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Signaling and scrambling with strongly long-range interactions.
Andrew Y Guo1,2, Minh C Tran1,2,3, Andrew M Childs1,4,5
1Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA.
Physical Review. A
|December 28, 2020
Summary
We established new bounds for signaling and scrambling times in strongly long-range interacting quantum systems. These findings advance our understanding of quantum dynamics in systems lacking locality, crucial for quantum computation.
Area of Science:
- Quantum Mechanics
- Condensed Matter Physics
- Quantum Information Theory
Background:
- Strongly long-range interacting quantum systems, defined by power-law decaying interactions (1/r^α), are crucial in quantum computation and simulation.
- These systems, relevant to quantum information scrambling and entanglement, lack a clear notion of locality, hindering a general understanding of their dynamics.
Purpose of the Study:
- To address the lack of understanding in the dynamics of strongly long-range interacting quantum systems.
- To establish rigorous bounds on the time scales for signaling and scrambling in these systems.
Main Methods:
- Proved two novel Lieb-Robinson-type bounds tailored for strongly long-range interacting systems.
- The first bound applies to systems with long-range hopping, specifically for α ⩽ D/2.
- The second bound addresses generic long-range interacting spin Hamiltonians for all α < D.
Main Results:
- Derived a saturable bound for signaling and scrambling times in systems with long-range hopping (α ⩽ D/2).
- Established a tight lower bound for signaling time to extensive subsystems in generic spin systems (α < D).
- Demonstrated that the many-site signaling time provides a lower bound for the scrambling time in these systems.
Conclusions:
- The derived bounds offer significant progress in understanding the dynamics of strongly long-range interacting quantum systems.
- These results are vital for advancing quantum information processing and theoretical models involving complex quantum interactions.
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