Quantum Physics

The last decade has seen a wave of characterizations of quantum theory using the formalism of generalized probability theory.

In this talk, I will introduce a novel operational approach to characterizing and reconstructing quantum theory which puts an observer’s information acquisition -- rather than the probability structure – centre stage. In particular, we consider an observer interrogating a system with binary questions and explain how an elementary set of rules governing the observer’s acquisition of information about the system leads to qubit quantum theory. The derivation is constructive, elucidating, among other things, the origin of entanglement, monogamy and more generally the correlation structure. This approach also yields a new characterization of pure states in terms of ‘conserved informational charges’ which, in turn, define the unitary group.

We study the separability of quantum states in bosonic system. Our main tool here is the "separability witnesses", and a connection between "separability witnesses" and a new kind of positivity of matrices--- "Power Positive Matrices" is drawn. Such connection is employed to demonstrate that multi-qubit quantum states with Dicke states being its eigenvectors is separable if and only if two related Hankel matrices are positive semidefinite. By employing this criterion, we are able to show that such state is separable if and only if it's partial transpose is non-negative, which confirms the conjecture in [Wolfe, Yelin, Phys. Rev. Lett. (2014)]. Then, we present a class of bosonic states in d⊗d system such that for general d, determine its separabilityNP-hard although verifiable conditions for separability is easily derived in case d=3,4.