47 research outputs found
Entropic Steering Criteria: Applications to Bipartite and Tripartite Systems
The effect of quantum steering describes a possible action at a distance via
local measurements. Whereas many attempts on characterizing steerability have
been pursued, answering the question as to whether a given state is steerable
or not remains a difficult task. Here, we investigate the applicability of a
recently proposed method for building steering criteria from generalized
entropic uncertainty relations. This method works for any entropy which satisfy
the properties of (i) (pseudo-) additivity for independent distributions; (ii)
state independent entropic uncertainty relation (EUR); and (iii) joint
convexity of a corresponding relative entropy. Our study extends the former
analysis to Tsallis and R\'enyi entropies on bipartite and tripartite systems.
As examples, we investigate the steerability of the three-qubit GHZ and W
states.Comment: 27 pages, 8 figures. Published version. Title change
Unlimited One-Way Steering
This work explores the asymmetry of quantum steering in a setup using
high-dimensional entanglement. We construct entangled states with the following
properties: one party (Alice) can never steer the state of the other
party (Bob), considering the most general measurements, and Bob can
strongly steer the state of Alice, demonstrating genuine high-dimensional
steering. In other words, Bob can convince Alice that they share an entangled
state of arbitrarily high Schmidt number, while Alice can never convince Bob
that the state is even simply entangled. In this sense, one-way steering can
become unlimited. A key result for our construction is a condition for the
joint measurability of all high-dimensional measurements subjected to the
combined effect of noise and loss, which is of independent interest.Comment: 4+4 page