Given a non-maximally entangled state, an operationally significant question is to quantitatively assess as to what extent the state is away from the maximally entangled state, which is of importance in evaluating the efficacy of the state for its various uses as a resource. It is this question which is examined in this paper for two-qubit pure entangled states in terms of different entanglement measures such as negativity (N), logarithmic negativity (LN), and entanglement of formation (EOF). Although these entanglement measures are defined differently, to what extent they differ in quantitatively addressing the earlier mentioned question has remained uninvestigated. The theoretical estimate in this paper shows that an appropriately defined parameter characterizing the fractional deviation of any given entangled state from the maximally entangled state in terms of N is quite different from that computed in terms of EOF, with their values differing up to $ {\sim} 15\% $ for states further away from the maximally entangled state. Similarly, the values of such fractional deviation parameters estimated using the entanglement measures LN and EOF also strikingly differ among themselves, with the maximum value of this difference being around 23%. This analysis is complemented by illustration of these differences in terms of empirical results obtained from a suitably planned experimental study. Thus, such an appreciable amount of quantitative non-equivalence between the entanglement measures in addressing the experimentally relevant question considered in the present paper highlights the requirement of an appropriate quantifier for such intent. We indicate directions of study that can be explored towards finding such a quantifier.

中文翻译：

---

再谈二量子位纯态的纠缠度之间的比较

给定一个非最大纠缠状态，一个重要的操作问题是定量评估该状态与最大纠缠状态之间的距离，这对于评估该状态作为资源的各种用途的有效性非常重要。本文针对两个量子位的纯纠缠态，以不同的纠缠度量（例如，负性（N），对数负性（LN）和形成纠缠（EOF））来研究此问题。尽管这些纠缠措施的定义不同，但在定量解决前面提到的问题方面在多大程度上仍存在差异。$ {\ sim} 15 \％$用于表示远离最大纠缠状态的状态。类似地，使用缠结度量LN和EOF估计的这种分数偏差参数的值也彼此之间显着不同，该差异的最大值约为23％。通过从适当计划的实验研究获得的经验结果来说明这些差异，可以对分析进行补充。因此，在解决本文所考虑的实验相关问题时，纠缠测度之间如此可观的定量不等价现象凸显了针对这种意图的适当量词的要求。我们指出了可以找到找到这样一个量词的研究方向。