Total quantum coherence and its applications
Abstract
Quantum coherence is the most fundamental feature of quantum mechanics. The usual understanding of it depends on the choice of the basis, that is, the coherence of the same quantum state is different within different reference framework. To reveal all the potential coherence, we present the total quantum coherence measures in terms of two different methods. One is optimizing maximal basisdependent coherence with all potential bases considered and the other is quantifying the distance between the state and the incoherent state set. Interestingly, the coherence measures based on relative entropy and l_2 norm have the same form in the two different methods. In particular, we show that the measures based on the noncontractive l_2 norm are also a good measure different from the basisdependent coherence. In addition, we show that all the measures are analytically calculable and have all the good properties. The experimental schemes for the detection of these coherence measures are also proposed by multiple copies of quantum states instead of reconstructing the full density matrix. By studying one type of quantum probing schemes, we find that both the normalized trace in the scheme of deterministic quantum computation with one qubit and the overlap of two states in quantum overlap measurement schemes can be well described by the change of total coherence of the probing qubit. Hence the nontrivial probing always leads to the change of the total coherence.
 Publication:

Quantum Information Processing
 Pub Date:
 September 2016
 DOI:
 10.1007/s111280161376y
 arXiv:
 arXiv:1607.07997
 Bibcode:
 2016QuIP...15.3773Y
 Keywords:

 Quantum coherence;
 Quantum entanglement;
 Purity;
 Quantum Physics
 EPrint:
 12 pages, 1 figure. To appear in QIP