We propose a scheme to utilize photons for ideal quantum transmission between atoms located at spatially separated nodes of a quantum network. The transmission protocol employs special laser pulses that excite an atom inside an optical cavity at the sending node so that its state is mapped into a time-symmetric photon wave packet that will enter a cavity at the receiving node and be absorbed by an atom there with unit probability. Implementation of our scheme would enable reliable transfer or sharing of entanglement among spatially distant atoms. [ S0031-9007(97) We consider a quantum network consisting of spatially separated nodes connected by quantum communication channels. Each node is a quantum system that stores quantum information in quantum bits and processes this information locally using quantum gates [1] . Exchange of information between the nodes of the network is accomplished via quantum channels. A physical implementation of such a network could consist, e.g., of clusters of trapped atoms or ions representing the nodes, with optical fibers or similar photon "conduits" providing the quantum channels. Atoms and ions are particularly well suited for storing qubits in long-lived internal states, and recently proposed schemes for performing quantum gates between trapped atoms or ions provide an attractive method for local processing within an atom͞ion node [2] [3] [4] . On the other hand, photons clearly represent the best qubit carrier for fast and reliable communication over long distances [5, 6] , since fast and internal-state-preserving transportation of atoms or ions seems to be technically intractable. To date, no process has actually been identified for using photons (or any other means) to achieve efficient quantum transmission between spatially distant atoms [7] . In this Letter we outline a scheme to implement this basic building block of communication in a distributed quantum network. Our scheme allows quantum transmission with (in principle) unit efficiency between distant atoms 1 and 2 (see Fig. 1 ). The possibility of combining local quantum processing with quantum transmission between the nodes of the network opens the possibility for a variety of novel applications ranging from entangled-state cryptography [8], teleportation [9] , and purification [10] , and is interesting from the perspective of distributed quantum computation [11] . The basic idea of our scheme is to utilize strong coupling between a high-Q optical cavity and the atoms [5] forming a given node of the quantum network. By applying laser beams, one first transfers the internal state of an atom at the first node to the optical state of the cavity mode. The generated photons leak out of the cavity, propagate as a wave packet along the transmission line, and enter an optical cavity at the second node. Finally, the optical state of the second cavity is transferred to the internal state of an atom. Multiple-qubit transmissions can be achieved by sequentially addressing pairs of atoms (one at each node), as entanglements between arbitrarily located atoms are preserved by the state-mapping process. The distinguishing feature of our protocol is that by controlling the atom-cavity interaction, one can absolutely avoid the reflection of the wave packets from the second cavity, effectively switching off the dominant loss channel that would be responsible for decoherence in the communication process. For a physical picture of how this can be accomplished, let us consider that a photon leaks out of an optical cavity and propagates away as a wave packet. Imagine that we were able to "time reverse" this wave packet and send it back into the cavity; then this would restore the original (unknown) superposition state of the atom, provided we would also reverse the timing of the laser pulses. If, on the other hand, we are able to drive the atom in a transmitting cavity in such a way that the outgoing pulse were already symmetric in time, the wave packet entering a receiving cavity would "mimic" this time reversed process, thus "restoring" the state of the first atom in the second one. The simplest possible configuration of quantum transmission between two nodes consists of two atoms 1 and 2 which are strongly coupled to their respective cavity modes (see Fig. 1 ). The Hamiltonian describing the interaction of each atom with the corresponding cavity mode
We remark that at the physical layer there is of course a notion of state transfer in all quantum networks, for example the transfer of a state from an optical cavity at one network node onto a photon to create entanglement between two nodes REF .
Quantum State Transfer and Entanglement Distribution among Distant Nodes in a Quantum Network
Physical Review Letters
Physics