Arbitrary Three-qubit State Research Articles

Complete analysis for three-qubit mixed-state discrimination

In this article, by treating minimum error state discrimination as a complementarity problem, we obtain the geometric optimality conditions. These can be used as the necessary and sufficient conditions to determine whether every optimal measurement operator can be nonzero. Using these conditions and an inductive approach, we demonstrate a geometric method and the intrinsic polytope for $N$-qubit mixed-state discrimination. When the intrinsic polytope becomes a point, a line segment, or a triangle, the guessing probability, the necessary and sufficient condition for the exact solution, and the optimal measurement are analytically obtained. We apply this result to the problem of discrimination to arbitrary three-qubit mixed states with given a priori probabilities and obtain the complete analytic solution to the guessing probability and optimal measurement.

Quantum State Sharing of An Arbitrary Three-qubit State Using Two Four-qubit Cluster States

A scheme of quantum state sharing(QSTS) an arbitrary three-qubit state is presented using two particular four-qubit cluster state as the quantum channel. With four Bell pairs state measurements and the local unitary operation, any one of the two agents has the access to reconstruct the original if he/she collaborates with the other one. DOI: http://dx.doi.org/10.11591/telkomnika.v11i5.2566 Full Text: PDF

Probabilistic teleportation of an arbitrary three-qubit state by using three sets of W-class states

A new application of the W-class state is investigated for quantum state sharing (QSTS) of an arbitrary three-qubit state with a certain probability. We demonstrate that three sets of W-class states can be used to realize the QSTS of an arbitrary three-qubit state involving Bell-state measurement, single-qubit measurement and one high dimensional unitary operation. The performance demonstrates that our scheme can considerably reduce the difficulty of physical implementation.

Optimal class-specific witnesses for three-qubit entanglement from Greenberger-Horne-Zeilinger symmetry

Recently, a new type of symmetry for three-qubit quantum states was introduced, the so-called Greenberger-Horne-Zeilinger (GHZ) symmetry. It includes the operations which leave the three-qubit standard GHZ state unchanged. This symmetry is powerful as it yields families of mixed states that are, on the one hand, complex enough from the physics point of view and, on the other hand, simple enough mathematically so that their properties can be characterized analytically. We show that by using the properties of GHZ-symmetric states it is straightforward to derive optimal witnesses for detecting class-specific entanglement in arbitrary three-qubit states.

Quantum state sharing of an arbitrary three-qubit state by using three sets of W-class states

A new application of the W-class state for quantum state sharing (QSTS) of an arbitrary three-qubit state with a certain probability is presented explicitly. We show that three sets of W-class states can be used to realize the QSTS of an arbitrary three-qubit state involving Bell-state measurement, single-qubit measurement and one high dimensional unitary operation. The performance demonstrates that our scheme can considerably reduce the difficulty of physical implementation.

A quantitative witness for Greenberger-Horne-Zeilinger entanglement

Along with the vast progress in experimental quantum technologies there is an increasing demand for the quantification of entanglement between three or more quantum systems. Theory still does not provide adequate tools for this purpose. The objective is, besides the quest for exact results, to develop operational methods that allow for efficient entanglement quantification. Here we put forward an analytical approach that serves both these goals. We provide a simple procedure to quantify Greenberger-Horne-Zeilinger–type multipartite entanglement in arbitrary three-qubit states. For two qubits this method is equivalent to Wootters' seminal result for the concurrence. It establishes a close link between entanglement quantification and entanglement detection by witnesses, and can be generalised both to higher dimensions and to more than three parties.

QUANTUM THREE-QUBIT W-STATE SHARING VIA POSITIVE OPERATOR-VALUED MEASUREMENT AND PROJECTIVE MEASUREMENT

In this paper, by using a proper positive operator-valued measurement, we propose a new tripartite scheme for probabilistically implementing quantum state sharing of an arbitrary unknown three-qubit state with two non-maximally entangled states, one is four-qubit state, another is three-qubit state. In the scheme, the Boss Alice partitions her unknown original state with two Bell-state measurements and a single-qubit projective measurement. Then she publishes her measurement results via a classical channel. With an agent Charlie's help, another agent Bob can recover the original state in probabilistic manner by performing a proper POVM.

Highly efficient remote preparation of an arbitrary three-qubit state via a four-qubit cluster state and an EPR state

An efficient protocol for remotely preparing an arbitrary three-qubit state is devised with a four-qubit cluster state and an Einstein---Podolsky---Rosen state as the shared quantum resource. Using an appropriate set of eight-qubit mutually orthogonal measurement basis, the remote three-qubit preparation is successfully completed with the probability of $${\frac{1}{8}}$$ in general case. Then to achieve our concerns of improving the probability of this protocol, some special ensembles of three-qubit states are minutely investigated. As a result, it is shown that the total probability of the RSP protocol, in these particular cases, can be improved to $${\frac{1}{4}}$$ and $${\frac{1}{2}}$$ , respectively, or even that the RSP protocol can be realized with unit success probability.

Deterministic joint remote preparation of an arbitrary three-qubit state via Einstein–Podolsky–Rosen pairs with a passive receiver

In this work, a useful protocol for deterministic joint remote preparation of an arbitrary three-qubit state using only Einstein–Podolsky–Rosen pairs is put forward. Our protocol, in clear contrast with a previous one, works for a receiver who, due to limited local equipments, is unable to carry out any measurements and controlled-NOT gates as well as to send classical communication. Therefore, the practical merit of our protocol is that it is applicable to situations in which the receiver has insufficient resource to meet the demand.

Quantum information splitting of an arbitrary three-qubit state via the cavity input–output process

We propose a realizable quantum information splitting (QIS) scheme for an arbitrary three-qubit state via the cavity input–output process. In our scheme, a four-qubit cluster state and a three-qubit Greenberger–Horne–Zeilinge (GHZ) state are used as quantum channel. The sender and controller only need to perform Bell-state measurements and a single-qubit measurement, respectively. The receiver can reconstruct the arbitrary three-qubit state by classical communication and local operations. Compared with the scheme in Nie et al. [Optics Communications 284 (2011) 1457], the quantum resources and classical information in our scheme are decreased by 5 qubits and 1 bit, respectively. Moreover, we replace the W-state category measurement in the former with Bell-state measurements and a single-qubit measurement, which is more simple and feasible in experiment.

Quantum splitting an arbitrary three-qubit state with χ-state

In this paper, we propose two schemes to remotely split an arbitrary three-qubit state. The ? and a GHZ state are used to construct the quantum channel. One scheme is completed by using the generalized Bell basis measurement of multi-particles. The other scheme is constructed by using the quantum primitives, which are described by the quantum circuit and photon architecture.

Deterministic joint remote preparation of an arbitrary three-qubit state via EPR pairs

A proposal, using six Einstein–Podolsky–Rosen pairs as the shared quantum resource, focuses on realizing the deterministic joint remote preparation of an arbitrary three-qubit state. With the right measurement bases and a series of proper Pauli operators, the state that we intend to joint remotely prepare is deemed to be obtained deterministically.

Entanglement of Three-Qubit Greenberger-Horne-Zeilinger–Symmetric States

The first characterization of mixed-state entanglement was achieved for two-qubit states in Werner's seminal work [Phys. Rev. A 40, 4277 (1989)]. A physically important extension concerns mixtures of a pure entangled state [such as the Greenberger-Horne-Zeilinger (GHZ) state] and the unpolarized state. These mixed states serve as benchmark for the robustness of multipartite entanglement. They share the symmetries of the GHZ state. We call such states GHZ symmetric. Here we give a complete description of the entanglement in the family of three-qubit GHZ-symmetric states and, in particular, of the three-qubit generalized Werner states. Our method relies on the appropriate parametrization of the states and on the invariance of entanglement properties under general local operations. An application is the definition of a symmetrization witness for the entanglement class of arbitrary three-qubit states.

基于Cluster态和Bell态的任意三粒子态远程制备

A novel scheme for remote preparation of an arbitrary three-qubit state using four-qubit cluster state and Bell state is proposed.The three-particle state can be perfectly prepared if the sender(Alice) performs the orthogonal complete measurement on her particles and the receiver(Bob) introduces an appropriate unitary transformation on his particles.For the two cases of remote state preparation,two different projective measurement bases are constructed at sender′s side and the corresponding success probabilities are calculated.The probability of success regarding this preparation scheme is calculated in both general and some particular cases.It is that in general such remote state preparation can be realized with a probability of 1/8.But in several special cases,the probability of success can be improved to 1/4,1/2 or even 1.

Quantum information splitting of an arbitrary three-qubit state by using a genuinely entangled five-qubit state and a Bell-state

A new application of the genuinely entangled five-qubit state introduced by Brown et al. (J Phys A 38(5), 1119---1131, 2005) is investigated for quantum information splitting (QIS) of an arbitrary ...

Perfect Teleportation of an Arbitrary Three-Qubit State by Using W-Class States

A new application of the W-class state is investigated for teleportation of an arbitrary three-qubit state. We demonstrate that three sets of W-class states can be used to realize the perfect teleportation of an arbitrary three-qubit state by performing only the three-qubit von Neumann measurements and local unitary operations.

Quantum Information Splitting of an Arbitrary Three-Qubit State by Using Cluster States and Bell States

A new application of cluster states is investigated for quantum information splitting (QIS) of an arbitrary three-qubit state. In our scheme, a four-qubit cluster state and a Bell state are shared by a sender (Alice), a controller (Charlie), and a receiver (Bob). Both the sender and controller only need to perform Bell-state measurements (BSMs), the receiver can reconstruct the arbitrary three-qubit state by performing some appropriately unitary transformations on his qubits after he knows the measured results of both the sender and the controller. This QIS scheme is deterministic.

CONTROLLED TELEPORTATION OF AN ARBITRARY THREE-QUBIT STATE THROUGH A GENUINE SIX-QUBIT ENTANGLED STATE AND BELL-STATE MEASUREMENTS

We demonstrate that a genuine six-qubit entangled state introduced by Tapiador et al. [J. Phys. A42 (2009) 415301] can be used to realize the deterministic controlled teleportation of an arbitrary three-qubit state by performing only the Bell-state measurements.

Joint remote preparation of an arbitrary three-qubit state via EPR-type pairs

In this work, we propose a scheme to realize a joint remote preparation of an arbitrary three-qubit state using six EPR-type pairs as the shared quantum resource. By determining the right measurement bases for the preparers and right ancilla-assisted unitary transformation/recovery operations for the receiver, our scheme applies to the most general case when all the coefficients of the state to be prepared and the EPR-type pairs are complex. The total success probability is found to be dependent only on the “smaller” coefficients of the EPR-type pairs shared between the receiver and one of the preparers.

Scheme for assisted cloning an unknown arbitrary three-qubit state

We present a scheme for perfect cloning or orthogonal complementing an unknown arbitrary three-qubit state with assistance. This cloning scheme is divided into two stages. In the first stage, the initial state can be teleported from a sender to a receiver probabilistically via three partially entangled states. In the second stage, the exact copying and orthogonal complementing of the three-qubit state can be created with unity fidelity in a probabilistic manner with the state preparer performing an appropriate tri-particle projective measurement. It is shown that for some special ensembles of the three-qubit state our assisted cloning scheme can be achieved exactly and deterministically.