Achieving the volume-law entropy regime with random-sign Dicke states

TL;DR

This paper demonstrates how introducing random signs into Dicke states can tune their entanglement to reach volume-law entropy, approaching that of Haar-random states, with practical realizations on shallow quantum circuits.

Contribution

It shows that sign randomness in Dicke states enhances entanglement, enabling exploration of volume-law regimes and practical implementation on quantum platforms.

Findings

Random-sign Dicke states achieve near Page's entropy estimates.

Entanglement can be tuned via sign structure in wave functions.

State complexity changes are measurable through pattern dissimilarity.

Abstract

Manipulating entanglement, which reflects non-local correlations in a quantum system and defines the complexity of describing its wave function, represents the extremely tough challenge in the fields of quantum computing, quantum information, and condensed matter physics. In this work, by the example of the well-structured Dicke states we demonstrate that the complexity of these real-valued wave functions can be accurately tuned by introducing a random-sign structure, which allows us to explore the regime of the volume-law entanglement. Importantly, setting nontrivial sign structure one can increase the entanglement entropy of the Dicke state to the values that are close to Page's estimates for Haar-random states. The practical realization of these random-sign Dicke states is possible on different physical platforms with shallow quantum circuits. On the level of the measurements the change in the quantum state complexity due to sign structure can be traced out with the dissimilarity measure that estimates multi-scale variety of patterns in bit-string arrays.