Paradoxes of measures of quantum entanglement and Bell's inequality violation in two-qubit systems

  • Authors:

  • Adam Miranowicz;Bohdan Horst;Andrzej Koper

  • Affiliations:

  • Faculty of Physics, Adam Mickiewicz University, 61-614 Poznań, Poland;Faculty of Physics, Adam Mickiewicz University, 61-614 Poznań, Poland;Faculty of Physics, Adam Mickiewicz University, 61-614 Poznań, Poland

  • Venue:
  • Journal of Computational Methods in Sciences and Engineering - Atomic and molecular nonlinear optics: Theory, Experiment and Computation A homage to the pioneering work of Stanisław Kielich (1925-1993)
  • Year:
  • 2010

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Abstract

We review some counterintuitive properties of standard measures describing quantum entanglement and violation of Bell's inequality (often referred to as "nonlocality") in two-qubit systems. By comparing the nonlocality, negativity, concurrence, and relative entropy of entanglement, we show: (i) ambiguity in ordering states with the entanglement measures, (ii) ambiguity of robustness of entanglement in lossy systems and (iii) existence of two-qubit mixed states more entangled than pure states having the same negativity or nonlocality. To support our conclusions, we performed a Monte Carlo simulation of 10$^6$ two-qubit states and calculated all the entanglement measures for them. Our demonstration of the relativity of entanglement measures implies also how desirable is to properly use an operationally-defined entanglement measure rather than to apply formally-defined standard measures. In fact, the problem of estimating the degree of entanglement of a bipartite system cannot be analyzed separately from the measurement process that changes the system and from the intended application of the generated entanglement.