Revealing Nonclassicality of Inaccessible Objects

Abstract

Some physical objects are hardly accessible to direct experimentation. It is then desirable to infer their properties based solely on the interactions they have with systems over which we have control. In this spirit, here we introduce schemes for assessing the non-classicality of the inaccessible objects as characterised by quantum discord. We consider two probes individually interacting with the inaccessible object, but not with each other. The schemes are based on monitoring entanglement dynamics between the probes. Our method is robust and experimentally friendly as it allows the probes and the object to be open systems, makes no assumptions about the initial state, dimensionality of involved Hilbert spaces and details of the probe-object Hamiltonian. We apply our scheme to a membrane-in-the-middle optomechanical system, to detect system-environment correlations in open system dynamics as well as non-classicality of the environment, and we foresee potential benefits for the inference of the non-classical nature of gravity.What should be known about an inaccessible object to conclude that it is "not classical"? Here we show, inspired by quantum communication scenarios, that it is sufficient to verify whether such object can be used to increase quantum entanglement between remote probeparticles that individually interact with it, but are not directly coupled to each other.Specifically, we prove that such gain in quantum entanglement is only possible if, during its evolution, the object shares with the probes quantum correlations in the form of quantum discord [1][2][3][4][5]. In turn, the presence of quantum discord between the probes and the object entails a non-classical feature of the object itself. According to the definition of discord, two or more subsystems share quantum correlations if there is no von Neumann measurement on one of them that keeps the total state unchanged. This can only happen when non-orthogonal (indistinguishable) states are involved in the description of the physical configuration of the measured subsystem. This indistinguishability is the non-classical feature that we aim to detect. We formulate analytical criteria revealing such non-classicality based on operations performed only on the probes, and without any detailed modelling of the inaccessible object in question.We emphasise that the non-classicality is revealed under a set of minimal assumptions. Namely: (i) The object may remain inaccessible at all times, i.e. it needs not be directly measured. In particular its quantum state and Hilbert space dimension can remain unknown throughout the whole assessment. Our method is thus valid when the object is an elementary system or an arbitrarily complex one; (ii) The details of the interaction between the object and the probes may also remain unspecified; (iii) Every party can be open to its own local environment. These properties make our method applicable to a large number of experimentally relevant situations.We demonstrate the revealing power of our criteria for non-classicality ...

Generalised uncertainty relations from superpositions of geometries

“…(53) This is analogous to Eq. (20). Again, subsequent post-measurement states |Ψ s1... sn , corresponding to sequential momentum measurements in the smeared-space model, may be constructed in like manner and depend on the values measured before.…”

Observable quantum entanglement due to gravity

“…Indeed, if ρ 12 (t) is a pure state at all times and entanglement increases, the dynamics could not have been mediated. The purity assumption requires the mediator to be uncorrelated from ρ 12 (t), and uncorrelated mediator is not capable of entangling the principal system, composed of particles 1 and 2 [13]. It would be valuable to generalise this argument to mixed states measured at finite number of time instances.…”

“…[6][7][8][9][10][11][12] proposed the observation of a probe mass interacting with the gravitational field generated by another mass. More recent proposals put gravity in a role of mediator of quantum correlations and are based on the fact that quantum entanglement between otherwise non-interacting objects can only increase via a quantum mediator [13][14][15]. Motivated by these proposals and by advances in optomechanics [16], in particular the cooling of massive mechanical (macroscopic) oscillators close to their quantum ground state [17][18][19] and the measurement of quantum entanglement of a two-mode system [20][21][22], we study two nearby cooled masses interacting gravitationally.…”

Photon Bunching in a Rotating Reference Frame

“…Both of these experimental classes can be seen, using the equivalence principle, as being implemented either in a uniform gravitational field or in Rindler space-time. There have been only a handful of proposals of type (ii), all of which are based on the same idea, namely that of one or more small masses interacting gravitationally [20][21][22][23]. The difficulty of type (ii) experiments can be appreciated by looking at the current experimental limits on the detection of weak gravitational forces [24,25].…”