We revisit the vexed question of how unpredictability can arise in a deterministic universe, focusing on unitary quantum theory. We discuss why quantum unpredictability is irrelevant for the possibility of what some people call `free-will’, and why existing `free-will’ arguments are themselves irrelevant to argue for or against a physical theory.
Peculiar phenomena appear in the discretization of a system invariant under reparametrization. The structure of the continuum limit is markedly different from the usual one, as in lattice QCD. First, the continuum limit does not require tuning a parameter in the action to a critical value. Rather, there is a regime where the system approaches a sort of asymptotic topological invariance (“Ditt-invariance”). Second, in this regime the expansion in the number of discretization points provides a good approximation to the transition amplitudes. These phenomena are relevant for understanding the continuum limit of quantum gravity. I illustrate them here in the context of a simple system.
The existence of incompatible observables is a cornerstone of quantum mechanics and a valuable resource in quantum technologies. Here we introduce a measure of incompatibility, called the mutual eigenspace disturbance (MED), which quantifies the amount of disturbance induced by the measurement of a sharp observable on the eigenspaces of another. The MED provides a metric on the space of von Neumann measurements, and can be efficiently estimated by letting the measurement processes act in an indefinite order, using a setup known as the quantum switch, which also allows one to quantify the noncommutativity of arbitrary quantum processes. Thanks to these features, the MED can be used in quantum machine learning tasks. We demonstrate this application by providing an unsupervised algorithm that clusters unknown von Neumann measurements. Our algorithm is robust to noise can be used to identify groups of observers that share approximately the same measurement context.
We extend the circuit model of quantum computation so that the wiring between gates is soft-coded within registers inside the gates. The addresses in these registers can be manipulated and put into superpositions. This aims at capturing indefinite causal orders and making their geometrical layout explicit: we express the quantum switch and the polarizing beam-splitter within the model. In this context, our main contribution is a full characterization of the anonymity constraints. Indeed, the names used as addresses should not matter beyond the wiring they describe, i.e. quantum evolutions should commute with “renamings”. We show that these quantum evolutions can still act non-trivially upon the names. We specify the structure of “nameblind” matrices.
The educational value of a fully diagrammatic approach in a scientific field has never been explored. We present Quantum Picturalism (QPic), an entirely diagrammatic formalism for all of qubit quantum mechanics. This framework is particularly advantageous for young learners as a novel way to teach key concepts such as entanglement, measurement, and mixed-state quantum mechanics in a math-intensive subject. This eliminates traditional obstacles without compromising mathematical correctness – removing the need for matrices, vectors, tensors, complex numbers, and trigonometry as prerequisites to learning. Its significance lies in that a field as complex as Quantum Information Science and Technology (QIST), for which educational opportunities are typically exclusive to the university level and higher, can be introduced at high school level. In this study, we tested this hypothesis, examining whether QPic reduces cognitive load by lowering complex mathematical barriers while enhancing mental computation and conceptual understanding. The data was collected from an experiment conducted in 2023, whereby 54 high school students (aged 16-18) underwent 16 hours of training spread over eight weeks. The post-assessments illustrated promising outcomes in all three specific areas of focus: (1) whether QPic can alleviate technical barriers in learning QIST, (2) ensures that the content and teaching method are age appropriate, (3) increases confidence and motivation in science and STEM fields. There was a notable success rate in terms of teaching outcomes, with 82% of participants successfully passing an end-of-training exam and 48% achieving a distinction, indicating a high level of performance. The unique testing and training regime effectively reduced the technical barriers typically associated with traditional approaches, as hypothesized.
Reference frames are crucial for describing local observers in general relativity. In quantum gravity, different proposals exist for how to treat reference frames. There are models with either classical or quantum reference frames. Recently, different choices appeared for investigating these possibilities at the level of the classical and quantum algebra of observables. One choice is based on the covariant phase space approach, using gravitational edge modes. In the canonical approach, there is another choice, relational clocks, built from matter or geometry itself. In this work, we extend existing results and show how to relate edge modes and geometrical clocks in linearized gravity. We proceed in three steps. First, we introduce an extension of the ADM (Arnowitt-Deser-Misner) phase space to account for covariant gauge fixing conditions and the explicit time dependence they add to Hamilton’s equations. Second, we show how these gauge fixing conditions recover a specific choice of geometrical clocks in terms of Ashtekar-Barbero connection variables. Third, we study the effect of the Barbero-Immirzi parameter on the generators of asymptotic symmetries and the corresponding charges. This parameter, which disappears from metric gravity, affects the generators for angle-dependent asymptotic symmetries and the corresponding super-translation charges, while it has no effect on the global charges.
The Einstein Equivalence Principle (EEP) is of crucial importance to test the foundations of general relativity. When the particles involved in the test exhibit quantum properties, it is unknown whether this principle still holds. A violation of the EEP would have drastic consequences for physics. A more conservative possibility is that the EEP holds in a generalised form for delocalised quantum particles. Here we formulate such a generalised EEP by extending one of its paradigmatic tests with clocks to quantum clocks that are in a quantum superposition of positions and velocities. We show that the validity of such a generalised version of the EEP is equivalent to the possibility of transforming to the perspective of an arbitrary Quantum Reference Frame (QRF), namely a reference frame associated to the quantum state of the clock. We further show that this generalised EEP can be verified by measuring the proper time of entangled clocks in a quantum superposition of positions in the Earth gravitational field. The violation of the generalised EEP corresponds to the impossibility of defining dynamical evolution in the frame of each clock, and results in a modification to the probabilities of measurements calculated in the laboratory frame. Hence, it can be verified experimentally, for instance in an atom interferometer.
Recent work on quantum reference frames (QRFs) has demonstrated that superposition and entanglement are properties that change under QRF transformations. Given their utility in quantum information processing, it is important to understand how a mere change of perspective can produce or reduce these resources. Here we find a trade-off between entanglement and subsystem coherence under a QRF transformation, in the form of a conservation theorem for their sum, for two pairs of measures. Moreover, we find a weaker trade-off for any possible pair of measures. Finally, we discuss the implications of this interplay for violations of Bell’s inequalities, clarifying that for any choice of QRF, there is a quantum resource responsible for the violation. These findings contribute to a better understanding of the quantum information theoretic aspects of QRFs, offering a foundation for future exploration in both quantum theory and quantum gravity.
We introduce a mathematical framework for symmetry-resolved entanglement entropy with a non-abelian symmetry group. To obtain a reduced density matrix that is block-diagonal in the non-abelian charges, we define subsystems operationally in terms of subalgebras of invariant observables. We derive exact formulas for the average and the variance of the typical entanglement entropy for the ensemble of random pure states with fixed non-abelian charges. We focus on compact, semisimple Lie groups. We show that, compared to the abelian case, new phenomena arise from the interplay of locality and non-abelian symmetry, such as the asymmetry of the entanglement entropy under subsystem exchange, which we show in detail by computing the Page curve of a many-body system with $SU(2)$ symmetry.
Quantum theory is often regarded as challenging to learn and teach, with advanced mathematical prerequisites ranging from complex numbers and probability theory to matrix multiplication, vector space algebra and symbolic manipulation within the Hilbert space formalism. It is traditionally considered an advanced undergraduate or graduate-level subject. In this work, we challenge the conventional view by proposing “Quantum Picturalism” as a new approach to teaching the fundamental concepts of quantum theory and computation. We establish the foundations and methodology for an ongoing educational experiment to investigate the question “From what age can students learn quantum theory if taught using a diagrammatic approach?”. We anticipate that the primary benefit of leveraging such a diagrammatic approach, which is conceptually intuitive yet mathematically rigorous, will be eliminating some of the most daunting barriers to teaching and learning this subject while enabling young learners to reason proficiently about high-level problems. We posit that transitioning from symbolic presentations to pictorial ones will increase the appeal of STEM education, attracting more diverse audience.
