Knowledge by direct measurement versus inference from steering

Abstract

If Alice and Bob start out with an entangled state |Ψ AB , Bob may update his state to |ϕ B either by performing a suitable measurement himself, or by receiving the information that a measurement by Alice has steered that state. While Bob's update on his state is identical, his update on Alice's state differs: if Bob has performed the measurement, he has steered the state |χ←(ϕ) A of Alice; if Alice has made the measurement, to steer |ϕ B on Bob she must have found a different state |χ→(ϕ) A. Based on this observation, a consequence of the well-known "Hardy's ladder", we show that information from direct measurement must trump inference from steering. The erroneous belief that both paths should lead to identical conclusions can be traced to the usual prejudice that measurements should reveal a pre-existing state of affairs. We also prove a technical result on Hardy's ladder: the minimum overlap between the steered and the steering state is 2 √ p0pn−1/(p0 + pn−1), where p0 and pn−1 are the smallest (non-zero) and the largest Schmidt coefficients of |Ψ AB .

Nonlocal single particle steering generated through single particle entanglement

“…However, its implementation must still be analysed and checked further in order to asses its probable applicability to the SGE for the quantum measurement of the spin direction of σ z only 77 ; thereby, by treating the internal and external DOF as quantum variables in the SGE, it becomes clear that there are instances where the resultant final state is not the same when measuring an observable than to infer its value from measuring other observable. There is another perspective on this analysis that considers the situation when the measurement is carried out at different places by different parties 59 . Furthermore, an additional issue arises when considering whether or not the Alice's apparatus is close to the particle or not; in our general discussion we implicitly take the point of view that she does not have any difficulty in placing the particle in her measuring apparatus, in the situation when she would get nothing the particle will appears at the place in Paris where Bob is.…”

Single-photon steering

“…New York city or Puebla city. Hence, if Bob also make measurements, then Bob and Alice would obtain similar or different results and process depending on whether or not they use generalized or projective measurements 38 . Therefore, in the single-photon entangled state that is customized adapted in the above scheme, the non-local features arises from independent measurements at two faraway places.…”