Quantum Information

I will discuss a concrete realization in N=4 SYM of the mechanism of cryptographic censorship: that sufficiently random time evolution in a holographic CFT incurs an event horizon in the bulk dual. I will show that perturbing half-BPS states by randomly distributing a large number of defects on them corresponds in the gravitational dual to exciting an extremal (horizonless) black hole to near-extremality. This random distribution of defects corresponds to acting with a typical random isometry on the half-BPS subspace. This allows us to interpret this process in the field theory as an extension of cryptographic censorship.

Our search for a quantum theory of gravity is aided by a unique and perplexing feature of the classical theory: General Relativity “knows” about its own quantum states (the entropy of a black hole), and about those of all matter (via the Quantum Focusing Conjecture). The results we are able to extract from classical gravity are inherently non-perturbative and increasingly sophisticated. Recent breakthroughs include a derivation of the entropy of Hawking radiation, a computation of the exact integer number of states of some black holes, a proof of the QFC, and the construction of gravitational holograms in general spacetimes. The nature of the oracle, and its full power, remain unknown.

The Ryu-Takayanagi formula implies that the entropy, a non-linear function of the state, is an observable in the semiclassical limit. This is a general phenomenon in a class of quantum error-correcting codes (QECC), but few specific area operators in the boundary CFT. In this work, I define a specific code in a holographic 2d CFT that includes all thermofield double states with arbitrary amounts of time evolution, but no bulk local degrees of freedom. While the naive area operator vanishes, it is possible to write down an area operator for appropriately classical states; the answer matches with previous results obtained from bulk considerations. Interestingly, this area operator involves an explicit coarse-graining. This suggests a construction for a non-isometric holographic map for these states.

The entanglement entropy for regions in a BMS field theory living at null infinity has been proposed to be holographically dual to certain ‘swing surfaces’ in flat space. We lift this construction to AdS/CFT and revisit both bulk and boundary aspects of this proposal.

In quantum gravity, the gravitational path integral involves a sum over topologies, representing the joining and splitting of multiple universes. To account for topology change, one is led to allow the creation and annihilation of both closed and open universes in a framework often called third quantization or universe field theory. We argue that since topology change in gravity is a rare event, its contribution to late-time physics should be universally governed by a Poisson distribution. In the Fock space of closed baby universes, this Poisson distribution corresponds to the statistics of the number operator in a coherent state, whereas allowing for the creation of asymptotic open universes calls for a non-commutative generalization of a Poisson process. We propose such an operator algebraic framework, called Poissonization, which takes as input the observable algebra and a (unnormalized) state of a quantum system and outputs a von Neumann algebra represented on its symmetric Fock space. Physically, our construction is a generalization of the coherent state vacua of bipartite quantum systems.

We construct algebras of diff-invariant observables in a global de Sitter universe with two observers and a free scalar QFT in two dimensions. In the limit when the observers have infinite mass and are localized along geodesics at the North and South poles, it was shown in previous work (CLPW) that their algebras are mutually commuting type II_1 factors. Away from this limit, we show that the algebras fail to commute and that they are type I non-factors. Physically, this is because the observers' trajectories are uncertain and state-dependent, and they may come into causal contact. We compute out-of-time-ordered correlators along an observer's worldline, and observe a Lyapunov exponent given by 4πβ_dS, as a result of observer recoil and de Sitter expansion. This should be contrasted with results from AdS gravity, and exceeds the chaos bound associated with the de Sitter temperature by a factor of two. We also discuss how the cosmological horizon emerges in the large mass limit and comment on implications for de Sitter holography.

In quantum systems with infinitely many degrees of freedom, states can be infinitely entangled across a pair of subsystems. But are there different forms of infinite entanglement? In the first part of my talk, I will present a von Neumann algebraic framework for studying information-theoretic properties of infinite systems. Using this framework, we find operational tasks that distinguish different forms of infinite entanglement, and, by analysing these tasks, we show that the type classification of von Neumann algebras (types I, II, III, and their respective subtypes) is in 1-to-1 correspondence with operational entanglement properties. Our findings promote the type classification from mere algebraic bookkeeping to a classification of infinite quantum systems based on their operational entanglement properties. In the second part, I will discuss what is known about the type classification of the von Neumann algebras arising in quantum many-body systems. Together with our results, this identifies new operational properties, e.g., embezzlement of entanglement, of well-known physical models, e.g., the critical transverse-field Ising chain or suitable Levin-Wen models. Joint work with: Alexander Stottmeister, Reinhard F. Werner, and Henrik Wilming

The entropy accumulation theorem (EAT) allows us to lower bound the min-entropy of a state that can be generated by a chain of quantum channels satisfying a Markov chain condition, and can be used to prove the security of QKD protocols, including device-independent ones. However, one of its drawbacks is that it only applies to states with a fairly rigid structure; in particular, the Markov chain condition must be satisfied exactly. What happens when we relax this assumption by allowing the required structure to be satisfies only approximately? Does doing so lead to interesting applications? We answer both questions by the affirmative: we present two flavours of approximate EAT, and show that it can be used to prove the security of parallel device-independent QKD, and to analyze QKD protocols under source correlations. Along the way, we will introduce the concept of "approximation chain" which underpins the new results.   This is joint work with Ashutosh Marwah; the talk will cover material from 2412.06723, 2402.12346, and 2308.11736.

Abstract: The experimental realization of increasingly complex quantum states in quantum devices underscores the pressing need for new methods of state learning and verification. Among the various classes of quantum states, fermionic systems hold particular significance due to their crucial roles in physics. Despite their importance, research on learning quantum states of fermionic systems remains surprisingly limited. In our work, we aim to present a comprehensive rigorous study on learning and testing states of fermionic systems. We begin by analyzing arguably the simplest important class of fermionic states—free-fermionic states—and subsequently extend our analysis to more complex fermionic states. We meticulously delineate scenarios in which efficient algorithms are feasible, providing experimentally practical algorithms for these cases, while also identifying situations where any algorithm for solving these problems must be inherently inefficient. At the same time, we present novel fundamental results of independent interest on fermionic systems, with additional applications beyond learning and characterizing quantum devices, such as many-body physics, resource theory of non-Gaussianity, and circuit compilation strategies. (Talk based on https://arxiv.org/pdf/2409.17953 , https://arxiv.org/pdf/2402.18665)