Performance of autonomous quantum thermal machines: Hilbert space dimension as a thermodynamical resource

Hilbert Space Quantum Mechanics

1 Vectors (Kets) 1 1.1 Dirac notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Qubit or spin half . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 Intuitive picture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.4 General d . . . . . . . . . . . . . . . . . . ...

Minimum Dimension of a Hilbert Space Needed to Generate a Quantum Correlation.

Consider a two-party correlation that can be generated by performing local measurements on a bipartite quantum system. A question of fundamental importance is to understand how many resources, which we quantify by the dimension of the underlying quantum system, are needed to reproduce this correlation. In this Letter, we identify an easy-to-compute lower bound on the smallest Hilbert space dime...

Quantum Mechanics beyond Hilbert Space

When describing a quantum mechanical system, it is convenient to consider state vectors that do not belong to the Hilbert space. In the rst part of this paper, we survey the various formalisms have been introduced for giving a rigorous mathematical justiication to this procedure: rigged Hilbert spaces (RHS), scales or lattices of Hilbert spaces (LHS), nested Hilbert spaces, partial inner produc...

Quantum physics on a general Hilbert space

Quantum physics on a general Hilbert space