Abstract
Unitary circuits subject to repeated projective measurements can undergo an entanglement phase transition (EPT) as a function of the measurement rate. This transition is generally understood in terms of a competition between the scrambling effects of unitary dynamics and the disentangling effects of measurements. We find that, surprisingly, EPTs are possible even in the absence of scrambling unitary dynamics, where they are best understood as arising from measurements alone. This finding motivates us to introduce measurement-only models, in which the “scrambling” and “unscrambling” effects driving the EPT are fundamentally intertwined and cannot be attributed to physically distinct processes. These models represent a novel form of an EPT, conceptually distinct from that in hybrid unitary-projective circuits. We explore the entanglement phase diagrams, critical points, and quantum code properties of some of these measurement-only models. We find that the principle driving the EPTs in these models is frustration, or mutual incompatibility, of the measurements. Surprisingly, an entangling (volume-law) phase is the generic outcome when measuring sufficiently long but still local (-body) operators. We identify a class of exceptions to this behavior (“bipartite ensembles”) which cannot sustain an entangling phase but display dual area-law phases, possibly with different kinds of quantum order, separated by self-dual critical points. Finally, we introduce a measure of information spreading in dynamics with measurements and use it to demonstrate the emergence of a statistical light cone, despite the nonlocality inherent to quantum measurements.
- Received 9 June 2020
- Revised 8 December 2020
- Accepted 5 January 2021
DOI:https://doi.org/10.1103/PhysRevX.11.011030
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
Measuring a quantum system affects its state and can degrade its quantum entanglement, a “spooky” correlation among particles that powers quantum computing. Recently, researchers showed that monitored quantum systems, whose evolution is punctuated by measurements, exhibit distinct “entanglement phases” as a function of the measurement rate. Intuitively, there is competition between the system’s chaotic dynamics and the measurements: The former generate entanglement while the latter destroy it. Contrary to this intuition, we show that even when the unobserved system has no dynamics of its own, measurements alone can support distinct entanglement phases and transitions. This is made possible by another unique feature of quantum measurements: Heisenberg’s uncertainty principle, whereby “incompatible” observables cannot be known at the same time.
The phase diagrams of these models reveal that the amount of “frustration,” or mutual incompatibility, between different measurements is what drives the entanglement phase transitions. While most of these models allow for an extensively entangled phase, we identify a class of exceptions where such a phase is impossible, based on the algebra of observables being measured. We also find that information obeys an emergent speed limit in these dynamics, despite the fact that measurements enable nonlocal “quantum teleportation.”
The experimental requirements for realizing these dynamics are very similar to those needed for the stabilization of “topologically encoded” quantum bits, which are some of the leading candidates for fault-tolerant quantum memories. This makes our results testable in near-term quantum computing devices.
