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 c
odes 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.
Quantum repeaters (QRs) provide a way of enabling long distance quantum communication by establishing entangled qubits between remote locations. We investigate a new approach to QRs in which quantum information can be faithfully transmitted via a noi
sy 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 required for our scheme has favorable poly-logarithmic scaling with the distance across which the communication is desired.
We introduce a new genuinely 2N qubit state, known as the mirror state with interesting entanglement properties. The well known Bell and the cluster states form a special case of these mirror states, for N=1 and N=2 respectively. It can be experiment
ally realized using $SWAP$ and multiply controlled phase shift operations. After establishing the general conditions for a state to be useful for various communicational protocols involving quantum and classical information, it is shown that the present state can optimally implement algorithms for the quantum teleportation of an arbitrary N qubit state and achieve quantum information splitting in all possible ways. With regard to superdense coding, one can send 2N classical bits by sending only N qubits and consuming N ebits of entanglement. Explicit comparison of the mirror state with the rearranged N Bell pairs and the linear cluster states is considered for these quantum protocols. We also show that mirror states are more robust than the rearranged Bell pairs with respect to a certain class of collisional decoherence.
We establish a theoretical understanding of the entanglement properties of a physical system that mediates a quantum information splitting protocol. We quantify the different ways in which an arbitrary $n$ qubit state can be split among a set of $k$
participants using a $N$ qubit entangled channel, such that the original information can be completely reconstructed only if all the participants cooperate. Based on this quantification, we show how to design a quantum protocol with minimal resources and define the splitting efficiency of a quantum channel which provides a way of characterizing entangled states based on their usefulness for such quantum networking protocols.
Quantum conversation is a way in which two parties can communicate classical information with each other using entanglement as a shared resource. We present this scheme using a multipartite entangled state after describing its generation through appr
opriate circuit diagrams. We make use of a discrimination scheme which allows one to perform a measurement on the system without destroying its entanglement. We later prove that this scheme is secure in a noiseless and a lossless quantum channel.
