Quantum Inf Process (2016) 15:3773–3784
Total quantum coherence and its applications
· Si-ren Yang
· Bao-qing Guo
Received: 17 December 2015 / Accepted: 22 June 2016 / Published online: 28 June 2016
© Springer Science+Business Media New York 2016
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 basis-dependent 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
norm have the same form in the two different methods. In
particular, we show that the measures based on the non-contractive l
norm are also
a good measure different from the basis-dependent 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.
This work was supported by the National Natural Science Foundation of China, under Grant No.
11375036, the Xinghai Scholar Cultivation Plan and the Fundamental Research Funds for the Central
Universities under Grant Nos. DUT15LK35 and DUT15TD47.
School of Physics and Optoelectronic Technology, Dalian University of Technology,
Dalian 116024, People’s Republic of China