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L6-06 · Bell inequalities and causal inequalities

Distinguish two tests of different model classes.

Level 6 icon Level 6 · Graduate
Objective. Distinguish two tests of different model classes.
Before this lesson. L5-08, L6-05
Hands-on lab. Entanglement and Bell tests

Learn

A Bell inequality bounds correlations in a specified local hidden-variable model. A causal inequality instead constrains correlations under a stated class of causal orders and operational assumptions. The two names do not refer to the same bound or the same experimental question.

A process can lack a decomposition into fixed causal orders without violating a particular causal inequality. An operator witness and an observed probability inequality use different information. A witness can rely on trusted apparatus details that are unavailable in a device-independent correlation test.

Before interpreting either test, identify its allowed settings, outputs, communication routes, and independence assumptions. Then state the null model and its numerical bound. A value outside a bound has meaning only for that model. Experimental uncertainty must be evaluated separately.

Practice

Solution

No. A trusted-instrument operator witness and a device-independent probability inequality impose different assumptions. The witness result alone does not establish that the observed distribution violates a causal inequality.

Check your understanding

Which statement is valid?

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C. The tests constrain different specified model classes

Bell locality and definite causal order are distinct assumptions. A valid interpretation must state the relevant model class instead of substituting one test for another.

Sources

This lesson draws on Araújo et al., 2015Oreshkov et al., 2012Chiribella et al., 2013.

Next: L6-07 · Process matrices and validity

References
  1. Araújo, M., Branciard, C., Costa, F., Feix, A., Giarmatzi, C., & Brukner, Č. (2015). Witnessing causal nonseparability. New Journal of Physics, 17(10), 102001. 10.1088/1367-2630/17/10/102001
  2. Oreshkov, O., Costa, F., & Brukner, C. (2012). Quantum correlations with no causal order. Nature Communications, 3(1). 10.1038/ncomms2076
  3. Chiribella, G., D’Ariano, G. M., Perinotti, P., & Valiron, B. (2013). Quantum computations without definite causal structure. Physical Review A, 88(2). 10.1103/PhysRevA.88.022318