@article {1994, title = {Keyring models: an approach to steerability}, journal = {Journal of Mathematical Physics}, volume = {59}, year = {2018}, month = {2018/01/02}, pages = {022103}, abstract = {

If a measurement is made on one half of a bipartite system then, conditioned on the outcome, the other half has a new reduced state. If these reduced states defy classical explanation \— that is, if shared randomness cannot produce these reduced states for all possible measurements \— the bipartite state is said to be steerable. Determining which states are steerable is a challenging problem even for low dimensions. In the case of two-qubit systems a criterion is known for T-states (that is, those with maximally mixed marginals) under projective measurements. In the current work we introduce the concept of keyring models \— a special class of local hidden state model. When the measurements made correspond to real projectors, these allow us to study steerability beyond T-states. Using keyring models, we completely solve the steering problem for real projective measurements when the state arises from mixing a pure two-qubit state with uniform noise. We also give a partial solution in the case when the uniform noise is replaced by independent depolarizing channels. Our results imply that Werner states, which are a special case of the previous states, are unsteerable under real projective measurements if and only if their efficiency is at most 2/π.

}, doi = {10.1063/1.5006199}, url = {http://aip.scitation.org/doi/full/10.1063/1.5006199}, author = {Carl Miller and Roger Colbeck and Yaoyun Shi} }