Related papers: Tsirelson's Problem and Asymptotically Commuting U…
The characterization of quantum correlations, being stronger than classical, yet weaker than those appearing in non-signaling models, still poses many riddles. In this work we show that the extent of binary correlations in a general class…
Using the analytic assembly map that appears in the Baum-Connes conjecture in noncommutative geometry, we generalise the $\Spin^c$-version of the Guillemin-Sternberg conjecture that `quantisation commutes with reduction' to (discrete series…
Everett's concept of relative state can be viewed as a map that contains information about correlations between measurement outcomes on two quantum systems. We demonstrate how geometric properties of the relative state map can be used to…
What is the connection of random matrices with integrable systems? Is this connection really useful? The answer to these questions leads to a new and unifying approach to the theory of random matrices. Introducing an appropriate time…
The so called bipartite non-signaling boxes are systems whose statistics is constrained solely by the principle of no instantaneous signaling between distant locations. Such systems can exhibit much stronger correlations than those admitted…
The characterization of the set of quantum correlations in Bell scenarios is a problem of paramount importance for both the foundations of quantum mechanics and quantum information processing in the device-independent scenario. However, a…
The Hilbert space formalism of quantum theory manifests a map between bipartite states and time evolutions, known as Jamiolkowski isomorphism. We extend this map in a physical setting to prove the equality of spatial correlations in…
We consider an interacting bipartite network through a Bayesian game-theoretic framework and demonstrate that weak measurements introduce an inherent asymmetry that is not present when using standard projective measurements. These…
We discuss complementarity relations in a bipartite continuous variable system. Building up from the work done on discrete d-dimensional systems, we prove that for symmetric two-mode states, quantum complementarity relations can be put in a…
It is shown, that for quantum systems the vectorfield associated with the equations of motion may admit alternative Hamiltonian descriptions, both in the Schr\"odinger and Heisenberg pictures. We illustrate these ambiguities in terms of…
We show how the separability problem is dual to that of decomposing any given matrix into a conic combination of rank-one partial isometries, thus offering a duality approach different to the positive maps characterization problem. Several…
Understanding the causal influences that hold among parts of a system is critical both to explaining that system's natural behaviour and to controlling it through targeted interventions. In a quantum world, understanding causal relations is…
The relations of antilinear maps, bipartite states and quantum channels is summarized. Antilinear maps are applied to describe bipartite states and entanglement. Teleportation is treated in this general formalism with an emphasis on…
We develop a bootstrap approach to Euclidean two-point correlators, in the thermal or ground state of quantum mechanical systems. We formulate the problem of bounding the two-point correlator as a semidefinite programming problem, subject…
We address the question, does a system A being entangled with another system B, put any constraints on the Heisenberg uncertainty relation (or the Schrodinger-Robertson inequality)? We find that the equality of the uncertainty relation…
A definition of quantum correlation is presented for an arbitrary bipartite quantum state based on the skew information. This definition not only inherits the good properties of skew information such as the contractivity and so on, but also…
Quantum entanglement is an enigmatic and powerful property that has attracted much attention due to its usefulness in new ways of communications, like quantum teleportation and quantum key distribution. Much effort has been done to quantify…
We derive several uncertainty relations for two arbitrary unitary operators acting on physical states of a Hilbert space. We show that our bounds are tighter in various cases than the ones existing in the current literature. Using the…
Understanding the core content of quantum mechanics requires us to disentangle the hidden logical relationships between the postulates of this theory. Here we show that the mathematical structure of quantum measurements, the formula for…
Symmetry is an important property of quantum mechanical systems which may dramatically influence their behavior in and out of equilibrium. In this paper, we study the effect of symmetry on tripartite entanglement properties of typical…