Mixture Of Eigenstates Research Articles

Hermite–Gaussian model for quantum states

In order to characterize quantum states within the context of information geometry, we propose a generalization of the Gaussian model, which we called the Hermite–Gaussian model. We obtain the Fisher–Rao metric and the scalar curvature for this model, and we show its relation with the one-dimensional quantum harmonic oscillator. Using this model we characterize some families of states of the quantum harmonic oscillator. We find that for eigenstates of the Hamiltonian, mixtures of eigenstates and even or odd superpositions of eigenstates, the associated Fisher–Rao metrics – which are relevant in the context of quantum parameter estimation theory – are diagonal. Finally, we consider the action of the amplitude damping channel and we discuss the relationship between the quantum decay and the different geometric indicators.

Strong local passivity in finite quantum systems.

Passive states of quantum systems are states from which no system energy can be extracted by any cyclic (unitary) process. Gibbs states of all temperatures are passive. Strong local (SL) passive states are defined to allow any general quantum operation, but the operation is required to be local, being applied only to a specific subsystem. Any mixture of eigenstates in a system-dependent neighborhood of a nondegenerate entangled ground state is found to be SL passive. In particular, Gibbs states are SL passive with respect to a subsystem only at or below a critical system-dependent temperature. SL passivity is associated in many-body systems with the presence of ground state entanglement in a way suggestive of collective quantum phenomena such as quantum phase transitions, superconductivity, and the quantum Hall effect. The presence of SL passivity is detailed for some simple spin systems where it is found that SL passivity is neither confined to systems of only a few particles nor limited to the near vicinity of the ground state.