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Port-based teleportation of continuous quantum variables

Jason Boisselle

Published Aug 27, 2014• 0 citations
OpenAlex

Abstract

Quantum teleportation allows to transmit quantum information using classical information and entanglement only. Port-based teleportation is a variation of this procedure that involves simpler recovery operations to obtain the transmitted quantum information. This provides significant advantages in different applications such as instantaneous non-local computation. \nWe study port-based teleportation for continuous variable systems. We connect this problem to hypothesis testing, generalizing a result already known for finite-dimensional systems. Similarly, we present a relation between entanglement fidelity and average fidelity valid for both finite and infinite-dimensional systems. Finally, we present a protocol that reduces port-based teleportation for infinite-dimensional systems to port-based teleportation of finite-dimensional systems which allows us to show that the former task is, at least in principle, possible with a finite amount of resources.

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Quantum teleportation allows to transmit quantum information using classical information and entanglement only. Port-based teleportation is a variation of this procedure that involves simpler recovery operations to obtain the transmitted quantum information. This provides significant advantages in different applications such as instantaneous non-local computation. \nWe study port-based teleportation for continuous variable systems. We connect this problem to hypothesis testing, generalizing a result already known for finite-dimensional systems. Similarly, we present a relation between entanglement fidelity and average fidelity valid for both finite and infinite-dimensional systems. Finally, we present a protocol that reduces port-based teleportation for infinite-dimensional systems to port-based teleportation of finite-dimensional systems which allows us to show that the former task is, at least in principle, possible with a finite amount of resources.
Abstract Port-based teleportation (PBT) is a generalisation of the standard teleportation protocol which does not require unitary operations by the receiver. This comes at the price of requiring N > 1 entangled pairs, while N = 1 for the standard teleportation protocol. The lack of correction unitaries allows PBT to be used as a fundamental theoretical tool to simulate arbitrary channels with a general resource, with applications to study fundamental limits of quantum communication, cryptography and sensing, and to define general programmable quantum computers. Here we introduce a general formulation of port-based teleportation in continuous variable systems and study in detail the N = 2 case. In particular, we interpret the resulting channel as an energy truncation and analyse the kinds of channels that can be naturally simulated after this restriction.
In this paper, we introduce optimal versions of a multi-port based teleportation scheme allowing to send a large amount of quantum information. We fully characterise probabilistic and deterministic case by presenting expressions for the average probability of success and entanglement fidelity. In the probabilistic case, the final expression depends only on global parameters describing the problem, such as the number of ports N , the number of teleported systems k , and local dimension d . It allows us to show square improvement in the number of ports with respect to the non-optimal case. We also show that the number of teleported systems can grow when the number N of ports increases as o(N) still giving high efficiency. In the deterministic case, we connect entanglement fidelity with the maximal eigenvalue of a generalised teleportation matrix. In both cases the optimal set of measurements and the optimal state shared between sender and receiver is presented. All the results are obtained by formulating and solving primal and dual SDP problems, which due to existing symmetries can be solved analytically. We use extensively tools from representation theory and formulate new results that could be of the separate interest for the potential readers.
Entanglement is a crucial resource in quantum information theory. We investigate the use of different forms of entangled states in continuous variable quantum teleportation, specifically the use of a finite-basis entanglement resource. We also consider the continuous variable teleportation of finite-basis states, such as qubits, and present results that point to the possibility of an efficient conditional scheme for continuous variable teleportation of such states with near-unit fidelity using finite-basis entanglement.
The wave-particle duality of light has led to two different encodings of optical quantum information. One approach, referred to as the discrete-variable (DV) one, relies on finite dimensional quantum systems, while the other one, referred to as the continuous-variable (CV) one, is based on wave-like states belonging to an infinite dimensional Hilbert space. These two encodings have historically been separated, but recently, new hybrid protocols which aim at combining the advantages of the two encodings have emerged [1] . In that prospect our recent demonstration of the measurement-induced generation of hybrid entanglement between discrete- and continuous-variable quantum states [2] , [3] , located at distant places and connected by a lossy channel, has opened the way to the implementation of hybrid protocols and heterogeneous quantum networks. Following the first protocols based on this resource, such as the remote preparation of continuous-variable qubits [4] , or a violation of an Einstein-Podolsky-Rosen steering inequality [5] , we will here report our latest experimental results on entanglement swapping and quantum teleportation protocols using hybrid entangled states based on different encodings [6] .
Teleportation allows Alice to send a pre-prepared quantum state to Bob using only pre-shared entanglement and classical communication. Here we show that it is possible to teleport a state which is also post -selected. Post-selection of a state Φ means that after Alice has finished her experiment she performs a measurement and only keeps runs of the experiment where the measurement outcome is Φ . We also demonstrate pre and post-selected port -based teleportation. Finally we use these protocols to perform instantaneous non-local quantum computation on pre and post-selected systems, and significantly reduce the entanglement required to instantaneously measure an arbitrary non-local variable of spatially separated pre and post-selected systems.
We analyse the problem of transmitting a number of unknown quantum states or one composite system in one go. We derive a lower bound on the performance of such process, measured in the entanglement fidelity. The obtained bound is effectively computable and outperforms the explicit values of the entanglement fidelity calculated for the pre-existing variants of the port-based protocols, allowing for teleportation of a much larger amount of quantum information. The comparison with the exact formulas and similar analysis for the probabilistic scheme is also discussed. In particular, we present the closed-form expressions for the entanglement fidelity and for the probability of success in the probabilistic scheme in the qubit case in the picture of the spin angular momentum.