EPR Revisited: Context-Indexed Elements of Reality and Operational Completeness
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918270593925120 |
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| author | Sienicki, Mikołaj Sienicki, Krzysztof |
| author_facet | Sienicki, Mikołaj Sienicki, Krzysztof |
| contents | We reframe the EPR argument through an operational lens, replacing the notion of fixed "elements of reality" with context-indexed conditional states - what's often referred to as a measurement assemblage. This move deliberately sidesteps the assumption of context-independent values for incompatible observables. Our updated version of the Reality Criterion works like this: if Alice measures observable x and obtains outcome a, then Bob's system must adopt a conditional state that ensures the corresponding outcome for that specific context. Crucially, we also assume operational completeness - a condition that quantum mechanics satisfies when we're dealing with quantum-reachable assemblages. Now, in any theory where one party cannot signal to the other (so-called one-sided no-signaling theories), perfect predictions do support drawing context-indexed inferences. But - and this is key - they don't legitimize assigning fixed values across all contexts. We rigorously demonstrate this distinction. To ground the argument, we offer examples: the qubit singlet scenario using Pauli settings and CJWR thresholds, a continuous-variable case based on the Reid criteria, and a counterexample in the spirit of the PR box, which highlights the boundaries of what quantum theory can actually reach. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_01930 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | EPR Revisited: Context-Indexed Elements of Reality and Operational Completeness Sienicki, Mikołaj Sienicki, Krzysztof Quantum Physics History and Philosophy of Physics We reframe the EPR argument through an operational lens, replacing the notion of fixed "elements of reality" with context-indexed conditional states - what's often referred to as a measurement assemblage. This move deliberately sidesteps the assumption of context-independent values for incompatible observables. Our updated version of the Reality Criterion works like this: if Alice measures observable x and obtains outcome a, then Bob's system must adopt a conditional state that ensures the corresponding outcome for that specific context. Crucially, we also assume operational completeness - a condition that quantum mechanics satisfies when we're dealing with quantum-reachable assemblages. Now, in any theory where one party cannot signal to the other (so-called one-sided no-signaling theories), perfect predictions do support drawing context-indexed inferences. But - and this is key - they don't legitimize assigning fixed values across all contexts. We rigorously demonstrate this distinction. To ground the argument, we offer examples: the qubit singlet scenario using Pauli settings and CJWR thresholds, a continuous-variable case based on the Reid criteria, and a counterexample in the spirit of the PR box, which highlights the boundaries of what quantum theory can actually reach. |
| title | EPR Revisited: Context-Indexed Elements of Reality and Operational Completeness |
| topic | Quantum Physics History and Philosophy of Physics |
| url | https://arxiv.org/abs/2511.01930 |