An Experimental Test of Quantum Nonseparability

Bernard d’Espagnat

Asher Peres

G. C. Ghirardi

A. C. de la Torre, Pedro Jose Catuogno, Sebastián Ferrando

Tamás Vértesi, R. Englman

Elementary quantum mechanical principles are applied to bipartite or multipartite systems to test the nonseparability of subsystems (or nonadditivity in the system Hamiltonian) through interchanging the ordering of subsystem (local) operators that cause transitions between energy eigenstates, whether applied to pure or mixed states. A tentative measure for quantifying nonseparability is proposed, based on complete sets of subsystem transition operators. This serves as an upper bound for experimental determinations of the intersubsystem coupling. Two- and three-qubit systems are numerically tested to establish criteria for the noninvariance of transition probabilities in them with respect to the sequence of excitations, and it is conjectured that sequence noninvariance can be used as a probe for subsystems' nonseparability.

Guillermo García-Pérez, Oskari Kerppo, Matteo A. C. Rossi +1 more

The description of the complex separability structure of quantum states in terms of partially ordered sets has been recently put forward. In this work, we address the question of how to efficiently determine these structures for unknown states. We propose an experimentally accessible and scalable iterative methodology that identifies, on solid statistical grounds, sufficient conditions for nonseparability with respect to certain partitions. In addition, we propose an algorithm to determine the minimal partitions (those that do not admit further splitting) consistent with the experimental observations. We test our methodology experimentally on a 20-qubit IBM quantum computer by inferring the structure of the 4-qubit Smolin and an 8-qubit W state. In the first case, our results reveal that, while the fidelity of the state is low, it nevertheless exhibits the partitioning structure expected from the theory. In the case of the W state, we obtain very disparate results in different runs on the device, which range from nonseparable states to very fragmented minimal partitions with little entanglement in the system. Furthermore, our work demonstrates the applicability of informationally complete positive operator-valued measurements for practical purposes on current noisy intermediate-scale quantum devices.