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Physical Review A

Teleportation ofN-dimensional states

Stig Stenholm, P. J. Bardroff

Published Dec 1, 1998• 96 citations
Publisher

Abstract

We present a general solution to the construction of such an entanglement in an N-dimensional Hilbert space that effects state teleportation. For $N>2$ the construction is nonunique and can be chosen to transfer the state to a preselected basis. We discuss possible applications to state preparation in various physical systems.

DOI
10.1103/physreva.58.4373

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We present a general solution to the construction of such an entanglement in an N-dimensional Hilbert space that effects state teleportation. For N>2N>2N>2 the construction is nonunique and can be chosen to transfer the state to a preselected basis. We discuss possible applications to state preparation in various physical systems.
We present a scheme for probabilistic transformation of special quantum states assisted by auxiliary qubits. In our scheme, if quantum states can be rewritten in a particular form, it is possible to transform such states into other states using lower-dimensional unitary operations that can be more easily realized in physical experiments. Furthermore, as an important application, we propose a generalized scheme that helps construct faithful quantum channels via various probabilistic channels when considering the existence of nonmaximally-entangled states.
We discuss the geometry of states of quantum systems in an n-dimensional Hilbert space in terms of an explicit parameterization of all such systems. The geometry of the space of pure as well as mixed states for n -state systems is discussed. The parameterization is particularly useful since it allows for the simple construction and isolation of various physically meaningful subspaces of the space of all density matrices. This is used to describe possible geometric phases, their calculation, and analyze entropy and purity (or linear entropy) functions. In particular we provide conditions under which nontrivial abelian and/or nonabelian geometric phases aris in these subspaces in terms of the given parameterization, an explicit example is given, and multidimensional ientopic surfaces are discused.
Establishing a quantum communication network would provide advantages in areas such as security and information processing. Such a network would require the implementation of quantum teleportation between remote parties. However, for photonic "qudits" of dimension greater than two, this teleportation always fails due to the inability to carry out the required quantum Bell-state measurement. A quantum communication protocol called Superdense Teleportation (SDT) can allow the reconstruction of a state without the usual 2-photon Bell-state measurements, enabling the protocol to succeed deterministically even for high dimensional qudits. This technique restricts the class of states transferred to equimodular states, a type of superposition state where each term can differ from the others in phase but not in amplitude; this restricted space of transmitted states allows the transfer to occur deterministically. We report on our implementation of SDT using photon pairs that are entangled in both polarization and temporal mode. After encoding the phases of the desired equimodular state on the signal photon, we perform a complete tomography on the idler photon to verify that we properly prepared the chosen state. Beyond our tabletop demonstration, we are working towards an implementation between a space platform in low earth orbit and a ground telescope, to demonstrate the feasibility of space-based quantum communication. We will discuss the various challenges presented by moving the experiment out of the laboratory, and our proposed solutions to make Superdense Teleportation realizable in the space setting.