arXiv subjects

Flaminia Giacomini

Publications and source records attributed to Flaminia Giacomini.

32 records · Page 2Linked to original sources

arXiv2021

Spacetime Quantum Reference Frames and superpositions of proper times

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 QRF, associated to a quantum particle in spacetime. Such formulation has the advantage of treating space and time on equal footing, and of describing the dynamical evolution of a set of quantum systems from the perspective of another quantum system, where the evolution parameter 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. Concretely, we consider 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, keeping the proper time in the local frame of the particle. This fully relational construction shows how the remaining particles evolve from the perspective of the QRF and includes the Page-Wootters mechanism for non interacting clocks when the external degrees of freedom are neglected. Finally, we observe a quantum superposition of gravitational redshifts and a quantum superposition of special-relativistic time dilations in the QRF.

quant-ph↗

arXiv2021

Relativistic Bell Test within Quantum Reference Frames

A still widely debated question in the field of relativistic quantum information is whether entanglement and the degree of violation of Bell's inequalities for massive relativistic particles are frame independent or not. At the core of this question is the effect that spin gets entangled with the momentum degree of freedom at relativistic velocities. Here, we show that Bell's inequalities for a pair of particles can be maximally violated in a special-relativistic regime, even without any post-selection of the momentum of the particles. To this end, we use the methodology of quantum reference frames, which allows us to transform the problem to the rest frame of a particle, whose state can be in a superposition of relativistic momenta from the viewpoint of the laboratory frame. We show that, when the relative motion of two particles is non-collinear, the optimal measurements for violation of Bell's inequalities in the laboratory frame involve "coherent Wigner rotations". Moreover, the degree of violation of Bell's inequalities is independent of the choice of the quantum reference frame. Our results open up the possibility of extending entanglement-based quantum communication protocols to relativistic regimes.

quant-ph↗

arXiv2021

The group structure of dynamical transformations between quantum reference frames

Recently, it was shown that when reference frames are associated to quantum systems, the transformation laws between such quantum reference frames need to be modified to take into account the quantum and dynamical features of the reference frames. This led to a relational description of the phase space variables of the quantum system of which the quantum reference frames are part of. While such transformations were shown to be symmetries of the system's Hamiltonian, the question remained unanswered as to whether they enjoy a group structure, similar to that of the Galilei group relating classical reference frames in quantum mechanics. In this work, we identify the canonical transformations on the phase space of the quantum systems comprising the quantum reference frames, and show that these transformations close a group structure defined by a Lie algebra, which is different from the usual Galilei algebra of quantum mechanics. We further find that the elements of this new algebra are in fact the building blocks of the quantum reference frames transformations previously identified, which we recover. Finally, we show how the transformations between classical reference frames described by the standard Galilei group symmetries can be obtained from the group of transformations between quantum reference frames by taking the zero limit of the parameter that governs the additional noncommutativity introduced by the quantum nature of inertial transformations.

quant-ph↗

arXiv2020

Comment on "Revisiting dynamics of quantum causal structures --when can causal order evolve?''

In the last few years, there has been increasing interest in quantum processes with indefinite causal order. Process matrices are a convenient framework to study such processes. Ref. [1] defines higher order transformations from process matrices to process matrices and shows that no continuous and reversible transformation can change the causal order of a process matrix. Ref. [2] argues, based on a set of examples, that there are situations where a process can change its causal order over time. Ref. [2] claims that the formalism of higher order transformations is not general enough to capture its examples. Here we show that this claim is incorrect. Moreover, a crucial example of Ref. [2] has already been explicitly considered in Ref. [1] and shown to be compatible with its results.

quant-ph↗

arXiv2020

Quantum clocks and the temporal localisability of events in the presence of gravitating quantum systems

The standard formulation of quantum theory relies on a fixed space-time metric determining the localisation and causal order of events. In general relativity, the metric is influenced by matter, and is expected to become indefinite when matter behaves quantum mechanically. Here, we develop a framework to operationally define events and their localisation with respect to a quantum clock reference frame, also in the presence of gravitating quantum systems. We find that, when clocks interact gravitationally, the time localisability of events becomes relative, depending on the reference frame. This relativity is a signature of an indefinite metric, where events can occur in an indefinite causal order. Even if the metric is indefinite, for any event we can find a reference frame where local quantum operations take their standard unitary dilation form. This form is preserved when changing clock reference frames, yielding physics covariant with respect to quantum reference frame transformations.

quant-ph↗

arXiv2020

A change of perspective: switching quantum reference frames via a perspective-neutral framework

Treating reference frames fundamentally as quantum systems is inevitable in quantum gravity and also in quantum foundations once considering laboratories as physical systems. Both fields thereby face the question of how to describe physics relative to quantum reference systems and how the descriptions relative to different such choices are related. Here, we exploit a fruitful interplay of ideas from both fields to begin developing a unifying approach to transformations among quantum reference systems that ultimately aims at encompassing both quantum and gravitational physics. In particular, using a gravity inspired symmetry principle, which enforces physical observables to be relational and leads to an inherent redundancy in the description, we develop a perspective-neutral structure, which contains all frame perspectives at once and via which they are changed. We show that taking the perspective of a specific frame amounts to a fixing of the symmetry related redundancies in both the classical and quantum theory and that changing perspective corresponds to a symmetry transformation. We implement this using the language of constrained systems, which naturally encodes symmetries. Within a simple one-dimensional model, we recover some of the quantum frame transformations of arXiv:1712.07207, embedding them in a perspective-neutral framework. Using them, we illustrate how entanglement and classicality of an observed system depend on the quantum frame perspective. Our operational language also inspires a new interpretation of Dirac and reduced quantized theories within our model as perspective-neutral and perspectival quantum theories, respectively, and reveals the explicit link between them. In this light, we suggest a new take on the relation between a `quantum general covariance' and the diffeomorphism symmetry in quantum gravity.

quant-ph↗

arXiv2019

Relativistic quantum reference frames: the operational meaning of spin

The spin is the prime example of a qubit. Encoding and decoding information in the spin qubit is operationally well defined through the Stern-Gerlach set-up in the non-relativistic (i.e., low velocity) limit. However, an operational definition of the spin in the relativistic regime is missing. The origin of this difficulty lies in the fact that, on the one hand, the spin gets entangled with the momentum in Lorentz-boosted reference frames, and on the other hand, for a particle moving in a superposition of velocities, it is impossible to "jump" to its rest frame, where spin is unambiguously defined. Here, we find a quantum reference frame transformation corresponding to a "superposition of Lorentz boosts," allowing us to transform to the rest frame of a particle that is in a superposition of relativistic momenta with respect to the laboratory frame. This enables us to first move to the particle's rest frame, define the spin measurements there (via the Stern-Gerlach experimental procedure), and then move back to the laboratory frame. In this way, we find a set of "relativistic Stern-Gerlach measurements" in the laboratory frame, and a set of observables satisfying the spin $\mathfrak{su}(2)$ algebra. This operational procedure offers a concrete way of testing the relativistic features of the spin, and opens up the possibility of devising quantum information protocols for spin in the special-relativistic regime.

quant-ph↗

arXiv2019

Information Content of the Gravitational Field of a Quantum Superposition

When a massive quantum body is put into a spatial superposition, it is of interest to consider the quantum aspects of the gravitational field sourced by the body. We argue that in order to understand how the body may become entangled with other massive bodies via gravitational interactions, it must be thought of as being entangled with its own Newtonian-like gravitational field. Thus, a Newtonian-like gravitational field must be capable of carrying quantum information. Our analysis supports the view that table-top experiments testing entanglement of systems interacting via gravity do probe the quantum nature of gravity, even if no ``gravitons'' are emitted during the experiment.

quant-ph↗

arXiv2019

Quantum mechanics and the covariance of physical laws in quantum reference frames

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.

quant-ph↗

arXiv2018

Quantum Superposition of Massive Objects and the Quantization of Gravity

We analyse a gedankenexperiment previously considered by Mari et al. that involves quantum superpositions of charged and/or massive bodies ("particles") under the control of the observers, Alice and Bob. In the electromagnetic case, we show that the quantization of electromagnetic radiation (which causes decoherence of Alice's particle) and vacuum fluctuations of the electromagnetic field (which limits Bob's ability to localize his particle to better than a charge-radius) both are essential for avoiding apparent paradoxes with causality and complementarity. We then analyze the gravitational version of this gedankenexperiment. We correct an error in the analysis of Mari et al. and of Baym and Ozawa, who did not properly account for the conservation of center of mass of an isolated system. We show that the analysis of the gravitational case is in complete parallel with the electromagnetic case provided that gravitational radiation is quantized and that vacuum fluctuations limit the localization of a particle to no better than a Planck length. This provides support for the view that (linearized) gravity should have a quantum field description.

quant-ph↗

arXiv2018

Thermal and spectral dimension of (generalized) Snyder noncommutative spacetimes

We report an investigation of the Snyder noncommutative spacetime and of some of its most natural generalizations, also looking at them as a powerful tool for comparing different notions of dimensionality of a quantum spacetime. It is known that (generalized-)Snyder noncommutativity, while having rich off-shell implications (kinematical Hilbert space), does not affect on-shell particles (physical Hilbert space), and we argue that physically meaningful notions of dimensionality should describe such spacetimes as trivially four-dimensional, without any running with scales. By studying the thermodynamics of a gas of massless particles living on these spacetimes, we find that indeed the Snyder model and its generalizations have constant thermal dimension of four. We also compute the spectral dimension of the Snyder model and its generalizations, finding that, as a result of its sensitivity to off-shell properties, it runs from the standard value of four in the infrared towards lower values in the ultraviolet limit.

hep-th↗

arXiv2018

Dynamics of quantum causal structures

It was recently suggested that causal structures are both dynamical, because of general relativity, and indefinite, due to quantum theory. The process matrix formalism furnishes a framework for quantum mechanics on indefinite causal structures, where the order between operations of local laboratories is not definite (e.g. one cannot say whether operation in laboratory A occurs before or after operation in laboratory B). Here we develop a framework for "dynamics of causal structures", i.e. for transformations of process matrices into process matrices. We show that, under continuous and reversible transformations, the causal order between operations is always preserved. However, the causal order between a subset of operations can be changed under continuous yet nonreversible transformations. An explicit example is that of the quantum switch, where a party in the past affects the causal order of operations of future parties, leading to a transition from a channel from A to B, via superposition of causal orders, to a channel from B to A. We generalise our framework to construct a hierarchy of quantum maps based on transformations of process matrices and transformations thereof.

quant-ph↗

arXiv2017

Entanglement of quantum clocks through gravity

In general relativity, the picture of spacetime assigns an ideal clock to each worldline. Being ideal, gravitational effects due to these clocks are ignored and the flow of time according to one clock is not affected by the presence of clocks along nearby worldlines. However, if time is defined operationally, as a pointer position of a physical clock that obeys the principles of general relativity and quantum mechanics, such a picture is at most a convenient fiction. Specifically, we show that the general relativistic mass-energy equivalence implies gravitational interaction between the clocks, while the quantum mechanical superposition of energy eigenstates leads to a non-fixed metric background. Based only on the assumption that both principles hold in this situation, we show that the clocks necessarily get entangled through time dilation effect, which eventually leads to a loss of coherence of a single clock. Hence, the time as measured by a single clock is not well-defined. However, the general relativistic notion of time is recovered in the classical limit of clocks.

quant-ph↗

arXiv2016

Indefinite causal structures for continuous-variable systems

In all our well-established theories, it is assumed that events are embedded in a global causal structure such that, for every pair of events, the causal order between them is always fixed. However, the possible interplay between quantum mechanics and general relativity may require a revision of this paradigm. The process matrix framework keeps the validity of quantum physics locally but does not assume the existence of a global causal order. It allows to describe causal structures corresponding to a quantum superposition of 'A is before B' and 'B is before A'. So far, the framework has been developed only for finite-dimensional systems, and a straightforward generalization to infinite dimensions leads to singularities. Such generalization is necessary for continuous-variable systems and is a prerequisite for quantum fields on indefinite causal structures. Here we develop the process-matrix framework for continuous-variable systems. We encounter and solve the problems of singularities. Moreover, we study an example of a process in infinite dimensions, and we derive correlations exhibiting intereference due to processes in which A is before B and B is before A.

quant-ph↗