A new theoretical framework proposes that gravity may arise from entropy, offering a fresh perspective on the deep connections between geometry, quantum mechanics and statistical physics. Developed by Ginestra Bianconi, a mathematical physicist at Queen Mary University of London, UK, and published in Physical Review D, this modified version of gravity provides new quantum information theory insights on the well-established link between statistical mechanics and gravity that is rooted in the thermodynamic properties of black holes.

Quantum relative entropy

At the heart of Bianconi’s theory is the concept of quantum relative entropy (QRE). This is a fundamental concept of information theory, and it quantifies the difference in information encoded in two quantum states. More specifically, QRE is a measure of how much information of one quantum state is carried by another quantum state.

Bianconi’s idea is that the metrics associated with spacetime are quantum operators that encode the quantum state of its geometry. Building on this geometrical insight, she proposes that the action for gravity is the QRE between two different metrics: one defined by the geometry of spacetime and another by the matter fields present within it. In this sense, the theory takes inspiration from John Wheeler’s famous description of gravity: “Matter tells space how to curve, and space tells matter how to move.” However, it also goes further, as it aims to make this relationship explicit in the mathematical formulation of gravity, framing it in a statistical mechanics and information theory action.

Additionally, the theory adapts QRE to the Dirac-Kähler formalism extended to bosons, allowing for a more nuanced understanding of spacetime. The Dirac-Kähler formalism is a geometric reformulation of fermions using differential forms, unifying spinor and tensor descriptions in a coordinate-free way. In simpler terms, it offers an elegant way to describe particles like electrons using the language of geometry and calculus on manifolds.

The role of the G-field

For small energies and low values of spacetime curvature (the “low coupling” regime), the equations Bianconi presents reduce to the standard equations of Einstein’s general theory of relativity. Beyond this regime, the full modified Einstein equations can be written in terms of a new field, the G-field, that gives rise to a non-zero cosmological constant. Often associated with the accelerated expansion of the universe, the cosmological constant contributes to the still-mysterious substance known as dark energy, which is estimated to make up 68% of the mass-energy in the universe. A key feature of Bianconi’s entropy-based theory is that the cosmological constant is actually not constant, but dependent on the G-field. Hence, a key feature of the G-field is that it might provide new insight into what the cosmological constant really is, and where it comes from.

The G-field also has implications for black hole physics. In a follow-up work, Bianconi shows that a common solution in general relativity known as the Schwarzschild metric is an approximation, with the full solution requiring consideration of the G-field’s effects.

What does this mean for quantum gravity and cosmology?

The existence of a connection between black holes and entropy also raises the possibility that Bianconi’s framework could shed new light on the black hole information paradox. Since black holes are supposed to evaporate due to Hawking radiation, the paradox addresses the question of whether information that falls into a black hole is truly lost after evaporation. Namely, does a black hole destroy information forever, or is it somehow preserved?

The general theory predicts that the QRE for the Schwarzschild black hole follows the area law, a key feature of black hole thermodynamics, suggesting that further exploration of this framework might lead to new answers about the fundamental nature of black holes.

Unlike other approaches to quantum gravity that are primarily phenomenological, Bianconi’s framework seeks to understand gravity from first principles by linking it directly to quantum information and statistical mechanics. When asked how she became interested in this line of research, she emphasizes the continuity between her previous work on the topology and geometry of higher-order networks, her work on the topological Dirac operator and her current pursuits.

“I was especially struck by a passage in Gian Francesco Giudice’s recent book Before the Big Bang, where a small girl asks, ‘If your book speaks about the universe, does it also speak about me?’” Bianconi says. “This encapsulates the idea that new bridges between different scientific domains could be key to advancing our understanding.”

Future directions

There is still much to explore in this approach. In particular, Bianconi hopes to extend this theory into second quantization, where fields are thought of as operators just as physical quantities (position, momentum, so on) are in first quantization. Additionally, the modified Einstein equations derived in this theory have yet to be fully solved, and understanding the full implications of the theory for classical gravity is an ongoing challenge.

Though the research is still in its early stages, Bianconi emphasizes that it could eventually lead to testable hypotheses. The relationship between the theory’s predicted cosmological constant and experimental measurements, for example, could offer a way to test it against existing data.

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Physicists at the Georgia Institute of Technology, US have introduced a novel way to generate entanglement between photons – an essential step in building scalable quantum computers that use photons as quantum bits (qubits). Their research, published in Physical Review Letters, leverages a mathematical concept called non-Abelian quantum holonomy to entangle photons in a deterministic way without relying on strong nonlinear interactions or irrevocably probabilistic quantum measurements.

Entanglement is fundamental to quantum information science, distinguishing quantum mechanics from classical theories and serving as a pivotal resource for quantum technologies. Existing methods for entangling photons often suffer from inefficiencies, however, requiring additional particles such as atoms or quantum dots and additional steps such as post-selection that eliminate all outcomes of a quantum measurement in which a desired event does not occur.

While post-selection is a common strategy for entangling non-interacting quantum particles, protocols for entangled state preparation that use post-selection are non-deterministic. This is because they rely upon making measurements, and the result of obtaining a certain state of the system after a measurement is associated with a probability, making it inevitably non-deterministic.

Non-Abelian holonomy

The new approach provides a direct and deterministic alternative. In it, the entangled photons occupy distinguishable spatial modes of optical waveguides, making entanglement more practical for real-world applications. To develop it, Georgia Tech’s Aniruddha Bhattacharya and Chandra Raman took inspiration from a 2023 experiment by physicists at Universität Rostock, Germany, that involved coupled photonic waveguides on a fused silica chip. Both works exploit a property known as non-Abelian holonomy, which is essentially a geometric effect that occurs when a quantum system evolves along a closed path in parameter space (more precisely, it is a matrix-valued generalization of a pure geometric phase).

In Bhattacharya and Raman’s approach, photons evolve in a waveguide system where their quantum states undergo a controlled transformation that leads to entanglement. The pair derive an analytical expression for the holonomic transformation matrix, showing that the entangling operation corresponds to a unitary rotation within an effective pseudo-angular momentum space. Because this process is fully unitary, it does not require measurement or external interventions, making it inherently robust.

Beyond the Hong-Ou-Mandel effect

A classic example of photon entanglement is the Hong–Ou–Mandel (HOM) effect, where two identical photons interfere at a beam splitter, leading to quantum correlations between them. The new method extends such interference effects beyond two photons, allowing deterministic entanglement of multiple photons and even higher-dimensional quantum states known as qudits (d-level systems) instead of qubits (two-level systems). This could significantly improve the efficiency of quantum information protocols.

Because state preparation and measurement are relatively straightforward in this approach, Bhattacharya and Raman say it is well-suited for quantum computing. Since the method relies on geometric principles, it naturally protects against certain types of noise, making it more robust than traditional approaches. They add that their technique could even be used to construct an almost universal set of near-deterministic entangling gates for quantum computation with light. “This innovative use of non-Abelian holonomy could shift the way we think about photonic quantum computing,” they say.

By providing a deterministic and scalable entanglement mechanism, Bhattacharya and Raman add that their method opens the door to more efficient and reliable photonic quantum technologies. The next steps will be to validate the approach experimentally and explore practical implementations in quantum communication and computation. Further in the future, it will be necessary to find ways of integrating this approach with other quantum systems, such as matter-based qubits, to enable large-scale quantum networks.

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