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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Qudit communication network

Jaewan Kim, Juhui Lee, Se-Wan Ji, Hyunchul Nha, Petr M. Anisimov, Jonathan P. Dowling

Published Oct 15, 2012• 1 citation
Publisher

Abstract

Optical coherent states can be interpreted as d-dimensional quantum systems, or qudits of even superposition of pseudo-number states. Cross-Kerr nonlinear interaction can generate the maximal entanglements of pseudo- phase and pseudo-number states from two opticl coherent states. Extended network of these entangled coherent states is a qudit cluster state and can be used as qudit communication network for d-dimensional teleportation or multi-user quantum cryptographic network.

DOI
10.1117/12.930452

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Optical coherent states can be interpreted as d-dimensional quantum systems, or qudits of even superposition of pseudo-number states. Cross-Kerr nonlinear interaction can generate the maximal entanglements of pseudo- phase and pseudo-number states from two opticl coherent states. Extended network of these entangled coherent states is a qudit cluster state and can be used as qudit communication network for d-dimensional teleportation or multi-user quantum cryptographic network.
Defining a computational basis of pseudo-number states, we interpret a coherent state of large amplitude, |α|⪢d/2π, as a qudit — a d-level quantum system — that is an even (meaning same size of amplitudes) superposition of d pseudo-number basis states. A pair of such coherent-state qudits can be maximally entangled by generalized Controlled-Z operation that is based on cross-Kerr nonlinearity, which can be weak for large d. Hence, a coherent-state optical qudit cluster state can be prepared by repetitive application of the generalized Controlled-Z operation to a set of coherent states. We thus propose an optical qudit teleportation as a simple demonstration of cluster state quantum computation.
A protocol of quantum communication is proposed in terms of the multi-qubit quantum teleportation through cluster states (Phys. Rev. Lett. \textbf{86}, 910 (2001)). Extending the cluster state based quantum teleportation on the basic unit of three qubits (or qudits), the corresponding multi-qubit network is constructed for both the qubits and qudits (multi-level) cases. The classical information costs to complete this communication task is also analyzed. It is also shown that this quantum communication protocol can be implemented in the spin-spin system on lattices.
Quantum Teleportation, the transfer of the state of one quantum system to another without direct interaction between both systems, is an important way to transmit information encoded in quantum states and to generate quantum correlations (entanglement) between remote quantum systems. So far, for photons, only superpositions of two distinguishable states (one "qubit") could be teleported. Here we show how to teleport a "qudit", i.e. a superposition of an arbitrary number d of distinguishable states present in the orbital angular momentum of a single photon using d beam splitters and d additional entangled photons. The same entanglement resource might also be employed to collectively teleport the state of d/2 photons at the cost of one additional entangled photon per qubit. This is superior to existing schemes for photonic qubits, which require an additional pair of entangled photons per qubit.
The authors of this paper propose an optical scheme for the generation of entangled coherent states which include the multi-mode and high-dimensional entangled coherent states.The scheme is based on the interaction of nonlinear Kerr medium and optical fields.The authors find that muliti-mode and high-dimensional entangled coherent states can be generated through proper selections of the fields′ initial states,the time of the interaction and the generalized bell measurement.The authors also find that the interaction of nonlinear Kerr media can generate entanglement when the states of input modes are prepared in coherent state and superposed Fock states.
Multiple photonic degrees of freedom can be explored to generate high-dimensional quantum states; commonly referred to as `qudits'. Qudits offer several advantages for quantum communications, including higher information capacity, noise resilience and data throughput, and lower information loss over different propagation mediums (free space, optical fibre, underwater) as compared to conventional qubits based communication system. However, qudits have been little exploited in literature, owing to their difficulty in transmission and detection. In this paper, for the first time, we develop and formulate the theoretical framework for transmission of classical information through entanglement distribution of qudits over two quantum channels in superposition of alternative causal order. For the first time we i) engineer quantum switch operation for 2-qudit systems and ii) formulate theoretical system model for entanglement distribution of qudits via quantum switch. Results show that entanglement distribution of a qudit provides a considerable gain in fidelity even with increase in noise.