Self-testing beyond multipartite qubits
Can every finite-dimensional pure multipartite entangled state be self-tested in a standard single-source Bell experiment, up to local isometries, unused auxiliary systems and unavoidable conjugation equivalences? Separately classify measurement sets under an
Problem statement
Can every finite-dimensional pure multipartite entangled state be self-tested in a standard single-source Bell experiment, up to local isometries, unused auxiliary systems and unavoidable conjugation equivalences? Separately classify measurement sets under an explicit certification convention.
Lean 4
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Background
Self-testing extracts a reference state and, when specified, its measurements from correlations alone. CHSH self-tests a singlet. The equivalence convention is essential: unused auxiliary systems and complex conjugation cannot simply be excluded by observed probabilities.
Established results cover every pure bipartite entangled state. A published March 2026 theorem also covers every pure multipartite entangled qubit state, beyond earlier GHZ, graph and Dicke examples. The remaining universal state question concerns arbitrary higher local dimensions in the standard Bell setting. Network protocols using auxiliary parties or entanglement answer a different question.
Conventional exact self-testing does not uniquely identify a genuinely mixed bipartite target in the analogous pure-state sense; “classify all mixed states” is not an untouched extension without changing the definition. Measurement certification likewise has hypotheses: all real projective measurements can be self-tested, while arbitrary complex POVMs require careful treatment of equivalence and dilation freedoms.
The residual programme separates the sharp pure-state existence question from measurement-specific necessary-and-sufficient criteria and robustness.
Progress & source assessment
Source catalogue review: 4 September 2026. Improved indicates partial progress, including qualified preprint claims.
published: All pure multipartite entangled qubit states admit self-tests in the standard Bell setting; arbitrary higher local dimensions remain a separate frontier. Evidence
- [1]'All pure multipartite entangled states of qubits can be self-tested', Nature Communications (24 March 2026) link
- [2]Coladangelo, Goh & Scarani, all pure bipartite states and the mixed-state obstruction, Nature Communications (2017) link
- [3]Chen, Mančinska & Volčič, self-testing all real projective measurements, Nature Physics (2024) link
- [4]Šupić & Bowles, 'Self-testing of quantum systems: a review', Quantum 4, 337 (2020) link
Recorded progress
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Discussion
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