Experimental classification of entanglement in arbitrary three-qubit pure states on an NMR quantum information processor

Abstract

We undertake experimental detection of the entanglement present in arbitrary three-qubit pure quantum states on an NMR quantum information processor. Measurements of only four observables suffice to experimentally differentiate between the six classes of states which are inequivalent under stochastic local operation and classical communication (SLOCC). The experimental realization is achieved by mapping the desired observables onto Pauli z-operators of a single qubit, which is directly amenable to measurement. The detection scheme is applied to known entangled states as well as to states randomly generated using a generic scheme that can construct all possible threequbit states. The results are substantiated via direct full quantum state tomography as well as via negativity calculations and the comparison suggests that the protocol is indeed successful in detecting tripartite entanglement without requiring any a priori information about the states.

Tripartite Entanglement: Foundations and Applications

“…In [158] are established sufficient conditions for detecting genuine tripartite entanglement, providing an operational point of view to measure and detect this type of entanglement. Experimental schemes to identify the entanglement classes of tripartite states can be accessed in [159,160].…”

Experimental demonstration of fully contextual quantum correlations on an NMR quantum information processor

“…where, To experimentally implement the KCBS-twin inequality capable of revealing fully contextual quantum correlations for an eight-dimensional quantum system, we used the molecule of 13 C -labeled diethyl fluoromalonate dissolved in acetone-D6, with the 1 H, 19 F and 13 C spin-1/2 nuclei being encoded as 'qubit one', 'qubit two' and 'qubit three', respectively (see Fig 2 for the molecular structure and corresponding NMR spectrum of the PPS state, and Table III for details of the experimental NMR parameters). The NMR Hamiltonian for a three-qubit system is given by [29]…”

Experimental detection of qubit-ququart pseudo-bound entanglement using three nuclear spins

“…The quantum circuit to achieve this is shown in Fig.3(a), and this circuit maps the state σ b → σ b such that B 1 σ b = I 3z σ b . The motivation for such a mapping [20][21][22] relies on the fact that in an NMR scenario, the expectation value I z , can be readily measured [51]. The crux of the temporal averaging technique relies on the fact that the five states composing the PPT entangled (a)…”

“…Even in situations where entanglement can be characterized theoretically, the experimental detection of entanglement is resource-intensive and remains a challenging task [16,17]. Several experimental efforts in this direction have tried to reduce the resources required to detect entanglement and have devised methods based on entanglement witnesses and positive maps to interrogate the presence of entanglement [18][19][20][21][22]. A range of experiments have been carried out to create and detect novel entangled states [23][24][25][26][27][28][29][30].…”

“…In order to experimentally detect entanglement in these states, three Pauli operators need to be measured in each case. To measure the required observables we utilized previously developed schemes [20][21][22] which unitarily map the desired state followed by NMR ensemble average measurements. In each case we also performed full quantum state tomography (QST) [48,49] to verify the success of the detection protocol as well as to establish that the experimentally created states are indeed PPT entangled.…”