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arXiv:quant-ph/9908036 · Physical Review Letters

Universal Teleportation with a Twist

Samuel L. Braunstein, Giacomo Mauro D’Ariano, Gerard J Milburn, Massimiliano Federico Sacchi

Published Apr 10, 2000• 152 citations
arXivHTMLPDF

Abstract

We give a transfer theorem for teleportation based on twisting the entanglement measurement. This allows one to say what local unitary operation must be performed to complete the teleportation in any situation, generalizing the scheme to include overcomplete measurements, non-Abelian groups of local unitary operations (e.g., angular momentum teleportation), and the effect of nonmaximally entangled resources.

DOI
10.1103/physrevlett.84.3486

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We give a transfer theorem for teleportation based on twisting the entanglement measurement. This allows one to say what local unitary operation must be performed to complete the teleportation in any situation, generalizing the scheme to include overcomplete measurements, non-Abelian groups of local unitary operations (e.g., angular momentum teleportation), and the effect of nonmaximally entangled resources.
Mathematical connection between the quantum teleportation, the most unique feature of quantum information processing, and the black hole final state is studied taking into account the nontrivial spacetime geometry. We use the twist operation for the generalized entanglement measurement and the final-state boundary conditions to obtain transfer theorems for the black hole evaporation. This would enable us to put together the universal quantum teleportation and the black hole evaporation in the unified mathematical footing. For a renormalized post selected final state of outgoing Hawking radiation, we found that the information content, quantified by the mixedness of the state, is preserved only in the special case of the final-state boundary condition in the microcanonical form, which resembles a perfect teleportation channel.
In accordance with the principle of superposition，for the teleportation of an arbitrary three-particle state via three pair nonmaximally entangled particles, the system state of particles can be expanded by Bell bases and transformation operator, and the teleportation can be realized only by performing a inverse transformation. The relation of transformation operators with unitary operation is discussed. The necessary condition to realize the teleportation is that the transformation operators have inverse operators.
A scheme for teleportation of n-particle arbitrary states via n pairs of EPR states is proposed.In the scheme,we discovered the internal relationship between the result of Alice's measurement and the unitary transformation performed by Bob(the receiver),and the corresponding expressions were described.Thus when Bob receiving the result of Alice' Bell measurement,he can ascertain immediately the corresponding unitary transformation he must performed in order to implement the teleportation protocol,which is particularly important for the case that n is very large.
A scheme of teleportation of the three-particle W entangled state via nonmaximally entangled Cluster state is proposed in the paper. Firstly, an auxiliary particle is introduced, and two particles in quantum channel carry out CNOT operation on it; secondly, distorted state caused by nonmaximally entangled quantum channel can be recovered by constructing unitary transform matrix; finally, the teleportation of entangled W state can be achieved with probability. The Bell measurement can be reduced and the resource of quantum channels can be saved for using one entangled Cluster state as quantum channel.
We develop an angular momentum representation and implementation of the Clifford+T set of unitaries for qutrits. We show that local gates from this set can be realized by the sole use of suitable rotations and one-axis-twisting operations, which are at most quadratic in the angular momentum operators and thus can be experimentally realized in many quantum systems. Controlled rotations are shown to only require linear angular momentum couplings and, as a consequence, the full qutrit Clifford+T set is shown to be expressed solely in terms of two-body angular momentum couplings, rotations and one-axis-twisting operations. By employing the Jordan-Schwinger map, we show an analogous implementation in terms of bosonic modes, improving on the number of modes with regard to a previous scheme. Moreover, we employ the cross-Kerr interaction in order to obtain any qutrit Clifford+T gate for bosonic modes. We illustrate our findings with simple schemes for preparing entangled states of interest.