Entanglement detection on an NMR quantum-information processor using random local measurements

Abstract

Random local measurements have recently been proposed to construct entanglement witnesses and thereby detect the presence of bipartite entanglement. We experimentally demonstrate the efficacy of one such scheme on a two-qubit NMR quantum information processor. We show that a set of three random local measurements suffices to detect the entanglement of a general two-qubit state. We experimentally generate states with different amounts of entanglement, and show that the scheme is able to clearly witness entanglement. We perform complete quantum state tomography for each state and compute state fidelity to validate our results. Further, we extend previous results and perform a simulation using random local measurements to optimally detect bipartite entanglement in a hybrid system of 2 ⊗ 3 dimensionality.

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.…”

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

“…Experimental implementation of the entanglement detection protocol is such that in a single shot (using only four experimental settings), we were able to determine if a state belongs to the W class or to the GHZ class. We use our own scheme to map the desired observables onto the z-magnetization of one of the subsystems, making it possible to experimentally measure its expectation value on NMR systems [36]. Mapping of the observables onto Pauli z-operators of a single qubit eases the experimental determination of the desired expectation value, since the NMR signal is proportional to the ensemble average of the Pauli z-operator.…”

Witnessing nonclassical correlations via a single-shot experiment on an ensemble of spins using nuclear magnetic resonance

“…Quantum discord was experimentally measured in systems such as NMR, that are described by a deviation density matrix [6][7][8]. Further, environment-induced sudden transitions in quantum discord dynamics and their preservation were investigated using NMR [9,10].…”