论文标题
直接确定使用统计相关器和一组互补测量的任意尺寸两分状态的纠缠单调
Direct determination of entanglement monotones for arbitrary dimensional bipartite states using statistical correlators and one set of complementary measurements
论文作者
论文摘要
与Qubits相比，更高维量子系统（QUDITS）具有实施各种信息理论任务的一种潜在更有效的手段。此类探索中无处不在的资源之一是纠缠。纠缠单调（EMS）至关重要，尤其是评估给定纠缠状态作为信息理论任务的资源的功效。到目前为止，确定EMS的调查一直集中在提供更紧密的下限。目前尚无通用计划可直接确定EMS。因此，尚未实现任何EM的经验确定。本文在理论上和实验上都填补了这一空白。首先，我们得出统计相关度量（即相互可预测性（MP），相互信息（MI）和Pearson相关系数（PCC）和标准EMS的分析关系，即在任意维度中的形成（EOF）（EOF）。作为概念的证明，我们然后通过实验测量两Qutrit纯状态的MP，MI和PCC，并使用这些派生关系确定其N和EOF。这是对实验者工具包的有用补充，其中通过使用有限数量的测量值（在这种情况下为1组测量值），可以直接在两部分任意尺寸系统中直接测量EMS。我们获得n的n值为0.907 $ \ pm $ 0.013，EOF为1.323 $ \ pm $ 0.022。由于本方案能够通过相同数量的测量值确定多个纠缠单调的单调，因此我们认为它可以作为定量比较和对比纠缠单调的操作含义的独特实验平台，同时显示其非单调性的性能以及给定的Bipartire pure Qudit状态。
Higher dimensional quantum systems (qudits) present a potentially more efficient means, compared to qubits, for implementing various information theoretic tasks. One of the ubiquitous resources in such explorations is entanglement. Entanglement Monotones (EMs) are of key importance, particularly for assessing the efficacy of a given entangled state as a resource for information theoretic tasks. Till date, investigations towards determination of EMs have focused on providing their tighter lower bounds. There is yet no general scheme available for direct determination of the EMs. Consequently, an empirical determination of any EM has not yet been achieved for entangled qudit states. The present paper fills this gap, both theoretically as well as experimentally. First, we derive analytical relations between statistical correlation measures i.e. Mutual Predictability (MP), Mutual Information (MI) and Pearson Correlation Coefficient (PCC) and standard EMs i.e. Negativity (N) and Entanglement of Formation (EOF) in arbitrary dimensions. As a proof of concept, we then experimentally measure MP, MI and PCC of two-qutrit pure states and determine their N and EOF using these derived relations. This is a useful addition to the experimenter's toolkit wherein by using a limited number of measurements (in this case 1 set of measurements), one can directly measure the EMs in a bipartite arbitrary dimensional system. We obtain the value of N for our bipartite qutrit to be 0.907 $\pm$ 0.013 and the EOF to be 1.323 $\pm$ 0.022. Since the present scheme enables determination of more than one entanglement monotone by the same limited number of measurements, we argue that it can serve as a unique experimental platform for quantitatively comparing and contrasting the operational implications of entanglement monotones as well as showing their non-monotonicity for a given bipartire pure qudit state.
