Quantum Speed Limit for Observables, Derived from Asymmetry, Relates to Coherence for Single Qubit Measurements

The fundamental limits on how quickly quantum systems evolve represent a critical challenge in developing advanced quantum technologies, and Agung Budiyono, Michael Moody, and Hadyan L. Prihadi, alongside Rafika Rahmawati and colleagues, have now established a new quantum speed limit governing the rate at which asymmetry and coherence, essential resources for quantum advantage, can be consumed. Their work demonstrates that the speed of a quantum process is fundamentally linked to the asymmetry of the system relative to the measured observable, providing a novel formulation of this limit. This research reveals a direct connection between weak measurements and the rate of asymmetry consumption, and importantly, establishes a complementary relationship for the speed of multiple, mutually unbiased measurements on a single qubit. By defining a thermodynamic speed limit, the team offers a significant step towards understanding and optimising the performance of future quantum devices.

The research demonstrates that the speed of an observable’s expectation value is constrained by the degree of asymmetry between the state and the observable itself, providing a quantifiable bound on how quickly information can be processed. This limit is directly measurable through weak quantum measurements and has relevance in the field of quantum metrology. Researchers showed that the quantum speed limit is also related to the precision with which values of an observable can be estimated, with the limit being upper-bounded by the quantum Fisher information, a measure of sensitivity to changes in a parameter.

Furthermore, the limit is intrinsically linked to quantum fluctuations, with the limit being upper-bounded by the genuine quantum fluctuations of the observable within the quantum state, establishing a fundamental difference from classical mechanics. The team also established a link between quantum contextuality and the speed limit, revealing that a non-vanishing quantum speed of an expectation value is sufficient to indicate quantum contextuality. Importantly, the team extended this speed limit to the realm of quantum thermodynamics, deriving a corresponding limit for the rate of nonequilibrium entropy production. This connection highlights that asymmetry and coherence are not merely abstract quantum features, but play a crucial role in determining the speed of thermodynamic processes. The findings reinforce the understanding that quantum asymmetry and coherence are essential resources for achieving advantages in information technologies and beyond.

Quantum Speed Limit Linked to State Asymmetry

Scientists have established a fundamental speed limit governing the rate at which quantum observables can change, directly linking this limit to the asymmetry and coherence within a quantum state. The research demonstrates that the speed of an observable’s expectation value is constrained by the degree of asymmetry between the state and the observable itself, providing a quantifiable bound on how quickly information can be processed. Experiments reveal this quantum speed limit is expressed as one-half of the trace-norm asymmetry. Researchers showed that the quantum speed limit is also related to the precision with which values of an observable can be estimated, with the limit being upper-bounded by the quantum Fisher information, a measure of sensitivity to changes in a parameter. Furthermore, the limit is intrinsically linked to quantum fluctuations, with the limit being upper-bounded by the genuine quantum fluctuations of the observable within the quantum state, establishing a fundamental difference from classical mechanics. The team also established a link between quantum contextuality and the speed limit, revealing that a non-vanishing quantum speed of an expectation value is sufficient to indicate quantum contextuality.

Quantum Speed Limit and Entropy Production

This work establishes a quantum speed limit for observables, formulated in terms of the asymmetry of a quantum state relative to the observable itself. The researchers demonstrate that this limit, determined by the degree of asymmetry, is directly measurable through weak quantum measurements and has relevance in the field of quantum metrology. Furthermore, the limit is intrinsically linked to the coherence present within the evolving quantum state, offering a novel perspective on the relationship between these fundamental quantum properties. The researchers acknowledge that the quantum speed limit vanishes in the high-temperature, semiclassical limit, indicating that the limit is most relevant when quantum effects are prominent. Future research may explore the implications of this speed limit in more complex quantum systems and its potential applications in optimizing quantum technologies.