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

Abstract

The existence of contextuality in quantum mechanics is a fundamental departure from the classical description of the world. Currently, the quest to identify scenarios which cannot be more contextual than quantum theory is at the forefront of research in quantum contextuality. In this work, we experimentally test two inequalities, which are capable of revealing fully contextual quantum correlations, on a Hilbert space of dimension eight and four respectively, on an NMR quantum information processor. The projectors associated with the contextuality inequalities are first reformulated in terms of Pauli operators, which can be determined in an NMR experiment. We also analyze the behavior of each inequality under rotation of the underlying quantum state, which unitarily transforms it to another pure state.

Experimental demonstration of the violation of the temporal Peres-Mermin inequality using contextual temporal correlations and noninvasive measurements

“…Nonlocal unitary operations were achieved by free evolution under the system Hamiltonian, of suitable duration under the desired scalar coupling with the help of embedded π refocusing pulses. The durations of the π 2 pulses for 1 H, 19 F, and 13 C nuclei were 9.55 µs at 18.14 W power level, 23.00 µs at a power level of 42.27 W, and 15.75 µs at a power level of 179.47 W, respectively.…”

“…We used the molecule of 13 C -labeled diethyl fluoromalonate dissolved in acetone-D6 as a three-qubit system, with the 1 H, 19 F and 13 C spin-1/2 nuclei being encoded as 'qubit one', 'qubit two' and 'qubit three', respectively. The NMR Hamiltonian for a three-qubit system in the rotating frame is [49]:…”

“…Since then there have been several state dependent and state independent proposals to test contextuality [11][12][13][14]. Experimental tests of quantum contextuality have been performed using photons [15], trapped ions [16,17], and nuclear spin qubits [18,19]. The original KS theorem was further extended to state independent inequalities and three experimentally testable inequalities were given which are valid for any noncontextual hidden variable theory and can be violated by any quantum state [20].…”

Monogamy relations of entropic non-contextual inequalities and their experimental realization

“…This mapping is particularly useful in the context of an NMR experimental setup where the expectation value of the Z operator is easily accessible and corresponds to the observed z magnetization of a nuclear spin in a particular quantum state. The normalized experimental intensities of the NMR signal then provide an estimate of the expectation value of the Pauli Z operator in that quantum state [45].…”

Efficient experimental characterization of quantum processes via compressed sensing on an NMR quantum processor

“…2(a). The spatial averaging techniques are used in the first block [46] to initialize system in the desired PPS, followed by the application of spin-selective rf pulses to prepare the desired input state. In the second block the pulse sequence corresponding to U CNN is applied on the input state and in the last block after application of tomographic pulses, the signal of the desired nucleus is recorded.…”