Replica Keldysh Field Theory Unifies Quantum-Jump Processes in Bosonic and Fermionic Systems

Measurement-induced phase transitions typically assume perfect detection, yet many real-world scenarios involve imperfect monitoring and more complex quantum processes. Felix Kloiber-Tollinger and Lukas M. Sieberer, from the Institute for Theoretical Physics at the University of Innsbruck, now present a comprehensive theoretical framework addressing these broader conditions. Their work develops a replica Keldysh field theory capable of describing general quantum-jump processes in both bosonic and fermionic systems, unifying descriptions of efficient detection, mixed-state dynamics, and even standard deterministic evolution. This achievement establishes a crucial link between phase transitions in driven open systems and those arising from measurement, and the researchers demonstrate its power by applying it to imbalanced and inefficient fermion counting in a one-dimensional lattice, revealing how undetected jumps fundamentally alter entanglement and correlation lengths. The resulting framework offers a versatile foundation for understanding measurement-induced phenomena across a wide range of monitored and open quantum systems.

This work addresses a significant gap in theoretical understanding by providing a unified description of pure-state trajectories under efficient detection and mixed-state dynamics emerging from inefficient monitoring, with deterministic evolution appearing as a limiting case. The team overcame a central technical challenge by averaging over quantum trajectories within the replica field-theory framework, accounting for both fluctuating jump times and jump types, a feat previously unresolved for state-dependent rates. The study pioneered a method for incorporating imperfect measurements, specifically inefficient detection, into the theoretical framework, using a detection efficiency parameter ranging from zero to one.

Researchers analytically extended existing models of balanced fermion counting to encompass imbalanced scenarios, where gain and loss rates differ, and incorporated the effects of inefficient detection. To demonstrate the formalism, scientists analyzed imbalanced and inefficient fermion counting in a one-dimensional lattice system, modeling fermion gain and loss as a quantum-jump process generated by fermionic annihilation and creation operators. The team showed analytically and through numerical simulations that, even with imbalanced rates, entanglement obeys an area law for any nonzero gain and loss rates, indicating the absence of a measurement-induced phase transition.,.

Measurement Drives Quantum Phase Transitions and Dynamics

Scientists developed a comprehensive theoretical framework for understanding measurement-induced phase transitions in quantum systems, extending beyond traditional scenarios of perfect detection to encompass both non-Hermitian measurements and inefficient detection. This work applies to both bosonic and fermionic systems, providing a unified description of dynamics ranging from efficient monitoring yielding pure quantum states to mixed-state evolution arising from inefficient measurement. The formalism establishes a direct connection between phase transitions in nonequilibrium steady states of driven open quantum matter and those induced by measurement, bridging previously disparate areas of research. Researchers investigated imbalanced and inefficient fermion counting in a one-dimensional lattice system, modeling fermion gain and loss at potentially unequal rates, with a fraction of jumps undetected.

For balanced rates, the team demonstrated that entanglement obeys an area law for any nonzero jump rate, revealing an extended quantum-critical regime emerging between two parametrically separated length scales, consistent with prior findings. However, the introduction of inefficient detection fundamentally alters this behavior, introducing a finite correlation length beyond which entanglement, quantified by fermionic logarithmic negativity, also obeys an area law. Measurements confirm that subsystem entropy exhibits volume-law scaling under inefficient detection, indicating a significant change in the system’s entanglement properties. The team analytically and numerically demonstrated that even with imbalanced rates, the qualitative behavior observed in balanced systems persists, eliminating the need for fine-tuning of parameters. Numerical simulations strongly support the analytical findings, validating the theoretical framework and its ability to accurately predict the behavior of complex quantum systems under realistic measurement conditions.,.

Measurement Transitions and Open System Dynamics

This research establishes a comprehensive theoretical framework for understanding measurement-induced phase transitions, extending beyond traditional scenarios of perfect detection to encompass both non-Hermitian measurements and inefficient detection. The team developed a replica Keldysh field approach that unifies descriptions of pure-state trajectories with mixed-state dynamics, demonstrating a direct connection between phase transitions in driven open systems and those arising from measurement processes. This formalism allows for the study of a broad range of monitored and open systems, offering a versatile foundation for future investigations. Applying this framework to imbalanced fermion counting in a one-dimensional lattice, the researchers found that entanglement obeys an area law for any non-zero jump rate when detection is efficient, with an extended critical regime emerging between length scales. Importantly, the introduction of inefficient detection leads to a finite correlation length, altering the entanglement behaviour and demonstrating volume-law scaling in subsystem entropy. Numerical simulations confirm these analytical findings, validating the accuracy of the developed formalism and its ability to accurately model complex quantum dynamics.