Information Geometry of Quantum Resources

Abstract

I review recent works showing that information geometry is a useful framework to characterize quantum coherence and entanglement. Quantum systems exhibit peculiar properties which cannot be justified by classical physics, e.g. quantum coherence and quantum correlations. Once confined to thought experiments, they are nowadays created and manipulated by exerting an exquisite experimental control of atoms, molecules and photons. It is important to identify and quantify such quantum features, as they are deemed to be key resources to achieve supraclassical performances in computation and communication protocols. The information geometry viewpoint elucidates the advantage provided by quantum superpositions in phase estimation. Also, it enables to link measures of coherence and entanglement to observables, which can be evaluated in a laboratory by a limited number of measurements.Keywords: quantum information, quantum coherence, quantum correlations, quantum metrology arXiv:1709.05531v2 [quant-ph]

Quantum Zeno effect in correlated qubits

“…Interestingly, F Q (t) is one of the best-studied quantities in quantum physics with a wide variety of applications. For instance, the quantum Fisher information sets bounds on the optimal estimation of parameters enconded in a quantum state [17][18][19], it helps to describe criticality and quantum phase transitions [20][21][22][23][24][25][26], it quantifies coherence and entanglement [27][28][29], it provides bounds on irreversibility in open quantum systems [30], and it also determines the best precision in thermometry [31].…”