Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

Keyring models: An Approach to Steerability



Carl A. Miller, Roger Colbeck, Yaoyun Shi


If a measurement is made on one half of a bipartite system then, conditioned on the outcome, the other half achieves 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. Classifying the steerability of states is a challenging problem even for low dimensions. In the case of two-qubit systems a criterion is known for T-states (that is, 2-qubit states that have a maximally mixed marginal on the first subsystem) under projective measurements. In the current work we introduce the concept of keychain models -- a special class of local hidden state models -- which allows us to study steerability outside the set of T-states. We use keychain models to give a complete classification steering within the set of partially entangled Werner states. We also give a partial classification of steering for states that arise from applying uniform noise to pure two-qubit states.
Journal of Mathematical Physics


nonlocality, entanglement


Miller, C. , Colbeck, R. and Shi, Y. (2018), Keyring models: An Approach to Steerability, Journal of Mathematical Physics, [online], (Accessed July 17, 2024)


If you have any questions about this publication or are having problems accessing it, please contact

Created February 5, 2018, Updated September 15, 2020