Despite the tremendous progress of quantum cryptography, efficient quantum communication over long distances (≥1000 km) remains an outstanding challenge due to fiber attenuation and operation errors accumulated over the entire communication distance. Quantum repeaters (QRs), as a promising approach, can overcome both photon loss and operation errors, and hence significantly speedup the communication rate. Depending on the methods used to correct loss and operation errors, all the proposed QR schemes can be classified into three categories (generations). Here we present the first systematic comparison of three generations of quantum repeaters by evaluating the cost of both temporal and physical resources, and identify the optimized quantum repeater architecture for a given set of experimental parameters for use in quantum key distribution. Our work provides a roadmap for the experimental realizations of highly efficient quantum networks over transcontinental distances.

Quantum repeaters (QRs) provide a way of enabling long distance quantum communication by establishing entangled qubits between remote locations. In this Letter, we investigate a new approach to QRs in which quantum information can be faithfully transmitted via a noisy channel without the use of long distance teleportation, thus eliminating the need to establish remote entangled links. Our approach makes use of small encoding blocks to fault-tolerantly correct both operational and photon loss errors. We describe a way to optimize the resource requirement for these QRs with the aim of the generation of a secure key. Numerical calculations indicate that the number of quantum memory bits at each repeater station required for the generation of one secure key has favorable poly-logarithmic scaling with the distance across which the communication is desired.PACS numbers: 03.67. Dd, 03.67.Hk, 03.67.Pp. Quantum communication across long distances (10 3 -10 4 km) can significantly extend the applications of quantum information protocols such as quantum cryptography [1] and quantum secret sharing [2, 3] which can be used for the creation of a secure quantum internet [4]. Quantum communication can be carried out by first establishing a remote entangled pair between the sender and the receiver and using teleportation to transmit information faithfully. However, there are two main challenges that have to be overcome. First, fiber attenuation during transmission leads to an exponential decrease in entangled pair generation rate. Second, several operational errors such as channel errors, gate errors, measurement errors and quantum memory errors severely degrade the quality of entanglement used for secure key generation. In addition, quantum states cannot be amplified or duplicated deterministically in contrast to classical information [5]. Establishing quantum repeater (QR) stations based on entanglement distribution is the only currently known approach to long-distance quantum communication using conventional optical fibers without exponential penalty in time and resources.A number of schemes have been proposed for long distance quantum communication using , most of which could be broadly classified into three classes. The first class of QRs [6][7][8][9] reduces the exponential scaling of fiber loss to polynomial scaling by introducing intermediate QR nodes. However, this scheme for long distance quantum communication is relatively slow [13], even after optimization [14], limited by the time associated with two-way classical communication between remote stations required for the entanglement purification process needed to correct operational errors [15]. In contrast, the second class of QRs introduce quantum encoding and classical error correction to replace the entanglement purification with classical error correction, handling all operational errors [10,16]. As a consequence, the entanglement generation rate further improves from 1/O(poly(L tot )) to 1/O(poly(log(L tot ))) where L tot is the total distance of communicat...

We investigate the usefulness of a recently introduced five qubit state by Brown et al .[1] for quantum teleportation, quantum state sharing and superdense coding. It is shown that this state can be utilized for perfect teleportation of arbitrary single and two qubit systems. We devise various schemes for quantum state sharing of an arbitrary single and two particle state via cooperative teleportation. We later show that this state can be used for superdense coding as well. It is found that five classical bits can be sent by sending only three quantum bits.

We provide various schemes for the splitting up of Quantum information into parts using the four and five partite cluster states. Explicit protocols for the Quantum information splitting (QIS) of single and two qubit states are illustrated. It is found that the four partite cluster state can be used for the QIS of an entangled state and the five partite cluster state can be used for QIS of an arbitrary two qubit state. The schemes considered here are also secure against certain eavesdropping attacks.

We investigate cat codes that can correct multiple excitation losses and identify two types of logical errors: bit-flip errors due to excessive excitation loss and dephasing errors due to quantum backaction from the environment. We show that selected choices of logical subspace and coherent amplitude significantly reduce dephasing errors. The trade-off between the two major errors enables optimized performance of cat codes in terms of minimized decoherence. With high coupling efficiency, we show that one-way quantum repeaters with cat codes feature a boosted secure communication rate per mode when compared to conventional encoding schemes, showcasing the promising potential of quantum information processing with continuous variable quantum codes.

The usefulness of the genuinely entangled six qubit state that was recently introduced by Borras et al. is investigated for the quantum teleportation of an arbitrary three qubit state and for quantum state sharing (QSTS) of an arbitrary two qubit state. For QSTS, we explicitly devise two protocols and construct sixteen orthogonal measurement basis which can lock an arbitrary two qubit information between two parties.

We investigate the usage of highly efficient error correcting codes of multilevel systems to protect encoded quantum information from erasure errors and implementation to repetitively correct these errors. Our scheme makes use of quantum polynomial codes to encode quantum information and generalizes teleportation based error correction for multilevel systems to correct photon losses and operation errors in a fault-tolerant manner. We discuss the application of quantum polynomial codes to one-way quantum repeaters. For various types of operation errors, we identify different parameter regions where quantum polynomial codes can achieve a superior performance compared to qubit based quantum parity codes.

We show that quantum Reed-Solomon codes constructed from classical Reed-Solomon codes can approach the capacity on the quantum erasure channel of d-level systems for large dimension d.We study the performance of one-way quantum repeaters with these codes and obtain a significant improvement in key generation rate compared to previously investigated encoding schemes with quantum parity codes and quantum polynomial codes. We also compare the three generation of quantum repeaters using quantum Reed-Solomon codes and identify parameter regimes where each generation performs the best.