Measurements conspire nonlocally to restructure critical quantum states

Abstract

We study theoretically how local measurements perfomed on critical quantum ground states affect long-distance correlations. These states are highly entangled and feature algebraic correlations between local observables. As a consequence, local measurements can have highly nonlocal effects. Our focus is on Tomonaga-Luttinger liquid (TLL) ground states, a continuous family of critical states in one dimension whose structure is parameterized by a Luttinger parameter $K$. We show that arbitrarily weak local measurements, performed over extended regions of space, can conspire to drive transitions in long-distance correlations. Conditioning first on a particular measurement outcome we show that there is a transition in the character of the post-measurement quantum state for $K<1$, and highlight a formal analogy with the effect of a static impurity on transport through a TLL. To investigate the full ensemble of measurement outcomes we consider averages of physical quantities which are necessarily nonlinear in the system density matrix. We show how their behavior can be understood within a replica field theory, and for the measurements that we consider we find that the symmetry of the theory under exchange of replicas is broken for $K<1/2$. A well-known barrier to experimentally observing the collective effects of multiple measurements has been the need to post-select on random outcomes. Here we resolve this problem by introducing cross-correlations between experimental measurement results and classical simulations, which act as resource-efficient probes of the transition. The phenomena we discuss are, moreover, robust to local decoherence.

15+6 pages

References in corpus (15)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Experimental quantum teleportation
• Matrix product states represent ground states faithfully
• Measurement-Induced Entanglement Transitions in the Quantum Ising Chain: From Infinite to Zero Clicks
• Effective Theory for the Measurement-Induced Phase Transition of Dirac Fermions
• Quantum gas microscopy for single atom and spin detection
• Postselection-free entanglement dynamics via spacetime duality
• Thermodynamics of the Spin Luttinger-Liquid in a Model Ladder Material
• Measurement-induced dark state phase transitions in long-ranged fermion systems
• Symmetry enriched phases of quantum circuits
• Measurement as a shortcut to long-range entangled quantum matter
• Quantum Circuits assisted by LOCC: Transformations and Phases of Matter
• Continuous Gaussian Measurements of the Free Boson CFT: A model for Exactly Solvable and Detectable Measurement-Induced Dynamics
• Probing sign structure using measurement-induced entanglement
• Nondestructive imaging of an ultracold lattice gas

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