Publicaties

1 - 10 of 39 resultaten

Zoek term:

Bounds on quantum evolution complexity via lattice cryptography Vrije Universiteit Brussel

Ben Craps, Marine De Clerck, Oleg Evnin, Philip Hacker, Maxim Pavlov
We address the difference between integrable and chaotic motion in quantum theory as manifested by the complexity of the corresponding evolution operators. Complexity is understood here as the shortest geodesic distance between the time-dependent evolution operator and the origin within the group of unitaries. (An appropriate `complexity metric' must be used that takes into account the relative difficulty of performing `nonlocal' operations that ...

Bounds on quantum evolution complexity via lattice cryptography Vrije Universiteit Brussel

Ben Craps, Marine De Clerck, Oleg Evnin, Philip Hacker, Maxim Pavlov
We address the difference between integrable and chaotic motion in quantum theory as manifested by the complexity of the corresponding evolution operators. Complexity is understood here as the shortest geodesic distance between the time-dependent evolution operator and the origin within the group of unitaries. (An appropriate `complexity metric' must be used that takes into account the relative difficulty of performing `nonlocal' operations that ...

Quantum chaos and the complexity of spread of states Vrije Universiteit Brussel

Vijay Balasubramanian, Javier Magan
We propose a measure of quantum state complexity defined by minimizing the spread of the wave-function over all choices of basis. Our measure is controlled by the "survival amplitude" for a state to remain unchanged, and can be efficiently computed in theories with discrete spectra. For continuous Hamiltonian evolution, it generalizes Krylov operator complexity to quantum states. We apply our methods to the harmonic and inverted oscillators, ...

Submerging islands through thermalization Vrije Universiteit Brussel

Vijay Balasubramanian, Ben Craps, Mikhail Khramtsov
We illustrate scenarios in which Hawking radiation collected in finite regions of a reservoir provides temporary access to the interior of black holes through transient entanglement "islands". Whether these islands appear and the amount of time for which they dominate - sometimes giving way to a thermalization transition - is controlled by the amount of radiation we probe. In the first scenario, two reservoirs are coupled to an eternal black ...

Complexity Growth in Integrable and Chaotic Models Vrije Universiteit Brussel

Vijay Balasubramanian
We use the SYK family of models with $N$ Majorana fermions to study the complexity of time evolution, formulated as the shortest geodesic length on the unitary group manifold between the identity and the time evolution operator, in free, integrable, and chaotic systems. Initially, the shortest geodesic follows the time evolution trajectory, and hence complexity grows linearly in time. We study how this linear growth is eventually truncated by ...

Violation of CHSH inequality and marginal laws in mixed sequential measurements with order effects Vrije Universiteit Brussel

Massimiliano Sassoli De Bianchi

We model a typical Bell-test experimental situation by considering that Alice and Bob perform incompatible measurements in a sequential way, with mixed orders of execution. After emphasizing that order effects will generally produce a violation of the marginal laws, we derive an upper limit for the observed correlations. More precisely, when Alice’s and Bob’s measurements are compatible, the marginal laws are obeyed and Tsirelson’s bound ...

Chaos in the butterfly cone Vrije Universiteit Brussel

Márk Mezei, Gabor Sarosi

A simple probe of chaos and operator growth in many-body quantum systems is the out of time ordered four point function. In a large class of local systems, the effects of chaos in this correlator build up exponentially fast inside the so called butterfly cone. It has been previously observed that the growth of these effects is organized along rays and can be characterized by a velocity dependent Lyapunov exponent, λ(v). We show that this ...

Quantum Complexity of Time Evolution with Chaotic Hamiltonians Vrije Universiteit Brussel

Vijay Balasubramanian

We study the quantum complexity of time evolution in large-N chaotic systems, with the SYK model as our main example. This complexity is expected to increase linearly for exponential time prior to saturating at its maximum value, and is related to the length of minimal geodesics on the manifold of unitary operators that act on Hilbert space. Using the Euler-Arnold formalism, we demonstrate that there is always a geodesic between the identity ...

Quantum entanglement in physical and cognitive systems Vrije Universiteit Brussel

Diederik Aerts, Jonito Aerts Arguëlles, Lester Beltran, Suzette Geriente, Massimiliano Sassoli De Bianchi, Sandro Sozzo, Tomas Veloz
We provide a general description of the phenomenon of entanglement in bipartite systems, as it manifests in micro and macro physical systems, as well as in human cognitive processes. We do so by observing that when genuine coincidence measurements are considered, the violation of the 'marginal laws', in addition to the Bell-CHSH inequality, is also to be expected. The situation can be described in the quantum formalism by considering the ...

Binding Complexity and Multiparty Entanglement Vrije Universiteit Brussel

Vijay Balasubramanian, Matthew DeCross, Arjun Kar, Onkar Parrikar
We introduce "binding complexity", a new notion of circuit complexity which quantifies the difficulty of distributing entanglement among multiple parties, each consisting of many local degrees of freedom. We define binding complexity of a given state as the minimal number of quantum gates that must act between parties to prepare it. To illustrate the new notion we compute it in a toy model for a scalar field theory, using certain multiparty ...