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

Concatenated quantum teleportation

Somshubhro Bandyopadhyay, Barry C. Sanders

Published Aug 18, 2005• 0 citations
Publisher

Abstract

Quantum teleportation should be able to teleport states or parts of states in arbitrarily large Hilbert spaces, which will require concatenation of quantum teleportation processes that operate for a fixed dimension. We introduce the concept of concatenated quantum teleportation and obtain exact expression for teleportation fidelities for two simple cases. We also derive the conditions when concatenated teleportation can be considered as quantum.

DOI
10.1117/12.620951

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Quantum teleportation should be able to teleport states or parts of states in arbitrarily large Hilbert spaces, which will require concatenation of quantum teleportation processes that operate for a fixed dimension. We introduce the concept of concatenated quantum teleportation and obtain exact expression for teleportation fidelities for two simple cases. We also derive the conditions when concatenated teleportation can be considered as quantum.
We analyze quantum teleportation for composite systems, specifically for concatenated teleporation (decomposing a large composite state into smaller states of dimension commensurate with the channel) and partial teleportation (teleporting one component of a larger quantum state). We obtain an exact expression for teleportation fidelity that depends solely on the dimension and singlet fraction for the entanglement channel and entanglement (measures by III concurrence) for the state; in fact quantum teleportation for composite systems provides an operational interpretation for III concurrence. In addition we obtain tight bounds on teleportation fidelity and prove that the average fidelity approaches the lower bound of teleportation fidelity in the high-dimension limit.
Quantum teleportation allows a "disembodied" transmission of unknown quantum states between distant quantum systems. Yet, all teleportation experiments to date were limited to a two-dimensional subspace of quantized multiple levels of the quantum systems. Here, we propose a scheme for teleportation of arbitrarily high-dimensional photonic quantum states and demonstrate an example of teleporting a qutrit. Measurements over a complete set of 12 qutrit states in mutually unbiased bases yield a teleportation fidelity of 0.75(1), which is well above both the optimal single-copy qutrit state-estimation limit of 1/2 and maximal qubit-qutrit overlap of 2/3, thus confirming a genuine and nonclassical three-dimensional teleportation. Our work will enable advanced quantum technologies in high dimensions, since teleportation plays a central role in quantum repeaters and quantum networks.
Summary form only given. Quantum teleportation is a transportation process of a quantum state where the quantum state is copied at a remote place while the original state id eliminated. We generalize the scheme of the quantum teleportation for "N-body" quantum states. Many-body quantum states are classified into uncorrelated and entangled states. An uncorrelated state can be factorized to the direct product of one-body states. The quantum teleportation of the uncorrelated state can be performed by teleporting its "one-body" states sequentially. Thus, teleporting uncorrelated states is trivial since it is practically equivalent to teleporting one body states. An entangled state, to the contrary, can not be factorized to the product of one-body states due to its entanglement.
Quantum teleportation is a transfer protocol of quantum states, which cannot be realized only with classical physics. The essence of this protocol is quantum entanglement, which was proposed by Einstein as a counter example for quantum mechanics. In terms of quantum information processing, quantum teleportation can be regarded as an “Identity” operation. So one can modify the quantum circuit to make an arbitrary operation and universal quantum computing. One of the application of the quantum computing is “quantum version of coherent communication”, which enables us to get the channel capacity beyond the classical limit (Shannon limit).