Generalized Bell-state Measurements Research Articles

Probabilistic Quantum Teleportation via 3-Qubit Non-maximally Entangled GHZ State by Repeated Generalized Measurements

We propose a scheme of repeated generalized Bell state measurement (GBSM) for probabilistic quantum teleportation of single qubit state of a particle (say, 0) using 3-qubit non-maximally entangled (NME) GHZ state as a quantum channel. Alice keeps two qubits (say, 1 and 2) of the 3-qubit resource and the third qubit (say, 3) goes to Bob. Initially, Alice performs GBSM on qubits 0 and 1 which may lead to either success or failure. On obtaining success, Alice performs projective measurement on qubit 2 in the eigen basis of $\sigma_{x}$. Both these measurement outcomes are communicated to Bob classically, which helps him to perform a suitable unitary transformation on qubit 3 to recover the information state. On the other hand, if failure is obtained, the next attempt of GBSM is performed on qubits 0 and 2. This process of repeating GBSM on alternate pair of qubits may continue until perfect teleportation with unit fidelity is achieved. We have obtained analytical expressions for success probability up to three repetitions of GBSM. The success probability is shown to be a polynomial function of bipartite concurrence of the NME resource. The variation of success probability with the bipartite concurrence has been plotted which shows the convergence of success probability to unity with GBSM repetitions.

Probabilistic quantum teleportation of shared quantum secret

Very recently, Lee et al. proposed a secure quantum teleportation protocol to transfer shared quantum secret between multiple parties in a network [Phys. Rev. Lett. 124 060501 (2020)]. This quantum network is encoded with a maximally entangled GHZ state. In this paper, we consider a partially entangled GHZ state as the entanglement channel, where it can achieve, probabilistically, unity fidelity transfer of the state. Two kinds of strategies are given. One arises when an auxiliary particle is introduced and a general evolution at any receiver’s location is then adopted. The other one involves performing a single generalized Bell-state measurement at the location of any sender. This could allow the receivers to recover the transmitted state with a certain probability, in which only the local Pauli operators are performed, instead of introducing an auxiliary particle. In addition, the successful probability is provided, which is determined by the degree of entanglement of the partially multipartite entangled state. Moreover, the proposed protocol is robust against the bit and phase flip noise.

Probabilistic hierarchically controlled teleportation of anarbitrary <italic>m</italic>-qudit state with a pure entangledquantum channel

<p indent=0mm>Quantum teleportation is a unique quantum information processing method in quantum communication. Researchers have shown considerable interest in hierarchically controlled teleportation by using quantum entangled states as the quantum channel. Protocols for the hierarchically controlled teleportation of an arbitrary single-qubit via a four-qubit χ state and a four-qubit cluster state have been proposed. We present a protocol for the hierarchically controlled teleportation of an arbitrary <italic>m</italic>-qudit (<italic>d</italic>-dimensional quantum system) state by using a partially entangled quantum state as the quantum channel. The sender performs <italic>m</italic> generalized Bell-state measurements on her <sc>2<italic>m</italic></sc> particles. To reconstruct the original state, the upper-grade receiver only needs to apply a unitary operation in accordance with one of the receivers’ measurement results, and the lower-grade receivers need to perform a unitary operation according to all the other receivers’ measurement results. The receivers can reconstruct the original state probabilistically by introducing an auxiliary qubit and performing a collective unitary transformation. The protocol has the advantage of having high channel capacity by using a high-dimensional entangled state as the quantum channel.

High success perfect transmission of 1-qubit information using purposefully delayed sharing of non-maximally entangled 2-qubit resource and repeated generalized Bell-state measurements

We propose a new scheme in which perfect transmission of 1-qubit information is achieved with high success using purposefully delayed sharing of non-maximally entangled 2-qubit resource and repeated generalized Bell-state measurements (GBSM). Alice possesses initially all qubits and she makes repeated GBSM on the pair of qubits, consisting of (1) the qubit of information state and (2) one of the two entangled resource qubits (taken alternately) until transmission with perfect fidelity is indicated. Alice then sends to Bob, the qubit not used in the last GBSM and also the result of this GBSM and Bob applies a suitable unitary transformation to replicate exactly the information state. Continued probabilistic transmission with unit fidelity is achieved by changing continuously the generalized Bell basis and also the pair of measured qubits of the collapsed states. We calculate the success probability up to the third repeated attempt of GBSM and plot it with concurrence of the entangled resource state. We also discuss the maximal average fidelity.

基于(2m+1)粒子纠缠态的任意m粒子态量子可控离物传态

提出了一个基于高维2m+1粒子纠缠态的任意m粒子态量子可控离物传态方案,发送方alice对需传送的未知态量子系统和手中的纠缠粒子执行m个广义bell基测量,控制方执行广义x基测量,依据预先共享量子纠缠态非定域相关性,接收方对手中的粒子执行相应的幺正操作就可以重建原来未知量子态.与其他方案相比,方案减少了任意高维多粒子态可控离物传送所需传送粒子数.我们进一步讨论了基于纯纠缠信道的概率量子可控离物传态方案,通过与发送方和控制方合作,接收方只需对手中的纠缠粒子和引入的附加粒子执行联合幺正演化和投影测量,就可以在他的粒子上概率的重建原来的未知量子态,最后,方案计算讨论了基于纯纠缠态量子可控离物传态成功概率与信道纠缠度之间的关系. abstract： a general scheme for controlled teleportation of an arbitrary m-qubit (high-dimensional quantum system) state with a d-dimensional (2m+1)-particle entangled state is presented.the arbitrary m-qubit state can be teleported if the sender (alice) performs m generalized bell state measurements on his particles and the controller (bob) performs single particle generalized xbasis measurement on his particle. the original m-qubit state can be reconstructed on the receiver's particles if the receiver (charlie) performs corresponding unitary operations on his particles according to the measurement results of the sender and the controller.the scheme has the advantage of transmitting much less particles for controlled teleportation of an unknown m-qubit state than others. moreover,the application of the scheme by using a nonmaximally entangled state as its quantum channel is discussed. the original m-qubit state can be probabilistically reconstructed on the receiver's particles if the receiver introduces an auxiliary qubit and performs the general unitary transformation on his entangled particles and the auxiliary qubit.the relationship betwe

Generalized quantum state sharing of the arbitrary two particles state

This paper has proposed a generalized quantum state sharing protocol of an arbitrary two-particle state using non-maximally GHZ states and generalized Bell state measurement. The sender Alice performs two-particle generalized Bell state measurements on her two particles in the state sharing process and the controller takes measurements on his particles and transfers the quantum information to the receiver with entanglement swapping by the cooperation of the other agents. It is found that the use of nonmaximally entangled state in quantum state sharing has enabled the secure sharing of the quantum state.

Generalized tripartite scheme for sharing arbitrary 2n-qudit state

Utilizing three non-maximally entangled qutrit pairs as quantum channels, we first propose a generalized tripartite scheme for sharing an arbitrary two-qutrit state with generalized Bell-state measurements. In the scheme if and only if the two recipients collaborate together, they can recover the split qutrit state with the probability determined uniquely by the smallest coefficients of the non-maximally entangled pairs. Afterwards, we further extend the scheme for sharing an arbitrary 2n-qudit state by taking 3n non-maximally entangled qudit pairs as quantum channels. Moreover, the scheme success probability relative to the inherent entanglement in quantum channels and its structure is simply discussed.

Probabilistic teleportation via a non-maximally entangled GHZ state

We present a scheme for probabilistic teleportation via a non-maximally entangled GHZ state. Quantum teleportation will succeed with a certain probability if the sender makes a generalized Bell state measurement, the cooperator performs a generalized $X$ basis measurement, and the receiver introduces an auxiliary particle, performs a collective unitary transformation and makes a measurement on the auxiliary particle. The success probability of the teleportation is given. We also obtain the maximum of the success probability of the teleportation.

An efficient scheme for generalized tripartite controlled teleportation of a two-quNit entangled state

A scheme for generalized controlled teleportation of an arbitrary two-quNit entangled state with N-dimensional partially Greenberger–Horne–Zeilinger (GHZ) state is proposed. A generalized Bell state measurement (BM) and a single-particle measurement in high dimensions are needed. According to the sender Alice's classical message, the receiver Charlie can restore the unknown two-quNit state with a certain probability by introducing an additional particle and performing a controlled-not (C-NOT) operation on his particles if she cooperates with the controller Bob. The total success probability and classical communication cost are calculated. We also generalize the scheme to the case where there are K controllers. It is shown that any one of the receivers can reconstruct the unknown state if he/she cooperates with all the controllers.

Teleportation of an arbitrary unknown N-qubit entangled state under the controlling of M controllers

A new quantum protocol to teleport an arbitrary unknown N-qubit entangled state from a sender to a fixed receiver under M controllers(M < N) is proposed. The quantum resources required are M non-maximally entangled Greenberger-Horne-Zeilinger (GHZ) state and N-M non-maximally entangled Einstein-Podolsky-Rosen (EPR) pairs. The sender performs N generalized Bell-state measurements on the 2N particles. Controllers take M single-particle measurement along x-axis, and the receiver needs to introduce one auxiliary two-level particle to extract quantum information probabilistically with the fidelity unit if controllers cooperate with it.

Quantum state sharing of an arbitrary m-qudit state with two-qudit entanglements and generalized Bell-state measurements

A scheme for quantum state sharing of an arbitrary m -qudit state is proposed with two-qudit entanglements and generalized Bell-state (GBS) measurements. In this scheme, the sender Alice should perform m two-particle GBS measurements on her 2 m qudits, and the controllers also take GBS measurements on their qudits and transfer their quantum information to the receiver with entanglement swapping if the agents cooperate. We discuss two topological structures for this quantum state sharing scheme, a dispersive one and a circular one. The former is better at the aspect of security than the latter as it requires the number of the agents who should cooperate for recovering the quantum secret larger than the other one.

Multiparty-controlled teleportation of an arbitrary m-qudit state with a pure entangled quantum channel

We present a general scheme for multiparty-controlled teleportation of an arbitrary m-qudit (d-dimensional quantum system) state by using non-maximally entangled states as the quantum channel. The sender performs m generalized Bell-state measurements on her 2m particles, the controllers take some single-particle measurements with the measuring basis Xd and the receiver only needs to introduce one auxiliary two-level particle to extract quantum information probabilistically with the fidelity unit if he cooperates with all the controllers. All the parties can use some decoy photons to set up their quantum channel securely, which will forbid a dishonest party to eavesdrop freely. This scheme is optimal as the probability that the receiver obtains the originally unknown m-qudit state equals the entanglement of the quantum channel.

Controlled teleportation of multi-qudit quantum information

We propose a scheme for realizing a controlled teleportation of random M-qudit quantum information under the control of N agents. The resource consumption includes a prearranged (2M + N + 1)-qudit entangled quantum channel and (2M + N + 1) log2 d-bit classical communication. And the quantum operations used in the teleportation process are a series of generalized Bell-state measurements, single-qudit measurements, qudit H-gates, qudit-Pauli gates and qudit phase gates. It is shown that the original state can be restored by the receiver only on condition that all the agents work in collaboration with each others. If one agent does not cooperate with the other, the original state cannot be fully recovered.

Controlled teleportation of high-dimension quantum-states with generalized Bell-state measurement

In this paper a scheme for controlled teleportation of arbitrary high-dimensional unknown quantum states is proposed by using the generalized Bell-basis measurement and the generalized Hadamard transformation. As two special cases, two schemes of controlled teleportation of an unknown single-qutrit state and an unknown two-qutrit state are investigated in detail. In the first scheme, a maximally entangled three-qutrit state is used as the quantum channel, while in the second scheme, an entangled two-qutrit state and an entangled three-qutrit state are employed as the quantum channels. In these schemes, an unknown qutrit state can be teleported to either one of two receivers, but only one of them can reconstruct the qutrit state with the help of the other. Based on the case of qutrits, a scheme of controlled teleportation of an unknown qudit state is presented.

Teleportation of Multi-qudit Entangled States

We propose a method to realize the teleportation of an unknown entangledstate that consists of many qudits through a partially entangled-quditquantum channel with the help of 2log2d-bit classicalcommunication. The operations used in the teleportation process includea generalized Bell-state measurement and a series of single-quditπ-measurements performed by Alice, a series of generalizedqudit-Pauli gates and two-level unitary gates, as well as a qubitmeasurement performed by Bob. For a maximally entangled quantum channel,the successful probability of the teleportation becomes unit.

Probabilistic teleportation of an arbitrary three-particle state

A scheme for teleporting an arbitrary and unknown three-particle state from a sender to either one of two receivers is proposed. The quantum channel is composed of a two-particle non-maximally entangled state and two three-particle non-maximally entangled W states. An arbitrary three-particle state can be perfectly teleported probabilistically if the sender performs three generalized Bell-state measurements and sends to the two receivers the classical result of these measurements and either one of the two receivers adopts an appropriate unitary transformation conditioned on the suitable measurement outcomes of the other receiver. All kinds of unitary transformations are given in detail.

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

We present a scheme for teleporting an arbitrary and unknown two-particle state from a sender to either one of two receivers. A partially entangled three-particle GHZ state and a partially entangled three-particle W state are used as the quantum channel. An arbitrary and unknown two-particle state can be perfectly teleported probabilistically if the sender performs two generalized Bell-state measurements while either one of two receivers introduces an appropriate unitary transformation with the help of the other receiver’s the Hadamard operation and simple measurements.

Probabilistic teleportation of an arbitrary two-particle state by two partial three-particle entangled W states

We present a scheme for teleporting an arbitrary and unknown two-particle state from a sender to either one of two receivers. The quantum channel is composed of two non-maximally three-particle entangled W states. An arbitrary two-particle state can be perfectly teleported probabilistically if both the sender performs two generalized Bell-state measurements and either one of two receivers adopts an appropriate unitary transformation, conditioned on the suitable measurement outcomes of the other receiver and classical information.

Probabilistic instantaneous quantum computation

The principle of teleportation can be used to perform a quantum computation even before its quantum input is defined. The basic idea is to perform the quantum computation at some earlier time with qubits which are part of an entangled state. At a later time a generalized Bell state measurement is performed jointly on the then defined actual input qubits and the rest of the entangled state. This projects the output state onto the correct one with a certain exponentially small probability. The sufficient conditions are found under which the scheme is of benefit.