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Device-Independent Certification of Genuinely Entangled Subspaces
Flavio Baccari1, Remigiusz Augusiak2, Ivan Šupić3
1Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, 85748 Garching, Germany.
Physical Review Letters
|January 15, 2021
Summary
This study introduces self-testing for complex quantum entanglement structures like the five-qubit and toric codes. It demonstrates that states violating a Bell inequality must reside within these specific code subspaces, even including mixed states.
Area of Science:
- Quantum Information Science
- Quantum Computing
- Quantum Error Correction
Background:
- Self-testing is a device-independent method to verify quantum systems with minimal trust.
- Current self-testing primarily applies to specific quantum measurements, channels, and pure entangled states.
- Generalizing self-testing to complex entanglement structures is an open challenge.
Purpose of the Study:
- To introduce and develop the concept of self-testing for more general entanglement structures.
- To present the first self-tests for entangled subspaces, specifically the five-qubit code and the toric code.
- To establish a connection between Bell inequality violations and membership in these quantum error-correcting code subspaces.
Main Methods:
- Utilizing Bell inequalities as a tool for device-independent characterization.
- Developing theoretical frameworks for self-testing of entangled subspaces.
- Analyzing the properties of quantum states that maximally violate chosen Bell inequalities.
Main Results:
- Successfully introduced self-testing for entangled subspaces, including the five-qubit code and the toric code.
- Demonstrated that quantum states maximally violating a specific Bell inequality are confined to the corresponding code subspace.
- Showed that this confinement to the code subspace includes mixed states, broadening the applicability of self-testing.
Conclusions:
- Self-testing can be extended to certify complex quantum error-correcting codes and their encoded states.
- Bell inequality violations provide a robust, device-independent signature for states within specific entangled subspaces.
- This work paves the way for device-independent certification of quantum computations and error correction protocols.
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