Direct determination of entanglement monotones for arbitrary dimensional bipartite states using statistical correlators and one set of complementary measurements

Abstract

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 (P CC) and standard EMs i.e. Negativity (N ) and Entanglement of Formation (E OF ) in arbitrary dimensions. As a proof of concept, we then experimentally measure MP, MI and P CC of two-qutrit pure states and determine their N and E OF 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 ± 0.013 and the E OF to be 1.323 ± 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.

Relating an entanglement measure with statistical correlators for two-qudit mixed states using only a pair of complementary observables

“…For a pure bipartite qutrit state, the validity of Eq. ( 35) has recently been demonstrated experimentally in [27].…”

“…A key shift in focus from the above-mentioned line of studies has been made in the latest study reported in a separate paper [27], where by harnessing the maximum complementarity of one or two pairs of mutually unbiased measurement bases, the EMs like Negativity (N) and Entanglement of Formation (EOF) of any bipartite pure state have been analytically related to the observable statistical correlators like MP, MI and PCC for any dimension. Moreover, this general scheme has been applied for the experimental determination of N and EOF of a prepared two qutrit pure photonic state, using the analytically derived relationships.…”