Quantum Information

Holography with branes and/or cutoff surfaces presents a promising approach to studying quantum gravity beyond asymptotically anti-de Sitter spacetimes. However, this generalized holography is known to face several inconsistencies, including potential violations of causality and fundamental entropic inequalities. In this talk, we address these challenges by investigating the bulk scattering process and its holographic realization. Specifically, we propose that causality of a radially propagating excitation should be an induced one originating from a fictitious boundary behind the brane/cutoff surface. We present its consistency by checking the connected wedge theorem supported from quantum cryptography and (strong) subadditivity of holographic entanglement entropies. While the induced light cone seemingly permits superluminal signaling, we argue that this causality violation can be an artifact of state preparation in our picture. This talk is based on 2308.00739 [10.1007/JHEP10(2023)104] with Beni Yoshida.

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Zoom link https://pitp.zoom.us/j/98252951858?pwd=RVNZUjNVM2JkZXRlSXJVbEZ6cUpsUT09

Obtaining a description of cosmology is a central open problem in holography. Studying simple models can help us gain insight on the generic properties of holographic cosmologies. In this talk I will describe the construction of entangled microstates of a pair of holographic CFTs whose dual semiclassical description includes big bang-big crunch AdS cosmologies in spaces without boundaries. The cosmology is supported by inhomogeneous heavy matter and it partially purifies the bulk entanglement of two auxiliary AdS spacetimes. In generic settings, the cosmology is an entanglement island contained in the entanglement wedge of one of the two CFTs. I will then describe the properties of the non-isometric bulk-to-boundary encoding map and comment on an explicit, state-dependent boundary representation of operators acting on the cosmology. Finally, if time allows, I will argue for a non-isometric to approximately-isometric transition of the encoding of "simple" cosmological states as a function of the bulk entanglement, with tensor network toy models of the setup as a guide.

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Zoom link https://pitp.zoom.us/j/93483219872?pwd=TGpJVVlaNDVGWTN5ZHpkTHp6a2hTZz09

Classical simulation techniques are widely used in quantum computation and condensed matter physics. In this talk I will describe algorithms for classically simulating measurement of an n-qubit quantum state in the standard basis, that is, sampling a bit string from the probability distribution determined by the Born rule. Our algorithms reduce the sampling task (known as weak simulation) to computing poly(n) amplitudes of n-qubit states (strong simulation). Two classes of quantum states are considered: output states of polynomial-size quantum circuits and ground states of local Hamiltonians with an inverse polynomial energy gap. We show that our algorithm can significantly accelerate quantum circuit simulations based on tensor network contraction and low-rank stabilizer decompositions. To sample ground state probability distributions we employ the fixed-node Hamiltonian construction, previously used in Quantum Monte Carlo simulations to address the fermionic sign problem. We implement the proposed sampling algorithm numerically and use it to sample from the ground state of Haldane-Shastry Hamiltonian with up to 56 qubits. 

Joint work with Giuseppe Carleo, David Gosset, and Yinchen Liu

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Zoom link https://pitp.zoom.us/j/93297869296?pwd=TVpRdVJmU3lWZjVQM3NNKzBucVVRUT09

Quantum systems typically reach thermal equilibrium rather quickly when coupled to an external thermal environment. The usual way of bounding the speed of this process is by estimating the spectral gap of the dissipative generator. However, the gap, by itself, does not always yield a reasonable estimate for the thermalization time in many-body systems: without further structure, a uniform lower bound on it only constraints the thermalization time to be polynomially growing with system size. In this talk, we will discuss that for all 2-local models with commuting Hamiltonians, the thermalization time that one can estimate from the gap is in fact much smaller than direct estimates suggest: at most logarithmic in the system size. This yields the so-called rapid mixing of dissipative dynamics. We will show this result by proving that a finite gap directly implies a lower bound on the modified logarithmic Sobolev inequality (MLSI) for the class of models we consider. The result is particularly relevant for 1D systems, for which we can prove rapid thermalization with a constant decay rate, giving a qualitative improvement over all previous results. It also applies to hypercubic lattices, graphs with exponential growth rate, and trees with sufficiently fast decaying correlations in the Gibbs state. This has consequences for the rate of thermalization towards Gibbs states, and also for their relevant Wasserstein distances and transportation cost inequalities.

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Zoom link https://pitp.zoom.us/j/91315419731?pwd=TGpFTjlHWEJZVWZkdTh6bDFKMjhQZz09

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