Scientific Series

Aside from quantum mechanics, other areas in physics constrain information processing. From relativity, we know information cannot move faster than the speed of light. In quantum gravity, we expect but don't fully understand additional constraints, for instance on how densely information can be stored. Can we develop an understanding of information processing in the context of quantum gravity? Towards doing so, we consider quantum information within ``holographic'' spacetimes, which have an alternative, non-gravitational, description. In that context questions about information processing in the presence of gravity can be translated to different questions about quantum information without gravity. As a specific example, we study constraints on computation within a gravitating region, and use the holographic description to argue that gravity constrains the complexity of operations that can happen inside the region. Along the way, we are led to new connections relating quantum gravity, position-based cryptography, quantum secret sharing and complexity theory. 

Topological quantum codes illustrate a variety of concepts in quantum many-body physics. They also provide a realistic and resource-efficient approach to building scalable quantum computers. In this talk, I will focus on fault-tolerant quantum computing with a new topological code, the 3D subsystem toric code (STC). The 3D STC can be realized on the cubic lattice by measuring small-weight local parity checks. The 3D STC is capable of handling measurement errors while performing reliable quantum error correction and implementing logical gates in constant time. This dramatically reduces the computational time overhead and gives the 3D STC a resilience to time-correlated noise.

The formalism of quantum theory over discrete systems is extended in two significant ways. First, tensors and traceouts are generalized, so that systems can be partitioned according to almost arbitrary logical predicates. Second, quantum evolutions are generalized to act over network configurations, in such a way that nodes be allowed to merge, split and reconnect coherently in a superposition. The hereby presented mathematical framework is anchored on solid grounds through numerous lemmas. Indeed, one might have feared that the familiar interrelations between the notions of unitarity, complete positivity, trace-preservation, non-signalling causality, locality and localizability that are standard in quantum theory be jeopardized as the partitioning of systems becomes both logical and dynamical. Such interrelations in fact carry through, albeit two new notions become instrumental: consistency and comprehension.

Joint work with Amélia Durbec and Matt Wilson

Reference: https://arxiv.org/abs/2110.10587

Zoom Link: https://pitp.zoom.us/j/97185954578?pwd=OC9mUzl4L3V4WDZzVEZoekpOS24wQT09

In this talk, I will revisit the calculation of infinite-dimensional symmetries that emerge in the vicinity of isolated horizons. In particular, I will focus my attention on extremal black holes, for which the isometry algebra that preserves a sensible set of asymptotic boundary conditions at the horizon strictly includes the BMS algebra. The conserved charges that correspond to this BMS sector, however, reduce to those of superrotation, generating only two copies of Witt algebra. For more general horizon isometries, in contrast, the charge algebra does include both Witt and supertranslations, being similar to BMS but s.str. differing from it. I will also show how this is extended to the case of black holes in the Einstein-Yang-Mills case, where a loop algebra associated to the gauge group is found to emerge at the horizon.

The formalism of general probabilistic theories provides a universal paradigm that is suitable for describing various physical systems including classical and quantum ones as particular cases. Contrary to the often assumed no-restriction hypothesis, the set of accessible measurements within a given theory can be limited for different reasons, and this raises a question of what restrictions on measurements are operationally relevant. We argue that all operational restrictions must be closed under simulation, where the simulation scheme involves mixing and classical post-processing of measurements. We distinguish three classes of such operational restrictions: restrictions on measurements originating from restrictions on effects; restrictions on measurements that do not restrict the set of effects in any way; and all other restrictions. As a setting to detect nonclassicality in restricted theories we consider generalizations of random access codes, an intriguing class of communication tasks that reveal an operational and quantitative difference between classical and quantum information processing. We formulate a natural generalization of them, called random access tests, which can be used to examine collective properties of collections of measurements. We show that the violation of a classical bound in a random access test is a signature of either measurement incompatibility or super information storability, and that we can use them to detect differences in different restrictions.
 

This talk consists of two parts. At first, I will focus on geometric obstructions to decoding Hawking radiation (python’s lunch). Harlow and Hayden argued that distilling information out of Hawking radiation is computationally hard despite the fact that the quantum state of the black hole and its radiation is relatively un-complex. I will trace this computational difficulty to a geometric obstruction in the Einstein-Rosen bridge connecting the black hole and its radiation. Inspired by tensor network models, I will present a conjecture that relates the computational hardness of distilling information to geometric features of the wormhole.

Then, with the long-term goal of studying quantum gravity in the lab, I will discuss a proposal for a holographic teleportation protocol that can be readily executed in table-top experiments. This protocol exhibits similar behavior to that seen in recent traversable wormhole constructions. I will introduce the concept of "teleportation by size" to capture how the physics of operator-size growth naturally leads to information transmission. The transmission of a signal through a semi-classical holographic wormhole corresponds to a rather special property of the operator-size distribution we call "size winding". 

Zoom Link: https://pitp.zoom.us/j/93957279481?pwd=eGVTU1MwOGNWNkMyYlRiWGo0QnFldz09

The mixing time of Markovian dissipative evolutions of open quantum many-body systems can be bounded using optimal constants of certain quantum functional inequalities, such as the logarithmic Sobolev constant, which is equivalent to some form of entropy decay. For classical spin systems, the positivity of such constants follows from a mixing condition on the Gibbs measure, via quasi-factorization results for the entropy. Inspired by the classical case, we present a strategy to derive the positivity of the logarithmic Sobolev constant associated to the dynamics of certain quantum systems from some clustering conditions on the Gibbs state of a local, commuting Hamiltonian. Subsequently, we apply it to show that for a finite-range, translation-invariant commuting Hamiltonian on a spin chain, the Davies semigroup describing the reduced dynamics resulting from the joint Hamiltonian evolution of a spin chain weakly coupled to a large heat bath thermalizes rapidly at any temperature. This, in particular, rigorously establishes the absence of dissipative phase transition for Davies evolutions over translation-invariant spin chains.
 

Bell’s theorem is typically understood as proof that quantum theory is incompatible with local hidden variable (LHV) models. In recent years, however, LHV models have been recognized as a particular and simple case of much more general causal networks that can give rise to new and stronger forms of nonclassicality. And, since nonlocality is a resource in a variety of applications, it is thus natural to ask whether these novel forms of nonclassical behavior can also be put to use in information processing. In this seminar, I will present recent results exploring quantum correlations in several such causal scenarios, ranging from foundational questions such as freedom of choice in Bell experiments to more applied situations covering cryptography, distributed computing, and game theory.

Zoom Link: TBD

In this talk, we will discuss the late time behavior of out of time ordered correlators (OTOC). First part of the talk, we argue the nonlinear behavior of OTOC for general chaotic system is controlled by a Dray t’Hooft like action. Second part of the talk, we will discuss the late time nonperturbative effects in OTOC and its relation with random unitary behavior.

Higgs inflation introduces a large non-minimal coupling between the Ricci scalar and Higgs that makes the cut-off scale well below the Planck scale. In the first part of the talk, we show that unitarity is indeed violated by a resonant production of longitudinal gauge bosons after inflation, calling for UV completion of Higgs inflation. We then show that unitarity is restored after summing over vacuum polarization-type diagrams that are leading-order in the large-N limit. Scattering amplitude develops a pole after the resummation, which we identify as the scalar component of the metric, or the scalaron. This phenomenon can be understood in the language of the non-linear sigma model (NLSM), with the scalaron identified as the sigma-meson that linearizes the NLSM.

Zoom Link: https://pitp.zoom.us/j/98015814051?pwd=YWdrWTJzbzJkdnFXRUxPWFJnNXVNQT09

Most of the efforts in searching for dark energy (DE) have focused on its gravitational signatures, and in particular on constraining its equation of state. However, there is a lot to be learned about DE by getting off the beaten track. I will first focus on non-gravitational interactions of DE with visible matter, leading to the possibility of "direct detection of dark energy" (analogous to direct detection of dark matter): I will argue that such interactions can and potentially may already have been detected in experiments such as XENON1T, while discussing complementary cosmological and astrophysical signatures. I will then discuss early- and late-time consistency tests of LCDM, and how these may shed light on (early and late) DE in relation to the Hubble tension. I will present two such tests based on the early ISW effect and the ages of the oldest astrophysical objects in the Universe.

A basic calculation in QFT is the construction of the Yukawa potential from a tree-level scattering amplitude. In the massless limit, this reproduces the 1/r potential. For gravity, scattering mediated by a massless graviton is thus consistent with the Newtonian potential.

In de Sitter spacetime, the cosmological constant gives rise to a mass-like term in the graviton propagator. This raises the question what the classical potential looks like when taking into account curvature effects.

In this talk, I will introduce an operator-based formalism to compute scattering amplitudes in curved spacetime, and I will show how to construct the Newtonian potential in a dS background. Remarkably, the potential gives rise to an additional repulsive force, and encodes the de Sitter horizon in a novel and non-trivial way.