Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars
| | Speaker: | 孙源 博士，南京师范大学
| | Inviter: | | Title:
| Quantumness of Ensemble via Coherence of Gram Matrix | Time & Venue:
| 2021.05.13 10:30-11:30 腾讯会议号： 852 317 225 | Abstract:
| The Gram matrix of a set of vectors, which encapsulates the relations between the constituent vectors, plays an important role in the exploration of both geometric and information-theoretic aspects of quantum state space. In view of its usefulness and importance, we study the Gram matrix of an ensemble of pure states (a set of pure states with a prior probability distribution) and reveal its fundamental properties. We highlight and exploit the fact that the Gram matrix of an ensemble can be formally regarded as a bona fide quantum state. The key idea is to employ coherence (with respect to the computational basis) of the Gram matrix (regarded as a quantum state) to quantify quantumness of the corresponding ensemble. In particular, we propose to use the $l_1$-norm of coherence and the relative entropy of coherence, of the Gram matrix, as two significant quantifiers of quantumness. We illustrate the effectiveness and power of these quantifiers of quantumness by evaluating them for several important ensembles arising from quantum measurement and quantum cryptography. We further compare the quantumness based on the Gram matrix with various other quantifiers of quantumness in the literature, and illuminate that although they are closely related in general, they have subtle differences and capture different aspects of ensembles, which shed light on the complexity of quantum ensembles.
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