nt - p h / 04 03 17 4 v 1 2 4 M ar 2 00 4 Bell - like inequalities for quantifying entanglement

We point out some subtleties of the task of quantifying en-tanglement that seem overlooked in the standard theory of entanglement measures. In the context of a new, operational approach to the issue, Bell-like inequalities prove useful for quantifying entanglement. E.g., we point out that the use of an entangled state in a protocol does not necessarily mean that entanglement as information resource has actually been employed in the execution of the protocol. Introduction.-Quantum entanglement measures [1] (and references therein) originate from the experience with the efficient quantum information/-computation (QIC) processing [2-6]: " the system is more entangled if it allows for better performance of some task (impossible without entangle-ment) " [1]. In this context, the Bell-like inequalities (BI) [7, 8] bear only the secondary role; BI usually serve for deciding whether or not a system is in entangled state–which, as it states, is only a crude estimation of entan-glement. Currently, the role of BI in QIC theory is mainly of the histori-cal/methodological nature with only weakly established relations with the existing measures of entanglement [9]. In this paper, we point out usefulness of BI as a " measure " of entangle-ment yet without referring to BI as a measure in the mathematical sense. We point out some subtleties of the task of quantifying entanglement in the operational approach to the issue. These subtleties seem generally overlooked in the standard theory, as different from our approach, which still bears generality and conceptual simplicity. In the context of our approach, BI bear the double role in quantifying entanglement. To this end, we emphasize the following conclusion (cf. Section 3): the use of an entangled state in a QIC protocol/algorithm does not necessarily mean that entanglement as information resource has actually been employed in the execution of the pro-tocol/algorithm. And BI may be used to decide whether or not entanglement as information resource has actually been employed. The contents of this paper are as follows. In Section 2, we keep the tracks of the standard approach [2] to the entanglement measures, yet pointing out a