Teleportation of Post-Selected Quantum States

Daniel Collins

H. H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL

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Abstract

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 $\it{post}$-selected. Post-selection of a state $\Phi$ means that after Alice has finished her experiment she performs a measurement and only keeps runs of the experiment where the measurement outcome is $\Phi$. We also demonstrate pre and post-selected $\it{port}$-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.

How can we send a quantum state from one place to another? It is tricky as quantum states tend to decohere, and the uncertainty principle prevents us from converting a quantum state to classical bits to be sent down our regular phone lines. $\textbf{Teleportation}$ is the solution. It uses pre-shared entanglement along with classical bits to send the quantum state, neatly avoiding decoherence and the uncertainty principle. Here we investigate teleporting a $\textbf{post-selected}$ state from one place to another. Post-selection means that we condition on a system being in a particular state at the end of the experiment. The post-selected state can be calculated at earlier times by retrodicting it $\textbf{backwards in time}$. Is it possible to teleport a state which retrodicts backwards in time, when we ourselves move forwards in time? We show how it can be done, and as an extension show how to perform instantaneous joint measurements and computations on post-selected multipartite systems.

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