Quantum Teleportation of an Arbitrary N-qubit State via EPR Channels

Abstract

This paper demonstrates that an arbitrary -qubit state can be faithfully and deterministically teleported from Alice to Bob via pairs of EPR channels. The analytical expression of the reconstruct criterion is derived explicitly in the most general case, with a strict proof through mathematical induction method. Introduction Quantum teleportation is a demonstration of the astonishing features of quantum mechanics, which can transport an unknown quantum state from one site to another via previously shared entanglement, classical communications and local operations. In 1993, Bennett et al. [1] proposed the first quantum teleportation protocol, using a maximally entangled two-qubit state to teleport an arbitrary single-qubit state. In 1997, this protocol was experimentally demonstrated [2]. Thereafter, perfect teleportation of an arbitrary single-qubit state, using tripartite GHZ state [3], fourpartite GHZ state [4], SLOCC equivalent W-class state [5] and cluster state [6] were proposed, respectively. Meanwhile, perfect teleportation of an arbitrary two-qubit state, using tensor product of two Bell states [7], tensor product of two orthogonal states [8], genuinely entangled five-qubit state [9], five-qubit cluster state [10] and six-qubit genuinely entangled state [11] were proposed, respectively. When it comes to N-qubit states, there are schemes that can only teleport certain kinds of states, such as N-qubit state of generalized Bell-type[12], N-qubit W state[13], N-qubit W-like state[14] and N-qubit GHZ state[15]. There are also research on the teleportation of an arbitrary N-qubit state employing various channels, e.g., non-maximally entangled Bell state channel [16], the composite GHZ-Bell channel [17], genuine multipartite entanglement quantum channel [18, 19] and N pairs of EPR channel [7, 20]. In [16], the scheme succeeds with unit fidelity but less than unit probability. All the schemes in [7, 17-20] can accomplish the teleportation deterministically. However, in [17-19], multi-particle joint measurement is required and no analytical expression of the criterion is provided. In [7], N Bell state measurements are required but no proof was provided. In [20], Latin square was used to deduce the criterion, which is not a strict proof for arbitrary N either. This motivates us to further study the teleportaion of an arbitrary N-qubit state via EPR channels to provide an explicit analytical expression of the reconstruct criterion as well as a strict proof. In this paper, we explicitly show that an arbitrary N-qubit state can be faithfully and deterministically teleported from Alice to Bob via N pairs of EPR channels. It only requires N Bell state measurements by the sender and N single-qubit transformations by the receiver. The strict proof through mathematical induction is presented and the analytical expression of the criterion for the receiver to reconstruct the desired state is derived explicitly in the most general case. Quantum Teleportation of an Arbitrary N-qubit State The most general form of a -qubit state is given by