The developments of special relativity and quantum mechanics marked beginning of modern physics age. The former has taught us that while space and time are frame dependent notions, there is a quantity---the space-time interval---whose value all inertial observers agree upon. This reveals, so to speak, a genuine fact of universe, a relativistic invariant. On other hand, since dawn of quantum mechanics, there is no consensus on what theory is all about. The situation is admittedly subtler: quantum theory is grounded on a complex vector space and very notions of and reference frame are controversial. Here we construct a theoretical framework within which a given combination of quantum resources is shown to be a Galilean invariant. To this end, we postulate a principle of relational symmetry between the observer and the observed and employ notion of quantum reference frame. Unitary transformations then follow that allow us to perceive physical resources seen from viewpoint of any quantum system. Interestingly, we find that one needs more than quantum coherence and quantum correlations to prove quantum resources covariance. Finally, we show that notion of physical reality implied by quantum mechanics is not absolute.
The developments of special relativity and quantum mechanics marked beginning of modern physics age. The former has taught us that while space and time are frame dependent notions, there is a quantity---the space-time interval---whose value all inertial observers agree upon. This reveals, so to speak, a genuine fact of universe, a relativistic invariant. On other hand, since dawn of quantum mechanics, there is no consensus on what theory is all about. The situation is admittedly subtler: quantum theory is grounded on a complex vector space and very notions of and reference frame are controversial. Here we construct a theoretical framework within which a given combination of quantum resources is shown to be a Galilean invariant. To this end, we postulate a principle of relational symmetry between the observer and the observed and employ notion of quantum reference frame. Unitary transformations then follow that allow us to perceive physical resources seen from viewpoint of any quantum system. Interestingly, we find that one needs more than quantum coherence and quantum correlations to prove quantum resources covariance. Finally, we show that notion of physical reality implied by quantum mechanics is not absolute.
Measurements invariably determine the physical state of a given ``observed system'' with respect to an ``observer system.'' This implies an inescapable two-body relationality upon which physical theories must rely. There has been a growing effort to understand how quantum mechanics can accommodate the notion of reference frame in its substratum and whether such approach would respect general covariance. With regard to quantum resources, it has been shown that coherence and entanglement are not invariant upon changes of quantum reference frames. Here, we construct a theoretical framework within which a given combination of quantum resources, including not only coherence and entanglement, is shown to be a physical invariant. Under the premise of the universality of quantum phenomena, the proven covariance between quantum reference frames then implies that the total quantumness accessible to any observer in the universe is absolute.
In general relativity, the description of spacetime relies on idealised rods and clocks, which identify a reference frame. In any concrete scenario, reference frames are associated to physical systems, which are ultimately quantum in nature. A relativistic description of the laws of physics hence needs to take into account such quantum reference frames (QRFs), through which spacetime can be given an operational meaning. Here, we introduce the notion of a spacetime quantum reference frame, associated to a quantum particle in spacetime. Such formulation has the advantage of treating space and time on equal footing, and of allowing us to describe the dynamical evolution of a set of quantum systems from the perspective of another quantum system, where the parameter in which the rest of the physical systems evolves coincides with the proper time of the particle taken as the QRF. Crucially, the proper times in two different QRFs are not related by a standard transformation, but they might be in a quantum superposition one with respect to the other.Concretely, we consider a system of N relativistic quantum particles in a weak gravitational field, and introduce a timeless formulation in which the global state of the N particles appears "frozen", but the dynamical evolution is recovered in terms of relational quantities. The position and momentum Hilbert space of the particles is used to fix the QRF via a transformation to the local frame of the particle such that the metric is locally inertial at the origin of the QRF. The internal Hilbert space corresponds to the clock space, which keeps the proper time in the local frame of the particle. Thanks to this fully relational construction we show how the remaining particles evolve dynamically in the relational variables from the perspective of the QRF. The construction proposed here includes the Page-Wootters mechanism for non interacting clocks when the external degrees of freedom are neglected. Finally, we find that a quantum superposition of gravitational redshifts and a quantum superposition of special-relativistic time dilations can be observed in the QRF.
Viewing frames of reference as physical systems, subject to the same laws as the systems they describe, is central to the relational approach in physics. Under the assumption that quantum mechanics universally governs all physical entities, this perspective naturally leads to the concept of quantum reference frames (QRFs). We investigate the perspective-dependence of position and momentum uncertainties, correlations, covariance matrices, and entanglement within the QRF formalism. We show that the Robertson-Schrödinger uncertainty relations are frame-dependent, and so are correlations and variances, which satisfy various constraints described as inequalities. However, the determinant of the total covariance matrix, linked to the uncertainty volume in phase space, as well as variance-based entanglement criteria, remains invariant under changes of reference frame. Under specific conditions, the purities of subsystems are also invariant for different QRFs, but in general, they are perspective-dependent. These invariants suggest fundamental, robust measures of uncertainty and entanglement that persist despite changes in observational perspective, potentially inspiring dedicated quantum information protocols as well as further foundational studies.
In physics, every observation is made with respect to a frame of reference. Although reference frames are usually not considered as degrees of freedom, in all practical situations it is a physical system which constitutes a reference frame. Can a quantum system be considered as a reference frame and, if so, which description would it give of the world? Here, we introduce a general method to quantise reference frame transformations, which generalises the usual reference frame transformation to a "superposition of coordinate transformations". We describe states, measurement, and dynamical evolution in different quantum reference frames, without appealing to an external, absolute reference frame, and find that entanglement and superposition are frame-dependent features. The transformation also leads to a generalisation of the notion of covariance of dynamical physical laws, to an extension of the weak equivalence principle, and to the possibility of defining the rest frame of a quantum system.
Under the principle that quantum mechanical observables are invariant under relevant symmetry transformations, we explore how the usual, non-invariant quantities may capture measurement statistics. Using a relativisation mapping, viewed as the incorporation of a quantum reference frame, we show that the usual quantum description approximates the relative one precisely when the reference system admits an appropriate localisable quantity and a localised state. From this follows a new perspective on the nature and reality of quantum superpositions and optical coherence.
Under the principle that quantum-mechanical observables are invariant under relevant symmetry transformations, we explore how the usual, non-invariant quantities may capture measurement statistics. Using a relativisation mapping, viewed as the incorporation of a quantum reference frame, we show that the usual quantum description approximates the relative one precisely when the reference system admits an appropriate localisable quantity and a localised state. From this follows a new perspective on the nature and reality of quantum superpositions and optical coherence.