Linear response of a pre- and post-selected system to an external field

Ravinder Rupchand Puri

Daniel Collins

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.

Mathias Frisch

Sumei Huang, G. S. Agarwal

We show the utility of the weak value amplification to observe the quantum interference between two close lying atomic coherent states in a post-selected atomic cat state, produced in a system of N identical two-level atoms weakly interacting with a single photon field. Through the observation of the negative parts of the Wigner distribution of the post-selected atomic cat state, we find that the post-selected atomic cat state becomes more nonclassical when the post-selected polarization state of the single photon field tends toward becoming orthogonal to its pre-selected state. We show that the small phase shift in the post-selected atomic cat state can be amplified via measuring the peak shift of its phase distribution when the post-selected state of the single photon field is nearly orthogonal to its pre-selected state. We find that the amplification factor of 15 [5] can be obtained for a sample of 10 [100] atoms. This effectively provides us with a method to discriminate between two close lying states on the Bloch sphere. We discuss possible experimental implementation of the scheme, and conclude with a discussion of the Fisher information.

Eugen Fick, Günter Sauermann

Matthew Leifer, Robert W. Spekkens

Many seemingly paradoxical effects are known in the predictions for outcomes of intermediate measurements made on pre- and post-selected quantum systems. Despite appearances, these effects do not demonstrate the impossibility of a noncontextual hidden variable theory, since an explanation in terms of measurement disturbance is possible. Nonetheless, we show that for every paradoxical effect wherein all the pre- and post-selected probabilities are 0 or 1 and the pre- and post-selected states are nonorthogonal, there is an associated proof of the impossibility of a noncontextual hidden variable theory. This proof is obtained by considering all the measurements involved in the paradoxical effect--the preselection, the post-selection, and the alternative possible intermediate measurements--as alternative possible measurements at a single time.