M-qubit State Research Articles

Quantum Cyclic Controlled Teleportation of Unknown States with Arbitrary Number of Qubits by Using Seven-qubit Entangled Channel

A novel theoretical scheme is proposed to implement quantum cyclic controlled teleportation (QCYCT) of three unknown states by utilizing a seven-qubit entangled state as the quantum channel, where Alice can transmit an unknown m-qubit state to Bob, Bob can transmit an unknown n-qubit state to Candy and Candy can transmit an unknown t-qubit state to Alice under the control of the supervisor David. Only controlled-not (CNOT) operations, Bell-state measurements, a single-qubit measurement and appropriate unitary operations are needed in this scheme, which can be realized in experiment easily. The desired state of each communicator can be recovered deterministically by using auxiliary particles. The direction of the cyclic controlled teleportation can also be altered throughout changing the selection of the particle pairs to be measured of each communicator. Compared with the previous QCYCT schemes, the proposed scheme possesses higher intrinsic efficiency in most cases and can transfer as many qubits as the communicators desire.

Minimum-error discrimination between two sets of similarity-transformed quantum states

Using the equality form of the necessary and sufficient conditions introduced in Jafarizadeh (Phys Rev A 84:012102 (9 pp), 2011), minimum error discrimination between states of the two sets of equiprobable similarity transformed quantum qudit states is investigated. In the case that the unitary operators describing the similarity transformations are generating sets of two irreducible representations and the states fulfill a certain constraint, the optimal set of measurements and the corresponding maximum success probability of discrimination are determined in closed form. In the cases that they are generating sets of reducible representations, there exist no closed-form formula in general, but the procedure can be applied properly in each case provided that the states obey some constraints. Finally, we give the maximum success probability of discrimination and optimal measurement operators for some important examples of mixed quantum states, such as generalized Bloch sphere m-qubit states, qubit states and their three special cases.

Probabilistic multiparty-controlled teleportation of an arbitrary m-qubit state with a pure entangled quantum channel against collective noise

We present two general schemes for multiparty-controlled teleportation of an arbitrary m-qubit state against two types of collective noise by using m pure entangled states as the quantum channel. The first is used to control teleporting for an arbitrary m-qubit state against a collective-dephasing noise with nonmaximally entangled quantum channel, and the second is in teleporting the m-qubit state against the collective-rotation noise. The receiver can reconstruct the original state with an auxiliary qubit and the corresponding unitary operations if he cooperates with all the controllers. The scheme is optimal as the probability that the receiver reconstructs the original state equals to the entanglement of the quantum channel.

Probabilistic Multiparty Joint Remote Preparation of an Arbitrary m-Qubit State with a Pure Entangled Channel Against Collective Noise

We present a scheme for multiparty joint remote preparation of an arbitrary m-qubit state with a multiparticle entangled quantum channel against collective noise. All the senders share the information of the prepared state and perform corresponding measurement according to their knowledge of the prepared state, the receiver can reconstruct the original state by performing corresponding unitary operation on his particles if he cooperates with all the senders. Moreover, the agents use decoherence-free subspace to tolerate the collective noise. This scheme has the advantage of having high success probability for multiparty joint remote preparation of an arbitrary m-qubit state via pure entangled states.

Protecting multi-qubit states in computational subspaces by nested dynamical decoupling sequences

We propose to nest 3M layers of explicitly constructed Uhrig’s dynamical decoupling sequences of local control operators to achieve universal high-order protection of arbitrary and unknown M-qubit states on a 2M-dimensional computational subspace. This is the case even if the mechanism responsible for population leakage from the computational subspace is unclear and the actual form of system–environment coupling is not given. Simple numerical experiments are carried out to illustrate our theoretical proposal.

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

Efficient Symmetric Five-Party Quantum State Sharing of an Arbitrary m-Qubit State

We present an efficient symmetric scheme for five-party quantum state sharing of an arbitrary m-qubit state with 2m three-particle entangled states. The implementations of this scheme only need to exploit the CNOT gate operations and the single-particle measurements, instead of the three-particle GHZ-state measurements, which makes it more convenient in a practical application than some previous schemes. In addition, its total efficiency can approach the maximal value in theory.

An efficient scheme for five-party quantum state sharing of an arbitrary m-qubit state using multiqubit cluster states

We present an efficient scheme for five-party quantum state sharing (QSTS) of an arbitrary m-qubit state with multiqubit cluster states. Unlike the three-partite QSTS schemes using the same quantum channel [Phys. Rev. A 78, 062333 (2008)], our scheme for sharing of quantum information among five parties utilizing a cluster state as an entangled resource. It is found that the six-partite cluster state can be used for QSTS of an entangled state, the five-partite cluster state can be used for QSTS of an arbitrary two-qubit state and also can be used for QSTS of an arbitrary m-qubit state. It involves two-qubit Bell-basis or three-qubit GHZ-basis measurements, not multipartite joint measurements, which makes it more convenient than some previous schemes. In addition, the total efficiency really approaches the maximal value.

An Efficient Scheme for Multiparty Multi-particle State Sharing

We present an efficient scheme for sharing an arbitrary m-qubit state with n agents. In our scheme, the sender Alice first shares m Bell states with the agent Bob, who is designated to recover the original m-qubit state. Furthermore, Alice introduces n − 1 auxiliary particles in the initial state |0⟩, applies Hadamard (H) gate and Controlled-Not (CNOT) gate operations on the particles, which make them entangled with one of m particle pairs in Bell states, and then sends them to the controllers (i.e., other n − 1 agents), where each controller only holds one particle in hand. After Alice performing m Bell-basis measurements and each controller a single-particle measurement, the recover Bob can obtain the original unknown quantum state by applying the corresponding local unitary operations on his particles. Its intrinsic efficiency for qubits approaches 100%, and the total efficiency really approaches the maximal value.

Asymmetric multi-party quantum state sharing of an arbitrary m-qubit state

We present a scheme for asymmetric multi-party quantum state sharing of an arbitrary m-qubit state with n agents. The sender Alice first shares m ? 1 Bell states and one n + 1-particle Greenberger---Horne---Zeilinger state with n agents, where the agent Bob, who is designated to recover the original m-qubit state, just keeps m particles and other agents (all controllers) n ? 1 particles, that is, each controller only holds one particle in hand. Subsequently, Alice performs m Bell-basis measurements on her 2m particles and each controller only need take a single-particle measurement on his particle with the basis X. Finally, Bob can recover the original m-qubit state with the corresponding local unitary operations according to Alice and all controllers' measurement results. Its intrinsic efficiency for qubits approaches 100%, and the total efficiency really approaches the maximal value, which is higher than those of the known symmetric schemes.

Asymmetric five-party quantum state sharing of an arbitrary m-qubit state

We present an asymmetric scheme for five-party quantum state sharing of an arbitrary m-qubit state with the maximally entangled states of two-particle and three-particle. It involves two-particle Bell-basis or three-particle GHZ-basis measurements, rather than five-particle entanglements and five-particle joint measurements, which makes it more convenient in a practical application than some previous schemes. In addition, except that the designated recover of the quantum secret just keeps m particles, other agents only hold one particle in their hands respectively, and thus they only need perform a single-particle measurement on the respective particle with the basis X. Its intrinsic efficiency for qubits approaches 100%, and the total efficiency really approaches the maximal value.

Efficient and economic five-party quantum state sharing of an arbitrary m-qubit state

We present an efficient and economic scheme for five-party quantum state sharing of an arbitrary m-qubit state with $2m$ three-particle Greenberger-Horne-Zeilinger (GHZ) states and three-particle GHZ-state measurements. It is more convenient than other schemes as it only resorts to three-particle GHZ states and three-particle joint measurement, not five-particle entanglements and five-particle joint measurements. Moreover, this symmetric scheme is in principle secure even though the number of the dishonest agents is more than one. Its total efficiency approaches the maximal value.

M-Qubit states embedded in Clifford algebras

The quantum theory of a finite quantum system with L degrees of freedom is usually set up by associating it with a Hilbert space of dimension d(L) and identifying observables and states in the matrix algebra . For the case d = 2m, m integer, this algebra can be identified with the Clifford algebra . The case of d = 2m dimensions is simply realized by a system with m dichotomic degrees of freedom, an m-qubit system for instance. The physically relevant new point is the appearance of a new (symmetry-?)group SO(2m). A possible interpretation of the space in which this group operates is proposed. It is shown that the eigenvalues of m-qubit-type states only depend on SO(2m)-invariants. We use this fact to determine state parameter domains (generalized Bloch spheres) for states classified as SO(2m)-tensors. The classification of states and interactions of components of a physical m-qubit system as k-tensors and pseudotensors (0 ⩽ k ⩽ m) leads to rules similar to those found in elementary quantum mechanics. The question of electromagnetic interactions is shortly broached. We sketch, pars pro toto, a graphical interpretation of tensor contractions appearing in perturbative expansions.

MULTIPARTY QUANTUM STATE SHARING OF m-QUBIT STATE

A scheme for quantum state sharing (QSTS) of a one-particle state is proposed for a three-particle GHZ state utilized as a quantum channel. After the sender (Alice) makes Bell-state measurements (BM) on her particles, and the controller (Charlie) performs a computational basis measurement (CM), the recipient (Bob) only needs to carry out a unitary transformation of the classical information from the sender and the controller. Finally, the scheme is generalized to multiparty QSTS of a one-qubit state with n agents and an m-qubit state with n agents.

Efficient symmetric multiparty quantum state sharing of an arbitrary m-qubit state

We present a scheme for symmetric multiparty quantum state sharing of an arbitrary m-qubit state with m Greenberger–Horne–Zeilinger states following some ideas from the controlled teleportation (2005 Phys. Rev. A 72 02338). The sender Alice performs m Bell-state measurements on her 2m particles and the controllers need only take some single-photon product measurements on their photons independently, not multipartite entanglement measurements, which makes this scheme more convenient than the latter. Also it does not require the parties to perform a controlled-NOT gate on the photons for reconstructing the unknown m-qubit state and it is an optimal one as its efficiency for qubits approaches 100% in principle.

Better bound on the exponent of the radius of the multipartite separable ball

We show that for an m-qubit quantum system, there is a ball of radius asymptotically approaching kappa 2^{-gamma m} in Frobenius norm, centered at the identity matrix, of separable (unentangled) positive semidefinite matrices, for an exponent gamma = (1/2)((ln 3/ln 2) - 1), roughly .29248125. This is much smaller in magnitude than the best previously known exponent, from our earlier work, of 1/2. For normalized m-qubit states, we get a separable ball of radius sqrt(3^(m+1)/(3^m+3)) * 2^{-(1 + \gamma)m}, i.e. sqrt{3^{m+1}/(3^m+3)}\times 6^{-m/2} (note that \kappa = \sqrt{3}), compared to the previous 2 * 2^{-3m/2}. This implies that with parameters realistic for current experiments, NMR with standard pseudopure-state preparation techniques can access only unentangled states if 36 qubits or fewer are used (compared to 23 qubits via our earlier results). We also obtain an improved exponent for m-partite systems of fixed local dimension d_0, although approaching our earlier exponent as d_0 approaches infinity.

Teleportation of a multiqubit state by an entangled qudit channel

We investigate the problem of teleportation of an M-qubit state by using an entangled qudit pair as a quan-tum channel and show that the teleportation of a multiparticle state can correspond to the teleportation of a multi-dimensional state. We also introduce a quantum-state converter composed of beamsplitter arrays, on/off-detectors and cross-Kerr couplers and demonstrate that the state conversion from an M-qubit to an N-dimensional qudit and vice versa can be implemented with this converter, where N = 2^M. Based on this, an experimentally feasible scheme for the teleportation of an M-qubit via an entangled N-level qudit pair channel is proposed.

Teleportation of a multiqubit state by an entangled qudit channel

We investigate the problem of teleportation of an M-qubit state by using an entangled qudit pair as a quantum channel and show that the teleportation of a multiparticle state can correspond to the teleportation of a multi-dimensional state. We also introduce a quantum-state converter composed of beamsplitter arrays, on/off-detectors and cross-Kerr couplers and demonstrate that the state conversion from an M-qubit to an N-dimensional qudit and vice versa can be implemented with this converter, where N = 2M. Based on this, an experimentally feasible scheme for the teleportation of an M-qubit via an entangled N-level qudit pair channel is proposed.

Unidirectional Quantum Remote Control: Teleportation of Control-State**The project supported by the National Fundamental Research Programme (2001CB309300) and the Zhejiang Provincial Natural Science Foundation of China under Grant No. 102068

We investigate the problem of teleportation of unitary operations by unidirectional control-state teleportation and propose a scheme called unidirectional quantum remote control. The scheme is based on the isomorphism between operation and state. It allows us to store a unitary operation in a control state, thereby teleportation of the unitary operation can be implemented by unidirectional teleportation of the control-state. We find that the probability of success for implementing an arbitrary unitary operation on arbitrary M-qubit state by unidirectional control-state teleportation is 4-M, and 2M ebits and 4M cbits are consumed in each teleportation.