Distill, Transform, Classify: NCKU Researchers Take a Deep Dive into Quantum Steerability

TAINAN, Taiwan, Oct. 24, 2022 /PRNewswire/ -- The performance of quantum information tasks relies on the resource of "quantum steering," a quantum correlation that sits between quantum entanglement and Bell nonlocality, and plays a central role in one-sided device-independent (1S-DI) quantum information processing and hybrid quantum networks.

However, as quantum networks become more complex, they produce significant noise, degrading quantum steering and compromising performance. To address this issue, it is necessary to solve an open problem related to quantum steering, namely the classification of steerable state assemblages.

Recently, the "steering distillation problem" has been solved where a strong connection has been shown between steerability and "measurement incompatibility," a fundamental concept in quantum physics that refers to the impossibility of measuring certain physical variables simultaneously, such as position and momentum. Additionally, recent studies have shown that a state assemblage is unsteerable only if the steering equivalent observables (SEO) are jointly measured. However, a question regarding the transformation of state assemblages into one another through local filters remains unanswered.

A group of international researchers led by Prof. Yueh-Nan Chen from National Cheng Kung University (NCKU), Taiwan, set out to study the classification problem of quantum steerability using local filters and its connection with measurement incompatibility. "We wanted to study the classification of quantum steerability while trying to understand how to choose the maximal steerability within a class," says Prof. Chen, explaining the motivation behind their study. Their study was published in Nature Communications on August 25, 2022.

In their investigation, the team focused on three features– distillation, convertibility, and classification, and considered the following scenario: a quantum bipartite state, ⍴_AB, is shared by two parties, Alice and Bob. Between them, Bob is the trusted party who only deals with the inputs and outputs and cannot interpret measurements on the state locally. On the other hand, Alice applies all controlled operations on the state and remotely steers Bob's state. It is then assumed that Alice makes a measurement x on the state and obtains a result a. Bob receives this information thereafter.

They aimed to use a local filter K to see how much steerability can be distilled using this filter and explored the classification of two or more assemblages belonging to the same SEO, which were then classified into the same class.

They found that the SEO was responsible for establishing the equivalence classes of state assemblages and related transformations through local filters. Further, the SEO incompatibility corresponded to the optimum steerability over a class. Additionally, they demonstrated the necessary existence of a bipartite state, ⍴_AB that offers steerability to an assemblage equal to the incompatibility of the measurements on the untrusted party (Alice). Finally, they looked at the best success rates and probabilities for distillation and dilution in the single-shot scenario.

The study, thus, successfully linked two fundamental concepts in quantum physics—the classification of quantum steerability related to measurement incompatibility and the maximal steerability in a class being the same as the representative measurement incompatibility.

"Our work can be used to enhance the performance of 1S-DI quantum information processes for applications in quantum key distribution and quantum random generation. Further, it could bridge the connection between Einstein-Podolsky-Rosen steering and the generalized Heisenberg uncertainty principle," highlights Prof. Chen, discussing the potential long-term applications of their work.

Reference
DOI: https://doi.org/10.1038/s41467-022-32466-y

Title of original paper: Complete classification of steerability under local filters and its relation with measurement incompatibility

Journal: Nature Communications

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SOURCE National Cheng Kung University (NCKU)