Quantum trajectories for entanglement phenomena

Ana Maria Dima, M. Dima

Edward R. Floyd

Bibliography ............................................................................................................50 Entanglement phenomena offer fine, didactic examples that demonstrate the application of quantum trajectories. Quantum entanglement phenomena are tractable to the quantum trajectory representation. Quantum trajectories render insight into entanglement phenomena of quantum systems. Entanglement is one of the prime features that distinguishes quantum mechanics from classical mechanics. Entanglement implies nonlocality as confirmed by the Aspect experiments [1-3]. Entangled quantum systems have nonclassical correlations that manifest nonlocal behavior for the system. The quantum trajectory representation can describe how entanglement induces nonlocality [4]. Within the foundations of quantum mechanics, a quantum trajectory representation of entangled systems is the key to resolving the nonintuitive behavior of wave packet spreading [4], the which-way paradox of the double-slit experiment [5], and the Einstein-Podolsky-Rosen (EPR) paradox [6].

Shivan Mittal, Bin Yan

Stochastic quantum trajectories, such as pure state evolutions under unitary dynamics and random measurements, offer a crucial ensemble description of many-body open system dynamics. Recent studies have highlighted that individual quantum trajectories also encode essential physical information. Prominent examples include measurement-induced phase transitions, where a pure quantum state corresponding to fixed measurement outcomes (trajectories) exhibits distinct entanglement phases, depending on the measurement rate. However, direct observation of this effect is hindered by an exponential postselection barrier, whereby the probability of realizing a specific trajectory is exponentially small. We propose a deterministic method to efficiently prepare quantum trajectories in polynomial time using imaginary time evolution and, thus, overcome this fundamental challenge. We demonstrate that our method applies to a certain class of quantum states, and argue that universal approaches do not exist for any quantum trajectories. Our result paves the way for experimentally exploring the physics of individual quantum trajectories at scale and enables direct observation of certain postselection-dependent phenomena.

徐峰, 王立飞, 崔晓东

Zejian Li, Anna Delmonte, Xhek Turkeshi +1 more

Measurement-induced phases exhibit unconventional dynamics as emergent collective phenomena, yet their behavior in tailored interacting systems - crucial for quantum technologies - remains less understood. We develop a systematic toolbox to analyze monitored dynamics in long-range interacting systems, relevant to platforms like trapped ions and Rydberg atoms. Our method extends spin-wave theory to general dynamical generators at the quantum trajectory level, enabling access to a broader class of states than approaches based on density matrices. This allows efficient simulation of large-scale interacting spins and captures nonlinear dynamical features such as entanglement and trajectory correlations. We showcase the versatility of our framework by exploring entanglement phase transitions in a monitored spin system with power-law interactions in one and two dimensions, where the entanglement scaling changes from logarithm to volume law as the interaction range shortens, and by dwelling on how our method mitigates experimental post-selection challenges in detecting monitored quantum phases.