Continuous gaussian measurements of the free boson CFT: A model for exactly solvable and detectable measurement-induced dynamics

Abstract

Hybrid evolution protocols, composed of unitary dynamics and repeated, weak or projective measurements, give rise to new, intriguing quantum phenomena, including entanglement phase transitions and unconventional conformal invariance. Defying the complications imposed by the non-linear and stochastic nature of the measurement process, we introduce a scenario of measurement-induced many body evolution, which possesses an exact analytical solution: bosonic Gaussian measurements. The evolution features a competition between the continuous observation of linear boson operators and a free Hamiltonian, and it is characterized by a unique and exactly solvable covariance matrix. Within this framework, we then consider an elementary model for quantum criticality, the free boson conformal field theory, and investigate in which way criticality is modified under measurements. Depending on the measurement protocol, we distinguish three fundamental scenarios (a) enriched quantum criticality, characterized by a logarithmic entanglement growth with a floating prefactor, or the loss of criticality, indicated by an entanglement growth with either (b) an area-law or (c) a volume-law. For each scenario, we discuss the impact of imperfect measurements, which reduce the purity of the wavefunction and are equivalent to Markovian decoherence, and present a set of observables, e.g., real-space correlations, the relaxation time, and the entanglement structure, to classify the measurement-induced dynamics for both pure and mixed states. Finally, we present an experimental tomography scheme, which grants access to the density operator of the system by using the continuous measurement record only.

Numerical evaluation and robustness of the quantum mean-force Gibbs state

“…This numerical approach allows one to simulate a system with linear coupling to a reservoir of harmonic oscillators, with arbitrary forms and strengths of system-reservoir coupling. The method has been applied to a variety of problems in open quantum systems [24][25][26][27][28][29][30][31][32]. It has also been used to make conceptual connections to the process tensor (PT) formulation of open quantum systems [33,34].…”

Topological order and entanglement dynamics in the measurement-only XZZX quantum code

“…In a quantum circuit, frequent local measurements, which do not commute with the generators of the unitary dynamics induce a phase transition in the dynamics of entanglement [1][2][3]. This phenomenon has been observed in random quantum circuits, where the unitary evolution is generated by Clifford [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] or Haar [1,3,[18][19][20][21][22][23][24][25][26] random gates and in Hamiltonian systems, where the unitary time evolution is continuous [27][28][29][30][31][32][33][34][35][36][37][38][39]. Due to the inherent randomness of the measurement process, the entanglement phase transitions do not manifest on the level of ensemble averaged, local order parameters but only in higher moments, or replicas of the state [11,20,31,<...>…”

Dynamics of measured many-body quantum chaotic systems

“…The necessity to deal with system replicas complicates the theoretical description of measurement dynamics [17][18][19][20][38][39][40][41][42][43]. However, external monitoring also implies a simplification: A continuously observed system is subject to noise representing the randomness of measurement outcomes [21,[44][45][46][47]. Decoherence due to this noise effectively projects states onto configurations diagonal in the measurement basis.…”