Quantum information distribution via entanglement

In the quantum teleportation scheme [1], quantum information of an unknown state of a d-level particle (an “input” particle) is faithfully transmitted from a sender (Alice) to a remote receiver (Bob) via an initially shared pair of maximally entangled particles. The distributed entangled particles shared by Alice and Bob function as a quantum information channel for the faithful transmission. Quantum teleportation has been demonstrated in several successful experiments [2]. It represents the basic building block of future quantum communication networks between distant parties [3]. In addition to the “one-to-one” quantum communication of teleportation, it is natural to consider “one-to-many” quantum communication via quantum channels, i.e. quantum broadcasting from a sender to several spatially separated receivers. However, it is not possible to perform “one-to-many” quantum communication perfectly, because the nocloning theorem [4] forbids perfect duplication of quantum information. Approximate methods for quantum cloning are known but these methods require all parties (the original and all the approximate copies) to be in one place. Our strategy for “one-to-many” quantum communication is to distribute quantum information of a particle from a sender to many distant receivers. Such a strategy, dubbed quantum telecloning, has been suggested in [5]. In the quantum telecloning scheme, information of an input qubit (a d = 2-level particle) is distributed into M particles which are optimal clones and M − 1 which are ancilla particles, all spatially separated from each other. This transmission is achieved by first establishing a particular initial entangled state between the sender and receivers. The protocol of quantum telecloning is then similar to that for original quantum teleportation [1], consisting of a joint measurement by Alice, 2-bit classical communication from Alice to Bob and a local operation by Bob. This “optimal broadcasting” of quantum information relies on the structure of the distributed entanglement which functions as a one to many quantum communication channel. Recently, the telecloning protocol has been generalized to the case of N (≤M) identical input qubits being distributed to M spatially separated parties by Dür [6]. In this generalization, the same entangled state of [5] is used for the quantum channel, but a more generalized POVM is performed for the joint measurement. We also consider variation of this distribution method for alternative applications. In this paper, we present optimal quantum information broadcasting for d-level particles, asymmetric telecloning of qubits, and quantum error correction via entanglement as examples of a generalization of quantum teleportation to one-to-many quantum communication. The important rule of our game is that the receivers are spatially separated from each other so that we do not allow any global operations among receivers. There is an alternative trivial way to distribute quantum information from a sender to many receivers if we allow the sender to run quantum networks that involve global operations of many particles. In this case, the sender first performs quantum networks for encoding one particle information into several particles in her site. Then she transmits the encoded particles to each receiver using the original teleportation scheme with two particle maximally entangled state [1]. For the transmission, M log2 d e-bits of entanglement are required to distribute quantum information of a d-level particle into the spatially separated M receivers. The sender performs the measurement M times and uses Md/2 bits of classical communication from the sender to receivers. On the other hand, in our direct information distribution scheme, multiparticle entanglement is used simultaneously for both encoding information and transmission. We need only a single joint measurement and require only d/2 bits of classical communication (announced publically to all