Volume 114, Number 3, May 2016
|Number of page(s)||6|
|Published online||31 May 2016|
Statistics of leading digits leads to unification of quantum correlations
Harish-Chandra Research Institute - Chhatnag Road, Jhunsi, Allahabad - 211019, India
Received: 15 December 2015
Accepted: 9 May 2016
We show that the frequency distribution of the first significant digits of the numbers in the data sets generated from a large class of measures of quantum correlations, which are either entanglement measures or belong to the information-theoretic paradigm, exhibit a universal behavior. In particular, for Haar uniformly simulated arbitrary two-qubit states, we find that the first-digit distributions corresponding to a collection of chosen computable quantum correlation quantifiers tend to follow the first-digit law, known as Benford's law, when the rank of the states increases. Considering a two-qubit state which is obtained from a system governed by paradigmatic spin Hamiltonians, namely, the XY model in a transverse field, and the XXZ model, we show that entanglement as well as information-theoretic measures violate Benford's law. We quantitatively discuss the violation of Benford's law by using a violation parameter, and demonstrate that the violation parameter can signal quantum phase transitions occurring in these models. We also comment on the universality of the statistics of the first significant digits corresponding to appropriate measures of quantum correlations in the case of multipartite systems as well as systems in higher dimensions.
PACS: 03.67.Mn – Entanglement measures, witnesses, and other characterizations / 75.10.Jm – Quantized spin models, including quantum spin frustration / 03.65.Aa – Quantum systems with finite Hilbert space
© EPLA, 2016
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.