Don Marolf
University of California Santa Barbara
January 2022
Quantum Euler angles and agency-dependent spacetime
Quantum gravity is expected to introduce quantum aspects into the description of reference frames. Here we set the stage for exploring how quantum gravity induced deformations of classical symmetries could modify the transformation laws among reference frames in an effective regime. We invoke the quantum group $SU_q(2)$ as a description of deformed spatial rotations and interpret states of a representation of its algebra as describing the relative orientation between two reference frames. This leads to a quantization of one of the Euler angles and to the new paradigm of agency-dependence: space is reconstructed as a collection of fuzzy points, exclusive to each agent, which depends on their choice of reference frame. Each agent can choose only one direction in which points can be sharp, while points in all other directions become fuzzy in a way that depends on this choice. Two agents making different choices will thus observe the same points with different degrees of fuzziness.
Witnessing the non-objectivity of an unknown quantum dynamics
Quantum Darwinism offers an explanation for the emergence of classical objective features — those we are used to at macroscopic scales — from quantum properties at the microscopic level. The interaction of a quantum system with its surroundings redundantly proliferates information to many parts of the environment, turning it accessible and objective to different observers. But given that one cannot probe the quantum system directly, only its environment, how to witness whether an unknown quantum property can be deemed objective or not? Here we propose a probabilistic framework to analyze this question and show that objectivity implies a Bell-like inequality. Among several other results, we show quantum violations of this inequality, a device-independent proof of the non-objectivity of quantum correlations that give rise to the phenomenon we name “collective hallucination”: observers probing distinct parts of the environment can agree upon their measurement outcome of a given observable but such outcome can be totally uncorrelated from the property of the quantum system that fixed observable should be probing. We also implement an appealing photonic experiment where the temporal degree of freedom of photons is the quantum system of interest, while their polarization acts as the environment. Employing a fully black-box approach, we achieve the violation of a Bell inequality, thus certifying the non-objectivity of the underlying quantum dynamics in a fully device-independent framework.
Experimental nonclassicality in a causal network without assuming freedom of choice
In a Bell experiment, it is natural to seek a causal account of correlations wherein only a common cause acts on the outcomes. For this causal structure, Bell inequality violations can be explained only if causal dependencies are modelled as intrinsically quantum. There also exists a vast landscape of causal structures beyond Bell that can witness nonclassicality, in some cases without even requiring free external inputs. Here, we undertake a photonic experiment realizing one such example: the triangle causal network, consisting of three measurement stations pairwise connected by common causes and no external inputs. To demonstrate the nonclassicality of the data, we adapt and improve three known techniques: (i) a machine-learning-based heuristic test, (ii) a data-seeded inflation technique generating polynomial Bell-type inequalities and (iii) entropic inequalities. The demonstrated experimental and data analysis tools are broadly applicable paving the way for future networks of growing complexity.
Experimental demonstration of input-output indefiniteness in a single quantum device
At the fundamental level, the dynamics of quantum fields is invariant under the combination of time reversal, charge conjugation, and parity inversion. This symmetry implies that a broad class of effective quantum evolutions are bidirectional, meaning that the exchange of their inputs and outputs gives rise to valid quantum evolutions. Recently, it has been observed that quantum theory is theoretically compatible with a family of operations in which the roles of the inputs and outputs is indefinite. However, such operations have not been demonstrated in the laboratory so far. Here we experimentally demonstrate input-output indefiniteness in a photonic setup, demonstrating an advantage in a quantum game and showing incompatibility with a definite input-output direction by more than 69 standard deviations. Our results establish input-output indefiniteness as a new resource for quantum information protocols, and enable the table-top simulation of hypothetical scenarios where the arrow of time could be in a quantum superposition.
Time, space and matter in the primordial universe
Time, space, and matter are categories of our reasoning, whose properties appear to be fundamental. However, these require a scrutiny as in the extreme regime of the primordial universe these present quantum properties. What does it mean for time to be quantum? What does it mean for space? Are space and time disappearing, or what is disappearing are simply the categories we have been using to understand them? Concepts such as the superposition of causal structures or the quantum granularity of space require our attention and should be clarified to understand the physics of the primordial universe. The novelty that this brings requires us to reflect on matter as well: How can matter be defined on a granular space? Is quantum gravity hinting us toward considering new types of matter? The answers to these questions, that touch the foundations of physics and the very concepts with which we organize our understanding of reality, require in the end of the journey to confront ourselves with empirical data. And for that, the universe itself provides us with the best of possible laboratories.
Radiative corrections to the Lorentzian EPRL spin foam propagator
We numerically estimate the divergence of several two-vertex diagrams that contribute to the radiative corrections for the Lorentzian EPRL spin foam propagator. We compute the amplitudes as functions of a homogeneous cutoff over the bulk quantum numbers, fixed boundary data, and different Immirzi parameters, and find that for a class of two-vertex diagrams, those with fewer than six internal faces are convergent. The calculations are done with the numerical framework sl2cfoam-next.
Metriplectic geometry for gravitational subsystems
In general relativity, it is difficult to localise observables such as energy, angular momentum, or centre of mass in a bounded region. The difficulty is that there is dissipation. A self-gravitating system, confined by its own gravity to a bounded region, radiates some of the charges away into the environment. At a formal level, dissipation implies that some diffeomorphisms are not Hamiltonian. In fact, there is no Hamiltonian on phase space that would move the region relative to the fields. Recently, an extension of the covariant phase space has been introduced to resolve the issue. On the extended phase space, the Komar charges are Hamiltonian. They are generators of dressed diffeomorphisms. While the construction is sound, the physical significance is unclear. We provide a critical review before developing a geometric approach that takes into account dissipation in a novel way. Our approach is based on metriplectic geometry, a framework used in the description of dissipative systems. Instead of the Poisson bracket, we introduce a Leibniz bracket – a sum of a skew-symmetric and a symmetric bracket. The symmetric term accounts for the loss of charge due to radiation. On the metriplectic space, the charges are Hamiltonian, yet they are not conserved under their own flow.
Tabletop Experiments for Quantum Gravity Are Also Tests of the Interpretation of Quantum Mechanics
Recently there has been a great deal of interest in tabletop experiments intended to exhibit the quantum nature of gravity by demonstrating that it can induce entanglement. We argue that these experiments also provide new information about the interpretation of quantum mechanics: under appropriate assumptions, $psi$-complete interpretations will generally predict that these experiments will have a positive result, $psi$-nonphysical interpretations predict that these experiments will not have a positive result, and for $psi$-supplemented models there may be arguments for either outcome. We suggest that a positive outcome to these experimenst would rule out a class of quantum gravity models that we refer to as $psi$-incomplete quantum gravity (PIQG) – i.e. models of the interaction between quantum mechanics and gravity in which gravity is coupled to non-quantum beables rather than quantum beables. We review some existing PIQG models and consider what more needs to be done to make these sorts of approaches more appealing, and finally we discuss a cosmological phenomenon which could be regarded as providing evidence for PIQG models.