Talks

The Bekenstein bound posits a maximum entropy for matter with finite energy confined to a spacetime region. It is often interpreted as a fundamental limit on the information that can be stored by physical objects. In this work, we test this interpretation by asking whether the Bekenstein bound imposes constraints on a channel's communication capacity, a context in which information can be given a mathematically rigorous and operationally meaningful definition. We first derive a bound on the accessible information and demonstrate that the Bekenstein bound constrains the decoding instead of the encoding. Then we study specifically the Unruh channel that describes a stationary Alice exciting different species of free scalar fields to send information to an accelerating Bob, who is therefore confined to a Rindler wedge and exposed to the noise of Unruh radiation. We show that the classical and quantum capacities of the Unruh channel obey the Bekenstein bound. In contrast, the entanglement-assisted capacity is as large as the input size even at arbitrarily high Unruh temperatures. This reflects that the Bekenstein bound can be violated if we do not properly constrain the decoding operation in accordance with the bound. We further find that the Unruh channel can transmit a significant number of zero-bits, which are communication resources that can be used as minimal substitutes for the classical/quantum bits needed for many primitive information processing protocols, such as dense coding and teleportation. We show that the Unruh channel has a large zero-bit capacity even at high temperatures, which underpins the capacity boost with entanglement assistance and allows Alice and Bob to perform quantum identification. Therefore, unlike classical bits and qubits, zero-bits and their associated information processing capability are not constrained by the Bekenstein bound. (This talk is based on the recent work (https://arxiv.org/abs/2309.07436) with Patrick Hayden.)

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Zoom link: https://pitp.zoom.us/j/98778081764?pwd=WktjNU84R3NWRXNyVmt1eDVMK2JnUT09

Abstract TBA

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Zoom link: https://pitp.zoom.us/j/97133792880?pwd=d1pxMThTd1R3YjZUVENiOWRLOUZpZz09

I will introduce a new picture of quantum dynamics that might be thought of as "gauging" Schrodinger's picture that results in many "local" Hilbert spaces [1]. Truncating the dimensions of the local Hilbert spaces in this new picture yields an exciting new kind of tensor network whose computational cost does not increase with increasing spatial dimension (for fixed bond dimension) [2]. More detail: Although quantum dynamics are local for local Hamiltonians, the locality is not explicit in the Schrodinger picture since the wavefunction amplitudes do not obey a local equation of motion. In the first part of this talk, I will introduce a new picture of quantum dynamics—the gauge picture—which is similar to Schrodinger's picture, but with the feature that spatial locality is explicit in the equations of motion. In a sense, the gauge picture might be thought of as the result of "gauging" the global unitary symmetry of quantum dynamics into a local symmetry[1]. In the second part of the talk, I discuss a new kind of tensor network ansatz that is inspired from the gauge picture. In the gauge picture, different regions of space are associated with different Hilbert spaces, which are related by gauge connections. By relaxing the unitary constraint on the gauge connections, we can truncate the Hilbert space dimensions associated with different regions to obtain an approximate description of quantum dynamics. This truncated gauge picture, which we dub "quantum gauge network", is intriguingly similar to a classical lattice gauge theory coupled to a Higgs field (which are "local" wavefunctions in the gauge picture), but with non-unitary connections. In one spatial dimension, a quantum gauge network can be easily mapped to a matrix product density operator, and a matrix product state can be mapped to a quantum gauge network. Unlike tensor networks such as PEPS, quantum gauge networks boast the advantage that for fixed bond dimension, the computational cost does not increase with the number of spatial dimensions! Encoding fermionic wavefunctions is also remarkably straightforward. We provide a simple algorithm for approximately simulating quantum dynamics of bosonic or fermionic Hamiltonians in any spatial dimension. We compare the new quantum dynamics algorithm to exact methods for fermion systems in up to three spatial dimensions [2]. [1] The Gauge Picture of Quantum Dynamics. arXiv:2210.09314 [2] Quantum Gauge Networks: A New Kind of Tensor Network. arXiv:2210.12151

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Zoom link: https://pitp.zoom.us/j/94596192271?pwd=MytzNUx4ZEZEemkvcEEzbllWM1J6QT09

The onset of the formation of structure in the early universe was marked by the monolithic collapse of smooth peaks in the initial density field. This process creates prompt rho ~ r^-1.5 density cusps of dark matter, which persist largely unaltered through the subsequent growth of dark matter halos around them. Consequently, in the standard collisionless dark matter paradigm, these prompt cusps are expected to be enormously abundant, and one resides at the center of every halo and subhalo. Prompt cusps present new opportunities to test the nature of dark matter. In annihilating dark matter models, the abundance of these features and the high density inside them greatly influence the intensity and morphology of the annihilation signal. For example, if the Galactic Center gamma-ray excess is due to annihilating dark matter, then a matching signal from unresolved prompt cusps should be detectable elsewhere. Moreover, the properties of prompt cusps are closely linked to details of the primordial density field. In warm dark matter models, prompt cusps are expected to be large enough to influence stellar motions within galaxies at detectable levels.

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Zoom link: https://pitp.zoom.us/j/98307421845?pwd=V3BqZmtyQ09XcjBwNEltTzFPTHJPUT09

In this informal talk, I shall give a short introduction to the field of higher-order quantum transformations, including its subfield of indefinite causal order. I shall discuss some of the motivations and important results in the field, current research directions and open problems, as well potential applications in quantum information processing.

In classical relativity we usually think of the metric signature as fixed, but quantum cosmology already forces us to consider more general situations such as transitions from Riemannian to Lorentzian signature. I will discuss the less studied phenomenon of an overall "flip" where all metric components change sign simultaneously (e.g., from "East Coast" to "West Coast" signature). Such an overall flip can represent saddle point solutions in quantum cosmology, or appear classically in the Plebański formalism or even a slight extension of Einstein--Hilbert gravity. Interestingly, at such a transition the cosmological constant can change both sign and magnitude, with a pure sign change being the most minimalistic proposal. Cosmological solutions transitioning classically between de Sitter and anti de Sitter can be found immediately, and the quantisation of a minisuperspace model turns out to be simpler than in the fixed signature case: in particular, the gravitational action reduces to a pure boundary term. Various other applications and the relation to unimodular gravity are also discussed.

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Zoom link: https://pitp.zoom.us/j/93255772501?pwd=bWhzZUVBOTM2a3QvTGlXVGJ5TlZnUT09

In quantum field theories, locality and unitarity are essential properties. For functorial field theories, locality is manifested through compatibility with cutting and gluing of manifolds, which can be fully encoded in the definition of fully extended functorial field theories. However, unitarity or reflection positivity (its Euclidean version) has so far only been defined for non-extended or invertible field theories. In this talk, I will address the challenge of defining reflection positivity for extended topological field theories, proposing a definition based on a version of higher dagger categories.

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Zoom link: https://pitp.zoom.us/j/93806769415?pwd=TVJFbWlJK0JyZCtjbHMvOWYxVUlRUT09