Three-particle Entangled State Research Articles

Probabilistic teleportation of a non-symmetric three-particle state

This paper proposes a scheme for teleporting a kind of essential three-particle non-symmetric entangled state, which is much more valuable than a GHZ and W state for some applications in quantum information processing. In comparison with previous proposal of teleportation, the resources of entangled states as quantum channel and the number of classical messages required by our scheme can be cut down. Moreover, it is shown that there exists a class of transformations which ensure the success of this scheme, because the two-particle transformation performed by the receiver in the course of teleportation may be a generic two-particle operation instead of a control-NOT (CNOT) operation. In addition, all kinds of transformations performed by sender and receiver are given in detail.

Generation of the nonlocal quantum entanglement of three three-level particles by local operations

We propose a scheme to realize the nonlocal quantum entanglement of three three-level particles by using a three-particle entangled state of three levels as a quantum channel with the aid of some local unitary transformations. This scheme can be directly generalized to the nonlocal quantum entanglement of N three-level particles.

Creation of Multipartite Entanglement and EntanglementTransfer via Heisenberg Interaction

We discuss how to create multipartite entanglement. By coupling a newparticle with entangled particles via Heisenberg interaction between twoparticles, we can prepare three-particle entangled states. For somespecial coupling strength, entanglement transfer can be achieved fromentangled pair AB to particles A and C that never interact bycoupling particle C with particle B, which can be used to createentanglement between two separated particles.

Probabilistic teleportation of an arbitrary two-particle state by a partial three-particle entangled GHZ state and a two-particle entangled state

We propose a scheme to teleport an arbitrary unknown two-particle state by a non-maximally three-particle entangled Greenberger–Horne–Zeilinger (GHZ) state and a non-maximally two-particle entangled state from a sender to either one of two receivers. We probabilistically teleport the arbitrary unknown two-particle state by performing two Bell-state measurements on the sender's side, introducing two appropriate unitary transformations on the receiver's side conditioned on a Hadamard operation and a projection measurement on the other possible receiver's side.

Remote State Preparation of a Greenberger–Horne–Zeilinger Class State

In this paper, we propose a scheme for the remote preparation of athree-particle Greenberger–Horne–Zeilinger class state by a two-particleentangled state and a three-particle entangled state. It is shown that, bythis scheme, only two classical bits and one two-particle projectivemeasurement are enough for such preparation.

Probabilistic Teleportation of the Three-Particle EntangledState by the Partial Three-Particle Entangled State and theThree-Particle Entangled W State

We present a scheme to teleport an unknownthree-particle entangled state from a sender to either one of tworeceivers. The partial three-particle entangled state and thethree-particle entangled W state are considered as the quantumchannels. An unknown three-particle entangled state can be perfectlyteleported probabilistically by performing two generalized Bellmeasurements and the Hadamard operation at the sender's side andintroducing an appropriate unitary transformation in each receiver'slaboratory conditioned on the simple measurement outcome of the other.All kinds of unitary transformations are given in details. Thisscheme can be directly generalized to teleport an unknownthree-particle entangled state from a sender to any one of Nreceivers by the partial three-particle entangled state and the (N + 1)-particle entangled W state.

Teleportation of an arbitrary three-particle state

We propose two schemes for teleporting an arbitrary three-particle state. In the first scheme, a two-particle state and a three-particle entangled state (both non-maximally entangled states) are used as quantum channels, while in the second scheme, three non-maximally entangled particle pairs are employed as quantum channels. We show that teleportation can be successfully realized with certain probability if a receiver adopts some appropriate unitary transformations. Their success probabilities and the classical communication costs are different.

Faithful Telecloning with Multiparticle Entanglement

We study the 1→N faithful telecloning of two linear-independentstates of a one-qubit system. Based on the analysis of the probabilisticcloning machine, we construct a multiparticle entangled state, and present atelecloning scheme under local operations and classical communication(LOCC). The success probability is greater than half of the optimalprobability of the probabilistic cloning machine. Specifically, we show howto prepare the three-particle entangled state needed by 1→2telecloning under LOCC using the Greenberger-Horne-Zeilinger state asa resource. All the operations in 1→2 telecloningare within the reach of current technology.

Quantum Teleportation of a Three-Particle Entangled State

We present a scheme for teleporting a three-particle entangled state to threeremote particles. In this scheme, three pairs of pure nonmaximally entangledstates are considered as quantum channels. It is found that by means of optimaldiscrimination between two nonorthogonal quantum states, probabilisticteleportation of the three-particle entangled state can be achieved.

Sufficient conditions for three-particle entanglement and their tests in recent experiments

We point out a loophole problem in some recent experimental claims to produce three-particle entanglement. The problem consists in the question whether mixtures of two-particle entangled states might suffice to explain the experimental data. In an attempt to close this loophole, we review two sufficient conditions that distinguish between N-particle states in which all N particles are entangled to each other and states in which only M particles are entangled (with M<N). It is shown that three recent experiments to obtain three-particle entangled states (Bouwmeester et al., Pan et al., and Rauschenbeutel et al.) do not meet these conditions. We conclude that the question whether these experiments provide confirmation of three-particle entanglement remains unresolved. We also propose modifications of the experiments that would make such confirmation feasible.

Teleportation of a two-particle entangled state

A scheme for teleporting a two-particle entangled state via a three-particle entangled state is proposed. It is shown that the probability of successful teleportation is twice the modulus square of the smaller Schmidt coefficient of the entangled three-particle state.

Three-Particle Entangled States of Continuum Variables

We introduce the three-particle entangled state of continuum variables,which is a generalization of Greenberger-Horne-Zeilinger entangledstates composed of discrete states. The completeness relation and partlynon-orthonormal property of such states are proven. Their Schmidtdecomposition is manifestly shown and their generation is brieflydiscussed.

Manipulating quantum entanglement with atoms and photons in a cavity

After they have interacted, quantum particles generally behave as a single nonseparable entangled system. The concept of entanglement plays an essential role in quantum physics. We have performed entanglement experiments with Rydberg atoms and microwave photons in a cavity and tested quantum mechanics in situations of increasing complexity. Entanglement resulted either from a resonant exchange of energy between atoms and the cavity field or from dispersive energy shifts affecting atoms and photons when they were not resonant. With two entangled particles (two atoms or one atom and a photon), we have realized new versions of the Einstein-Podolsky-Rosen situation. The detection of one particle projected the other, at a distance, in a correlated state. This process could be viewed as an elementary measurement, one particle being a ``meter'' measuring the other. We have performed a ``quantum nondemolition'' measurement of a single photon, which we detected repeatedly without destroying it. Entanglement is also essential to understand decoherence, the process accounting for the classical appearance of the macroscopic world. A mesoscopic superposition of states (``Schr\odinger cat'') gets rapidly entangled with its environment, losing its quantum coherence. We have prepared a Schr\odinger cat made of a few photons and studied the dynamics of its decoherence, in an experiment which constitutes a glimpse at the quantum/classical boundary. We have also investigated entanglement as a resource for the processing of quantum information. By using quantum two-state systems (qubits) instead of classical bits of information, one can perform logical operations exploiting quantum interferences and taking advantage of the properties of entanglement. Manipulating as qubits atoms and photons in a cavity, we have operated a quantum gate and applied it to the generation of a complex three-particle entangled state. We finally discuss the perspectives opened by these experiments for further fundamental studies.

Entanglement-assisted local transformations between inequivalent classes of three-particle entangled states

We show that bipartite and tripartite entangled states cannot be used as catalysis states to enable local transformations inbetween inequivalent classes of three-particle entangled states which are non-interchangeable under local transformations. We find the optimal protocol for conversion of a certain family of the W-states and an EPR-pair into the GHZ-state.

Probabilistic Teleportation of the Three-Particle EntangledState via Entanglement Swapping

A scheme of teleportation of a three-particle entangled state viaentanglement swapping is proposed. It is shown that if a two-particleentangled state and a three-particle entangled state (both are not maximumentangled states) are used as quantum channels, probabilisticteleportation of the three-particle entangled state can be realized.

Generating three-particle entanglement states

We propose a scheme to generate three-particle entangled state from sources of nonmaximally entangled pure states.

Bit-flip-error rejection in optical quantum communication

An optical scheme for the error-free transfer of quantum information through a noisy quantum channel is proposed. The scheme is inspired by quantum error-correction schemes, but it avoids the currently unfeasible requirement for a controlled-NOT operation between single photons. The quantum communication scheme presented here rejects bit-flip errors instead of correcting them and combines quantum-measurement properties of three-particle entangled states with properties of the quantum teleportation protocol.

Step-by-step engineered multiparticle entanglement

After quantum particles have interacted, they generally remain in an entangled state and are correlated at a distance by quantum-mechanical links that can be used to transmit and process information in nonclassical ways. This implies programmable sequences of operations to generate and analyze the entanglement of complex systems. We have demonstrated such a procedure for two atoms and a single-photon cavity mode, engineering and analyzing a three-particle entangled state by a succession of controlled steps that address the particles individually. This entangling procedure can, in principle, operate on larger numbers of particles, opening new perspectives for fundamental tests of quantum theory.

Two-particle entanglement as a property of three-particle entangled states

In a recent article [Phys. Rev. A 54, 1793 (1996)] Krenn and Zeilinger investigated the conditional two-particle correlations for the subensemble of data obtained by selecting the results of the spin measurements by two observers 1 and 2 with respect to the result found in the corresponding measurement by a third observer. In this paper we write out explicitly the condition required in order for the selected results of observers 1 and 2 to violate Bell's inequality for general measurement directions. It is shown that there are infinitely many sets of directions giving the maximum level of violation. Further, we extend the analysis by the authors to the class of triorthogonal states |Psi> = c_1 |z_1>|z_2>|z_3> + c_2 |-z_1>|-z_2>|-z_3>. It is found that a maximal violation of Bell's inequality occurs provided the corresponding three-particle state yields a direct (all or nothing) nonlocality contradiction.

Perfect correlations of three-particle entangled states in cavity QED.

Compared to two-particle states, entangled states of three or four particles can lead to a much stronger test of local realism than is possible with Bell inequalities. It is the purpose of this paper to mention an exactly soluble quantum model in which entanglement of atomic states with cavity photon states leads to a perfectly correlated three-particle state. We demonstrate how to realize this model atom-field system and to create and observe such states, in the context of cavity quantum electrodynamics.