Abstract
We consider the pooling of quantum states when Alice and Bob both have one part of a tripartite system and, on the basis of measurements on their respective parts, each infers a quantum state for the third part . We denote the conditioned states which Alice and Bob assign to by and , respectively, while the unconditioned state of is . The state assigned by an overseer, who has all the data available to Alice and Bob, is . The pooler is told only , , and . We show that for certain classes of tripartite states, this information is enough for her to reconstruct by the formula . Specifically, we identify two classes of states for which this pooling formula works: (i) all pure states for which the rank of is equal to the product of the ranks of the states of Alice’s and Bob’s subsystems; (ii) all mixtures of tripartite product states that are mutually orthogonal on .
- Received 2 January 2007
DOI:https://doi.org/10.1103/PhysRevA.75.042104
©2007 American Physical Society