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Ebits at a distance: quantum algorithms and circuits for teleportation of quantum resources

Ntevetzakis Georgios

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Summary

An ebit is a pair of quantum mechanically entangled qubits i.e. locally un-factorizable state vectors of bipartite quantum states. The ebits constitute building blocks of the theoretical analyses and the technological tasks which are put forward in the area of quantum computation and information. Functioning as computational and communicational resource ebits are used in various quantum algorithms, most notably the state teleportation and quantum gate teleportation algorithms. This work addresses the problem of creating ebits at a distance by various low complexity elementary teleportation algorithms. The construction of quantum circuits follows the LOCC-SE protocol, according to which the allowed state transformations are restricted to local operations (LO), classical communication (CC) and shared quantum entanglement (SE). Explicitly the work investigates two types of quantum resource teleportation: in the first type single qubit state and gate teleportation is achieved, while in the second one the achievement concerns the state and gate teleportation of ebits, namely non-local quantum resources. The work investigates a unifying formalism for the respective quantum algorithms and provides relevant analytic proofs, quantum circuits and quantification of the classical and quantum resources required for their implementation.

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