Regular Article

Measuring quantumness: from theory to observability in interferometric setups^★

¹ INFN, Sezione di Napoli, 80126 Napoli, Italy
² Morgan Stanley Analytics, 1095, Budapest, Hungary
³ Abdus Salam ICTP, Strada Costiera 11, 34151 Trieste, Italy
⁴ NEST, Scuola Normale Superiore & Istituto Nanoscienze-CNR, 56126 Pisa, Italy
⁵ Dipartimento di Ingegneria Industriale, Università di Salerno, 84084 Fisciano (SA), Italy
⁶ Dipartimento di Fisica, Università di Napoli, 80126 Napoli, Italy
⁷ Dipartimento di Fisica and MECENAS, Università di Bari, 70126 Bari, Italy
⁸ Istituto Nazionale di Ottica (INO-CNR), 50125 Firenze, Italy
⁹ INFN, Sezione di Bari, 70126 Bari, Italy
¹⁰ Clarendon Laboratory, Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, UK
¹¹ Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543 Singapore, Singapore
¹² Department of Physics, National University of Singapore, 2 Science Drive 3, 117542 Singapore, Singapore

^a e-mail: saverio.pascazio@ba.infn.it

Received: 27 September 2018
Received in final form: 20 October 2018
Published online: 18 December 2018

Abstract

We investigate the notion of quantumness based on the noncommutativity of the algebra of observables and introduce a measure of quantumness based on the mutual incompatibility of quantum states. We show that such a quantity can be experimentally measured with an interferometric setup and that, when an arbitrary bipartition of a given composite system is introduced, it detects the one-way quantum correlations restricted to one of the two subsystems. We finally show that, by combining only two projective measurements and carrying out the interference procedure, our measure becomes an efficient universal witness of quantum discord and nonclassical correlations.