Non-classicality criteria from phase-space representations and information-theoretical constraints are maximally inequivalent

Abstract

We consider two celebrated criteria for defining the non-classicality of bipartite bosonic quantum systems, the first stemming from information theoretic concepts and the second from physical constraints on the quantum phase-space. Consequently, two sets of allegedly classical states are singled out: i) the set C composed of the so called classical-classical (CC) states---separable states that are locally distinguishable and do not possess quantum discord; ii) the set P of states endowed with a positive P-representation (P-classical states)---mixture of Glauber coherent states that, e.g., fail to show negativity of their Wigner function. By showing that C and P are almost disjoint, we prove that the two defining criteria are maximally inequivalent. Thus, the notions of classicality that they put forward are radically different. In particular, generic CC states show quantumness in their P-representation and, viceversa, almost all P-classical states have positive quantum discord, hence are not CC. This inequivalence is further elucidated considering different applications of P-classical and CC states. Our results suggest that there are other quantum correlations in nature than those revealed by entanglement and quantum discord.

5 pages, no figures, close to published version

References in corpus (15)

• Entanglement detection
• Quantum discord and the power of one qubit
• No-local-broadcasting theorem for quantum correlations
• Interpreting quantum discord through quantum state merging
• Operational interpretations of quantum discord
• Quantum discord for general two--qubit states: Analytical progress
• Negativity and contextuality are equivalent notions of nonclassicality
• Linking Quantum Discord to Entanglement in a Measurement
• All non-classical correlations can be activated into distillable entanglement
• Optimal measurements to access classical correlations of two-qubit states
• Sub-shot-noise photon-number correlation in mesoscopic twin-beam of light
• Monogamy properties of quantum and classical correlations
• Nonclassical correlation properties of radiation fields
• Broadcast copies reveal the quantumness of correlations
• Activating optomechanical entanglement

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