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arXiv:quant-ph/9712027 · Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences

Quantum communication and the creation of maximally entangled pairs of atoms over a noisy channel

H. J. Briegel, Wolfgang Dür, S. J. van Enk, J. I. Cirac, P. Zoller

Published Aug 15, 1998• 7 citations
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Abstract

We show how to create maximally entangled EPR pairs between spatially distant atoms, each of them inside a high–Q optical cavity, by sending photons through a general, noisy channel, such as a standard optical fiber. An error correction scheme that uses few auxiliary atoms in each cavity effectively eliminates photoabsorption and other transmission errors. This realizes the ‘absorption free channel’. A concatenation protocol using the absorption free channel allows for quantum communication with single qubits over distances much larger than the coherence length of the channel.

DOI
10.1098/rsta.1998.0252

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We show how to create maximally entangled EPR pairs between spatially distant atoms, each of them inside a high–Q optical cavity, by sending photons through a general, noisy channel, such as a standard optical fiber. An error correction scheme that uses few auxiliary atoms in each cavity effectively eliminates photoabsorption and other transmission errors. This realizes the ‘absorption free channel’. A concatenation protocol using the absorption free channel allows for quantum communication with single qubits over distances much larger than the coherence length of the channel.
We suggest a method to perform a quantum logic gate between distant quantum bits (qubits) by off-resonant field-atom dispersive interactions. The scheme we present is shown to work ideally even in the presence of errors in the photon channels used for communication. The stability against errors arises from the paradoxical situation that the transmitted photons carry no information about the state of the qubits. In contrast to a previous proposal for ideal communication [Phys. Rev. Lett. 78, 4293 (1997)] our proposal only involves single atoms in the sending and receiving devices.
The natural choice of physical qubit for quantum communication is the photon: a photon can be transmitted quickly from the sender to a distant receiver and the technology for creating, manipulating, distributing, and measuring light pulses is well established. Many of these classical techniques can also be employed for quantum communication protocols. We will therefore focus our attention on optical setups for quantum communication. We will study a number of optical setups in the next few sections and use the conventions introduced in Chapter 4 to analyze them. In particular, we will assume that the qubits are encoded in the degrees of freedom of a single photon. Some of the main technical challenges in quantum communication arise from this need to work with single photon pulses. For instance, photons do not interact with each other in vacuum or linear media, and interactions between two photons in non-linear optical media are relatively small, so that realizing entangling two photon gates via coherent interactions is a challenging task. The quantum communication schemes discussed here circumvent this technical problem to a large extent. They only use non-linear optical materials for parametric down-conversion to create Bell-pairs of photons and then exploit standard linear optical devices and photo-detectors to manipulate them. No further non-linear entangling gates are required. Parametric down-conversion In non-linear optical media a single photon can be down-converted into a pair of photons. In this coherent process the incoming photon is destroyed and two photons of lower energy are created.
The creation of a quantum network is an important goal of quantum information processing. Long distance quantum communication with high fidelity is the main obstacle in achieving this goal. A scheme to transmit qubits without fidelity decrease over the noisy channel is presented. Using the idea of ‘time-bin entanglement’, the scheme works without any auxiliary particles and there is no resources increase with the length of the channel. A protocol proposed by Kalamidas [18] is suitable to realize our scheme with the current experimental technology.
Fiber-based classical communication is all-optical and uses light pulses reamplified and reshaped every 50-100 km in classical repeaters. Most compatible with this would be a quantum communication system which is also all-optical with quantum processing units placed in similar intervals. However, existing all-optical quantum communication protocols either require complicated quantum error correction steps for logical-qubit recoveries at every few kilometers or, over larger quantum repeater segments, they would at least depend on sharing complex multi-photon entangled states. Here we propose an all-optical memory-based quantum repeater for long-distance quantum communication, with quantum memories at each repeater station realized in the form of fiber loops combined with suitable quantum error correction codes for photon-loss protection. By sending only single-photon states through the fibers connecting the stations, such repeaters can operate in the classical infrastructure's long-segment regime. We analyze the performance of our scheme for the Gottesman-Kitaev-Preskill code, including a concatenation with the Steane code, as well as the single-photon quantum parity code for total distances up to 10000 km.