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The design of efficient quantum circuits is an important issue in quantum computing. It is in general a formidable task to find a highly optimized quantum circuit for a given unitary matrix. We propose a quantum circuit design method that has the following unique feature: It allows to construct efficient quantum circuits in a systematic way by reusing and combining a set of highly optimized quantum circuits. Specifically, the method realizes a quantum circuit for a given unitary matrix by implementing a linear combination of representing matrices of a group, which have known fast quantum circuits. We motivate and illustrate this method by deriving extremely efficient quantum circuits for the discrete Hartley transform and for the fractional Fourier transforms. The sound mathematical basis of this design method allows to give meaningful and natural interpretations of the resulting circuits. We demonstrate this aspect by giving a natural interpretation of known teleportation circuits.

Multi-hop teleportation is a quantum teleportation scheme for transferring quantum states on a large scale. In this paper, a new multi-hop teleportation protocol is investigated for transferring arbitrary N-qubit states between M-neighbor nodes. In this scheme, intermediate nodes are connected with each other by symmetric entangled Bell states as quantum channels. First, one-hop teleportation of single-qubit, two-qubit and N-qubit states are introduced, then this method is generalized to two-hop and multi-hop teleportation for N-qubit. Also, we calculate the efficiency of this scheme.

The present work proposes a scheme to teleport a tripartite coherent state using an unparalleled four-component state as a quantum channel. The scheme involves linear optical devices like beam splitters and phase shifters. It is shown that, even by taking an uncompromising quantum model, almost a complete teleportation can be achieved with an impressive number of photons. It is also shown that the teleportation fails only if zero photons are found in all the three output modes or zero in two output modes and a nonzero even/odd photon in one mode. However, the probability of getting these output modes is almost negligible.

Here we aim at setting the principles of and quantifying translational entanglement by collisions and half-collisions. In collisions, the resonance width s and the initial phase-space distributions are shown to determine the degree of post-collisional momentum entanglement. Half-collisions (dissociation) are shown to yield different types of approximate EPR states. We analyse a feasible realization of translational EPR entanglement and teleportation via cold-molecule Raman dissociation and subsequent collisions, resolving both practical and conceptual difficulties it has faced so far.

We show a general W state of N-particle entanglement. Using four pairs of two-particle non-maximally entanglement states, we give a general scheme of probabilistic teleportation of the four-particle general W state by constructing a 5 × 5 projection transformation matrix different from the other references. The general scheme overcomes the difficulty of having to introduce an auxiliary state |0>_A in order to get a complex unitary transformation matrix. Thus, we need not perform more operations and measurements than the past researches. We then give a general scheme of the probabilistic teleportation of the N-particle general W state by means of N pairs of general entanglement particles, and the scheme may be applied to all the researches and calculation about the probabilistic teleportation of N-particle entanglement general state by means of N pairs of general entanglement particles, and may simplify their researches, calculation, physical operations and measurements.

We present two schemes for probabilistically teleporting a two-atom entangled state using a three-atom partially entangled state as the quantum channel in cavity QED with the help of separate atomic measurements. The first scheme is only based on the interaction between two driven atoms and a quantized cavity mode in the large detuning limit, so the effects of both cavity decay and the thermal field are eliminated. In the second scheme, it is necessary to introduce an additional resonant cavity besides the thermal cavity to realize the teleportation, and the corresponding success probability is improved.

We present a scheme that can realize quantum cloning of an unknown two-particle entangled state and its orthogonal-complement state with assistance offered by a state preparer, via entangled cluster state as quantum channel. The first stage of the scheme requires usual teleportation via a maximally four-particle entangled cluster state as quantum channel. In the second stage of the scheme, with the assistance (through a two-particle projective measurement) of the preparer, the perfect copies and complement copies of an unknown two-particle entangled state can be obtained. We also put forward a scheme for the teleportation by using nonmaximally entangled quantum channel. The clones and complement clones of unknown state can be produced with certain probability in the latter scheme.

In a recent paper N. Ba An (Phys. Rev. A68, 022321 (2003)) proposed a scheme to teleport a single particle state, which is superposition of coherent states |α〉 and |-α〉 using a 4-partite state, a beam splitter, and phase shifters and concluded that the probability for successful teleportation is only 1/4 in the limit |α| → 0 and 1/2 in the limit |α| → ∞. In this paper, we modify this scheme and find that an almost perfect success can be achieved if |α|² is appreciable. For example, for |α|² = 5, the minimum of average fidelity for teleportation, which is the minimum of sum of the product of probability for occurrence of any case and the corresponding fidelity evaluated for an arbitrary chosen information state, is 0.9999.

We investigate the problem of teleportation of tripartite entangled coherent state (ECS) using linear optical devices such as beam splitters, phase shifters, and two-mode number measurements. The scheme is based on the maximally four-partite ECS with bipartite maximal entanglement as the quantum channel to teleportation tripartite ECS. Our scheme is efficient in the sense that for mean number of photons equal to 2, the minimum of average fidelity (MAF) for teleportation an arbitrary tripartite entangled state is 1-2.3 × 10^-7. We also generalize the tripartite scheme into multipartite case and calculate the MAF for the schemes in multipartite cases.

Quantum entanglement and teleportation of two qubit X-states subject to heat bath is investigated by partial teleportation protocol. We obtain the analytical expressions of the average fidelity for the X-states with one-side decoherence and two-side decoherence. The quality of quantum teleportation with various initial states is investigated by explicitly calculating the concurrence, the output concurrence and the average fidelity. The results demonstrate that the model is suitable for teleportation, which depends on the initial state. However, the mean thermal occupation number of bath and decoherence could induce the decrease of the output entanglement and the average fidelity in the quantum teleportation processing. We also find the quantum teleportation protocol of one-side decoherence is more robust than that of under two-side decoherence.

Noisy entangled resource and non-standard teleportation operations result in imperfect teleportation. In this paper, we derive an explicit expression for the output states of imperfect teleportation processes, thereby establishing a correspondence between teleportation and quantum channels. This result offers a different insight into teleportation. Also, it enables us to derive an expression for the fidelity of teleportation. Our results analytically reveal the dependence of the output states and the fidelity on the entangled resource and teleportation operations. The Nielsen–Caves teleportation formalism is used in the derivation.

We investigate the entanglement of pair coherent states in the phase damping channel by adopting the relative entropy of entanglement and propose a protocol of teleportation via pair coherent states. The fidelity of the protocol is then analyzed and the influence of phase damping on the teleportation fidelity examined.

By using the two-mode Einstein–Podolsky–Rosen (EPR) pair eigenstates or the two-mode squeezed vacuum as quantum channel we study the quantum teleportation of any form of single-mode quantum states (which include discrete and continuous variable quantum states). The elegant properties of the EPR pair eigenstates bring much convenience to our discussion.

Schemes for the teleporting of the cavity mode state and the unknown atomic state are proposed in cavity quantum electrodynamics (QED) without joint Bell-state measurement (BSM). The presented schemes are implemented with separate atomic measurements instead of any type of joint measurement. The discussion of the scheme indicates that it can be realized by current technologies.

We propose a feasible scheme for teleporting an unknown atomic state by using non-maximally entangled states in cavity QED. The distinct advantage of the scheme is that, not only can the teleportation and distillation procedure be realized simultaneously, but the scheme is also insensitive to the cavity decay and thermal field with the assistance of a strong classical driving field. In addition, the joint Bell-state measurement can be distinguished via detecting the atomic state.

The teleportation via the channel of the thermal equilibrium states in anisotropic Heisenberg XYZ chains is analyzed. It is found that there are the critical temperatures below which entanglement teleportation can be realized. Entanglement teleportation is enhanced through anisotropic XYZ chains in contrast to the isotropic Heisenberg one. Anisotropic spin exchanges can increase these critical temperatures for the teleportation. Entanglement can be transferred in the ferromagnetic anisotropic Heisenberg chain while it cannot be done in the ferromagnetic isotropic one. The average fidelity of the teleportation can be improved in the antiferromagnetic chains.

Teleportation of quantum gates using partially entangled states is considered. Different from the known probability schemes, we propose and study a method for teleporting a prototypical single-qubit rotation on a remote receiver with unit fidelity and unit probability by using two partially entangled pairs. The method is applicable to any two partially entangled pairs satisfying the condition that their smaller Schmidt coefficients γ and η are (2γ+2η-2γη-1)≥0. In our scheme, the sender's local generalized measurement described by a positive operator-valued measurement (POVM) lies at the heart. We construct the required POVM. The fact that the controlled teleportation of single-qubit rotation could be realized exactly using two partially entangled pairs is also notable. A sender could teleport a rotation on a remote receiver, an arbitrary one of the two receivers, via the control of the other in a network.

N rotations can be teleported simultaneously onto a group of remote qubits deterministically or probabilistically with the aid of an entangled qudit pair. We present a scheme for such a kind of remote control of quantum gate. We are mainly focused on the remote rotation around a fixed axis. We first present an explicit scheme for deterministically and exactly teleporting the N rotations by using a maximally entangled qudit pair as quantum channel. We also put forward a scheme for probabilistically implementing the N remote rotations with unit fidelity by employing a partially entangled qudit pair as the quantum channel. An analysis of the scheme indicates that use of partially entangled quantum channel for teleporting the N rotations leads to the problem of "the general optimal information extraction".

Thermal entanglement of a two-qubit Heisenberg XXZ chain in the presence of different Dzyaloshinskii–Moriya (DM) anisotropic antisymmetric interactions and entanglement teleportation using two independent Heisenberg chains as quantum channel are investigated. It is found that the anisotropic coupling coefficient J_z (z-component exchange constant) and DM interactions can excite the entanglement, and x-component DM interaction D_x has a more remarkable influence than the z-axis DM interaction D_z for exchange constant J > 0 (antiferromagnetic) case, which is contrary to coupling coefficient J < 0 (ferromagnetic) case. The output entanglement and fidelity increase with increasing z-axis coupling parameter J_z for both the antiferromagnetic J > 0 case and ferromagnetic J < 0 case. By introducing the different DM interactions, it is superior to teleportate initial state by using the D_z interaction in the model for J > 0 case. But for J < 0 case, the D_x interaction is better, and the output concurrence and fidelity can reach the maximum value 1 with suitable D_x.

An optical scheme of the quantum teleportation of superposed coherent states from light pulse to the atoms in Bose–Einstein condensate in terms of optical elements is presented. Beam splitters, photodetectors, cross-Kerr medium, and coherent state sources are needed in this scheme. The probability of successful teleportation is also obtained.