Statistical mechanics of quantum measurement and quantum entanglement

Introduction

This proposal will provide five key planks for a new "statistical mechanics of measurement and entanglement" that is made necessary by several lines of progress.

Historical Context

Historically, the powerful theory of emergence in complex quantum systems was developed largely for many-body systems evolving with a time-independent Hamiltonian, usually very close to their ground state. Now, we must understand universality and emergence for a much broader range of quantum dynamical systems.

Reasons for the New Approach

The reasons are several:

1. Highly controllable quantum simulators are becoming experimental reality: instead of being constrained to Schrödinger dynamics with a fixed Hamiltonian, an ideal device allows arbitrary combinations of unitary evolution, repeated local measurements, and control operations. This larger arena allows new dynamical phases, as demonstrated by the measurement phase transition co-invented by the PI.
2. The "hydrodynamics" of many-body systems far from their ground state - perhaps coupled to an environment - is richer than expected, even for dynamics with a fixed Hamiltonian. New methods also mean it can be understood and computed in detail.

Ambitious Objectives

The ambitious objectives of STAQQ are:

1. Develop the theory of criticality due to measurement. Entanglement phase transitions are fundamentally different from simple ordering transitions - they require new tools.
2. Map out the broader landscape of dynamical phases in nonunitary quantum systems (with environmental decoherence and/or control operations).
3. Extend powerful computational tools developed (partly by the PI) in simple random circuit models to realistic condensed matter/cold atom Hamiltonians - yielding a detailed theory for the emergence of hydrodynamics (broadly construed).
4. Develop classical analogues of the measurement transitions above - a new branch of classical critical phenomena.
5. Use insights from quantum dynamics to understand "beyond-field-theory" quantum phase transitions, where standard tools fail.