Frontiers of quantum physics

Abstract:

For N hard-core bosons on an arbitrary lattice with d sites and independent of additional interaction terms we prove that the hard-core constraint itself already enforces a universal upper bound on the Bose-Einstein condensate given by Nmax=(N/d)(d-N+1). This bound can only be attained for one-particle states |φ) with equal amplitudes with respect to the hard-core basis (sites) and when the corresponding N-particle state |Ψ) is maximally delocalized. This result is generalized to the maximum condensate possible within a given sublattice. We observe that such maximal local condensation is only possible if the mode entanglement between the sublattice and its complement is minimal. We also show that the maximizing state |Ψ) is related to the ground state of a bosonic "Hubbard star" showing Bose-Einstein condensation.

Abstract:

We consider the characterization of quantum superposition states beyond the pattern "dead and alive". We propose a measure that is applicable to superpositions of multiple macroscopically distinct states, superpositions with different weights as well as mixed states. The measure is based on the mutual information to characterize the distinguishability between the multiple branches of the superposition. This allows us to overcome limitations of previous proposals, and to bridge the gap between general measures for macroscopic quantumness and measures for Schrödinger-cat type superpositions. We discuss a number of relevant examples, provide an alternative definition using basis-dependent quantum discord and reveal connections to other proposals in the literature. Finally, we also show the connection between the size of quantum states as quantified by our measure and their vulnerability to noise.