara time contour, the transient dynamics of an essentially arbitrary initial pure or mixed state can be traced. In this way, the time-dependent expectation values of one-particle observables can be obtained within an approximation that neglects spatial correlations beyond the extension of the reference cluster. The necessary computational effort is very moderate. A detailed discussion and simple test calculations are presented to demonstrate the strengths and the shortcomings of the proposed approach. The non-equilibrium CPT is systematic and is controlled in principle by the inverse cluster size. It interpolates between the non-interacting and the atomic or decoupled-cluster limit which are recovered exactly and is found to predict the correct dynamics at very short times in a general non-trivial case. The effects of initial-state correlations on the subsequent dynamics and the necessity to extend the Keldysh contour by the imaginary Matsubara branch are analyzed carefully and demonstrated numerically. It is furthermore shown that the approach can describe the dissipation of spin and charge to an uncorrelated bath with an essentially arbitrary number of degrees of freedom.

Faithful teleportation with arbitrary pure or mixed resource states

We study faithful teleportation systematically with arbitrary entangled states as resources. The necessary conditions of mixed states to complete perfect teleportation are proved. Based on these results, the necessary and sufficient conditions of faithful teleportation of an unknown state |ϕ⟩ in with an entangled resource ρ in and are derived. It is shown that for ρ in , ρ must be a maximally entangled state, while for ρ in , ρ must be a pure maximally entangled state. Moreover, we show that the sender's measurements must be all projectors of maximally entangled pure states. The relations between the entanglement of the formation of the resource states and faithful teleportation are also discussed.

Joint remote state preparation of arbitrary two- and three-qubit states

We present a scheme for joint remote preparation of an arbitrary two-qubit pure state in a probabilistic manner from a spatially separated multi-sender to one receiver; the scheme is then extended to the arbitrary three-qubit case. We show that by adding some classical communication and local operations, the success probability of preparation can be increased to four times for two-qubit states and eight times for three-qubit states, and can reach one under certain conditions.

Entanglement Dynamics of Arbitrary Two-Qubit Pure States under Amplitude and Phase Damping Channels

Analytic results are presented for the entanglement evolution for arbitrary two-qubit pure state under amplitude damping and particularly phase damping channel. The disentanglement time and the relationship between it and the form of initial state are given explicitly. The lower bounds of disentanglement time are obtained and shown to be the monotone functions of initial concurrence.

Transfer from Arbitrary Pure State to Target Mixed State for Quantum Systems

AbstractConsidering two-level quantum systems, this paper proposes a control strategy that drives an arbitrary pure state to target mixed state via three-step controls. The first step is the preparation of eigenstate: the state of system controlled is driven to eigenstate from an arbitrary pure state. The second one is to drive the eigenstate prepared to the mixed state in which not all of the off-diagonal elements in the density matrices are zeros. In this step, one needs to use an auxiliary system and achieves the transfer through the interaction between controlled system and auxiliary system. If the target state is the mixed state in which all of the off-diagonal elements in the density matrices are zeros, then one needs to perform the third step: to drive the mixed state obtained in the second step to the target mixed state. Numerical simulation experiments and results analysis are given. The control strategy proposed in this paper is useful in the application of quantum computation.

A generalized tripartite scheme for splitting an arbitrary 2-qubit state with three 2-qubit partially entangled states and the Kraus measurement

We put forward a generalized tripartite scheme for splitting an arbitrary 2-qubit pure state with three 2-qubit non-maximally entangled states as quantum channels. The scheme for the first time incorporates the Kraus measurement into quantum information splitting scheme. In contrast to the similar scheme using the same quantum channels and the ancilla-entangled measurement, our scheme is superior in terms of operation and complexity, success probability, resource consumption and efficiency.

REMOTE PREPARATION OF AN ARBITRARY TWO-PARTICLE PURE STATE VIA NONMAXIMALLY ENTANGLED STATES AND POSITIVE OPERATOR-VALUED MEASUREMENT

A scheme for remotely preparing an arbitrary two-particle pure state is proposed by employing bipartite nonmaximally entangled states as quantum channels. During the preparation, two auxiliary particles and an optimal positive operator-valued measurement are introduced. The preparation of two-particle pure states can be remotely realized with certain success probability (SP). And the SP of our scheme is exactly worked out. It turns out that the SP depends inherently on the quantum channels employed beforehand. Furthermore, we find that, as far as two special ensembles of two-particle states are concerned, i.e. real and equatorial-like, the SP can be enhanced to quadruple.

Invariance of the bit error rate in the ancilla-assisted homodyne detection

We investigated the minimum achievable bit error rate of discriminating binary coherent states by homodyne measurements with the help of arbitrary ancilla states coupled via beam splitters. We took into account arbitrary pure ancillary states those were updated in real-time by those partial measurements and classical feedforward operations where the partial measurements were made by homodyne detections with a common fixed phase. It was shown that the minimum bit error rate of the system was invariant under these operations. We also discussed how generalize the homodyne detection beyond the scheme which made the bit error rate invariant.

Effects of impurity on fidelity of quantum state transfer via spin channels

By adopting the concept of fidelity, we investigated efficiency of quantum state transfer with the XX chain as the quantum channel. Different from the previous works, we concentrated on effects of spin and magnetic impurity on fidelity of quantum state transfer. Our results revealed that the spin impurity cannot prevent one from implementing perfect transfer of an arbitrary one-qubit pure state across the spin channel, however, the presence of magnetic impurity or both spin and magnetic impurities may destroy the otherwise perfect spin channels.

Local unitary equivalence and entanglement of multipartite pure states

The necessary and sufficient conditions for the equivalence of arbitrary n-qubit pure quantum states under Local Unitary (LU) operations derived in [B. Kraus Phys. Rev. Lett. 104, 020504 (2010)] are used to determine the different LU-equivalence classes of up to five-qubit states. Due to this classification new parameters characterizing multipartite entanglement are found and their physical interpretation is given. Moreover, the method is used to derive examples of two n-qubit states (with n>2 arbitrary) which have the properties that all the entropies of any subsystem coincide, however, the states are neither LU-equivalent nor can be mapped into each other by general local operations and classical communication.

QUANTUM STATE SPLITTING WITH YEO–CHUA GENUINE ENTANGLED STATE

Utilizing the four-qubit genuine entangled state presented by Yeo and Chua [Phys. Rev. Lett.96 (2006) 060502], we propose a tripartite quantum state splitting scheme for a sender to achieve the bipartition of his/her arbitrary two-qubit pure state between two sharers. During the scheme design, two novel and important ideas originated, respectively, from Phys. Rev. A74 (2006) 054303 and J. Phys. B41 (2008) 145506 are adopted to enhance the security and optimize resource consumption, operation complexity, and intrinsic efficiency. In the scheme, first the sender performs two Bell-state measurements and publishes the results. Afterwards, if and only if the two sharers cooperate together, they can perfectly restore the sender's quantum pure state by executing first a two-qubit collective unitary operation and then two single-qubit unitary operations.

Quantum Fisher Information in Two-Qubit Pure States

In terms of quantum Fisher information (QFI), a quantity χ 2 was introduced by Pezzé and Smerzi (Phys. Rev. Lett. 102 100401, 2009). They pointed out that the inequality χ 2<1 was a sufficient condition for multiparticle entanglement. For the two-qubit symmetric states, we found that the inequality χ 2<1 is a necessary and sufficient condition for entanglement and spin squeezing, and that χ 2 is equal to the second kind of spin squeezing parameter \(\xi _{2}^{2}\). For the two-qubit asymmetric states, it is only a sufficient condition. In order to make it a necessary and sufficient condition, we extend the concept of the QFI and χ 2, and generalize the relations among the entanglement measurement, the spin squeezing parameters and χ 2 in symmetric pure states to arbitrary pure states.

Residual effect on the robustness of multiqubit entanglement

We investigate the relation between the entanglement and the robustness of a multipartite system to a depolarization noise. We find that the robustness of a two-qubit system in an arbitrary pure state depends completely on its entanglement. However, this is not always true in a three-qubit system. There is a residual effect on the robustness of a three-qubit system in an arbitrary superposition of Greenberger-Horne-Zeilinger state and W state. Its entanglement determines the trend of its robustness. However, there is a splitting on its robustness under the same entanglement. Its robustness not only has the same periodicity as its three-tangle but also alters with its three-tangle synchronously. There is also a splitting on the robustness of an $n$-qubit ($n>3$) system although it is more complicated.

Controlled Teleportation of an Arbitrary Two-Particle Pure or Mixed State by Using a Five-Qubit Cluster State

A new scheme for controlled teleportation of an arbitrary two-particle pure or mixed state with the help of a five-qubit cluster state is proposed in detail. In this scheme, a five-particle cluster state is shared by a sender, a controller and a receiver. At first, the sender performs a four-qubit von-Neumann measurement on the qubits at hand, and the controller performs a Hadamard measurement on his qubit. Then the receiver can reconstruct the arbitrary two-particle pure or mixed state by performing some appropriate unitary transformations on his particles after he knows the measure results of the sender and the controller. This controlled teleportation scheme is deterministic.

Emergence of Canonical Ensembles from Pure Quantum States

We consider a system weakly interacting with a bath as a thermodynamic setting to establish a quantum foundation of statistical physics. It is shown that even if the composite system is initially in an arbitrary nonequilibrium pure quantum state, the unitary dynamics of a generic weak interaction almost always drives the subsystem into the canonical ensemble, in the usual sense of typicality. A crucial step is taken by assuming that the matrix elements of the interaction Hamiltonian have random phases, while their amplitudes are left unrestricted.