September 9, 2020
RIKEN
Keio University
A joint research team, consisting of Researcher Tomotaka Kuwahara from the Mathematical Science Team, Generic Technology Research Group at the RIKEN Center for Advanced Intelligence Project, and Professor Keiji Saito from the Department of Physics, Faculty of Science and Technology at Keio University, has discovered a new law concerning "quantum entanglement" in the lowest energy state (ground state) of a system of many particles that move according to quantum mechanics (a quantum many-body system).
This research is expected not only to lead to a deeper understanding of quantum entanglement but also to provide new insights into numerical calculation approaches for quantum many-body systems, and further, to offer useful knowledge to a wide range of fields, including quantum computers and quantum machine learning.
When a system of particles obeying quantum mechanics is divided into two regions, the conjecture that "the amount of quantum entanglement between the regions is approximately proportional to the size of their boundary" is known as the "area law conjecture for quantum entanglement." A mathematical proof for this conjecture has existed for situations where the interactions between particles are weak and the particles tend to move independently (i.e., short-range correlations exist). However, how the validity of the area law is affected by the type and strength of interactions has long been a major unresolved problem.
The joint research team has now proven an area law for the ground state of a wide range of one-dimensional quantum many-body systems with an energy gap, which implies that quantum entanglement is smaller than in high-energy states, and has clarified its mechanism. This demonstrates that the condition of short-range interactions, previously thought to be essential for the area law, is not fundamental. It has been revealed for the first time that the area law can hold even with strong, long-range interactions.
This research was published in the online scientific journal "Nature Communications" on September 8.
Please see below for the full press release.