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arXiv:1512.05168 · Quantum Measurements and Quantum Metrology

Teleportation in an indivisible quantum system

E.O. Kiktenko, Aleksey K. Fedorov, V.I. Man’ko

Published Jan 1, 2016• 5 citations
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Abstract

Abstract Teleportation protocol is conventionally treated as a method for quantum state transfer between two spatially separated physical carriers. Recent experimental progress in manipulation with high-dimensional quantum systems opens a new framework for implementation of teleportation protocols. We show that the one-qubit teleportation can be considered as a state transfer between subspaces of the whole Hilbert space of an indivisible eight-dimensional system. We explicitly show all corresponding operations and discuss an alternative way of implementation of similar tasks.

DOI
10.1515/qmetro-2016-0003

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Abstract Teleportation protocol is conventionally treated as a method for quantum state transfer between two spatially separated physical carriers. Recent experimental progress in manipulation with high-dimensional quantum systems opens a new framework for implementation of teleportation protocols. We show that the one-qubit teleportation can be considered as a state transfer between subspaces of the whole Hilbert space of an indivisible eight-dimensional system. We explicitly show all corresponding operations and discuss an alternative way of implementation of similar tasks.
Teleportation protocol is conventionally treated as a method for quantum state transfer between two spatially separated physical carriers. Recent experimental progress in manipulation with high-dimensional quantum systems opens a new framework for implementation of teleportation protocols. We show that the one-qubit teleportation can be considered as a state transfer between subspaces of the whole Hilbert space of an indivisible eight-dimensional system. We explicitly show all corresponding operations and discuss an alternative way of implementation of similar tasks.
Through the process of quantum teleportation, a transfer of quantum information takes place from one particle to another while maintaining zero physical movement between the two. Quantum teleportation requires two entangled particles along with projective measurements followed by exchanging two bits of classical information. The process requires quantum mechanics principles which combine superposition with entanglement. Quantum entanglement occurs when two or more particles create an inseparable relationship that cuts off a separate description of an individual particle. Experimental realizations of quantum teleportation continue to operate on different physical platforms which include photons as well as atoms and superconducting circuits. Applications of Quantum teleportation includes quantum computing, secure communication, and cryptography. In future Scientists believe that a breakthrough in quantum computing technology could make teleportation a reality, including the ability to teleport a whole human. This paper provides the present research in quantum teleportation, including the theoretical framework, experimental implementations, and potential applications. We also discuss the challenges and limitations of quantum teleportation and propose future directions for research.
Quantum teleportation is one of the most enigmatic protocols realized so far in the area of quantum information, allowing for the transfer of quantum information assisted by an entangled state. It was a subject of science fiction 20 years ago, but now is a fundamental experimental protocol and quantum primitive for quantum information processing tasks. There have been many successful realizations of teleportation ranging from those using photons, atoms, and hybrid systems and long-range teleportation beyond 100km has already been achieved multiple times. These however typically involve explicitly single particle systems or effective few-particle systems. For larger (visible to the naked eye) objects involving many particles, teleportation is typically more difficult due to the fast decoherence such macroscopic objects suffer. In this case, the entanglement disappears almost as soon as it is created, making it useless for such tasks. More recently, teleportation was accomplished in the continuous variables (CV) framework between two atomic ensembles [1]. As remarkable as these achievements are, teleportation schemes that are known today (qubit/CV) do not allow us to teleport more complex quantum states at the macroscopic level. For example, while it is possible in principle to extend teleportation to multiple qubits, on a macroscopic level this is prohibitively complicated and highly susceptible to decoherence. For atomic ensemble CV based schemes, the teleported states are restricted to small displacements from the completely Sx-polarized state on the Bloch sphere.
We investigate the problem of teleporting an unknown qubit state to a recipient via a channel of 2L2{\mathcal L}2L qubits. In this procedure a protocol is employed whereby L{\mathcal L}L Bell state measurements are made and information based on these measurements is sent via a classical channel to the recipient. Upon receiving this information the recipient determines a local gate which is used to recover the original state. We find that the 22L2^{2\mathcal L}22L-dimensional Hilbert space of states available for the channel admits a decomposition into four subspaces. Every state within a given subspace is a perfect channel, and each sequence of Bell measurements projects 2L2{\mathcal L}2L qubits of the system into one of the four subspaces. As a result, only two bits of classical information need be sent to the recipient for them to determine the gate. We note some connections between these four subspaces and ground states of many-body Hamiltonian systems, and discuss the implications of these results towards understanding entanglement in multi-qubit systems.
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.