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Revealing quantum contextuality using a single measurement device
Quantum Physics · Submitted 31 Jan 2021
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We show that any non-contextual ontological model fails to explain the statistics of outcomes of a single carefully constructed positive operator valued measure (POVM) executed sequentially on a quantum system.
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The abstract, sentence by sentence
In this work we analyse the notion of measurement non-contextuality (MNC) and identify contextual scenarios which involve sequential measurements of only a single measurement device. We show that any non-contextual ontological model fails to explain the statistics of outcomes of a single carefully constructed positive operator valued measure (POVM) executed sequentially on a quantum system. The context of measurement arises from the different configurations in which the device can be used. We develop an inequality from the non-contextual (NC) ontic model, and construct a quantum situation involving measurements from the KCBS inequality. We show that the resultant statistics arising from this device violate our NC inequality. This device can be generalised by incorporating measurements from arbitrary $n$-cycle contextuality inequalities of which $n = 5$ corresponds to the KCBS inequality. We show that the NC and quantum bounds for various scenarios can be derived more easily using only the functional relationships between the outcomes for larger values $n$. This makes it one of the simpler contextual inequalities to analyse.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | In this work we analyse the notion of measurement non-contextuality (MNC) and identify contextual scenarios which involve sequential measurements of only a single measurement device. | contribution 0.99 | 0.91 | 0.11 | asserted 0.99 |
| s1 | We show that any non-contextual ontological model fails to explain the statistics of outcomes of a single carefully constructed positive operator valued measure (POVM) executed sequentially on a quantum system. | result 0.96 | 0.91 | 0.72 | asserted 1.00 |
| s2 | The context of measurement arises from the different configurations in which the device can be used. | interpretation 0.71 | 0.19 | 0.06 | asserted 1.00 |
| s3 | We develop an inequality from the non-contextual (NC) ontic model, and construct a quantum situation involving measurements from the KCBS inequality. | method 0.68 | 0.93 | 0.07 | asserted 1.00 |
| s4 | We show that the resultant statistics arising from this device violate our NC inequality. | result 1.00 | 0.94 | 0.41 | asserted 1.00 |
| s5 | This device can be generalised by incorporating measurements from arbitrary $n$-cycle contextuality inequalities of which $n = 5$ corresponds to the KCBS inequality. | contribution 0.88 | 0.83 | 0.13 | asserted 0.90 |
| s6 | We show that the NC and quantum bounds for various scenarios can be derived more easily using only the functional relationships between the outcomes for larger values $n$. | result 0.45 | 0.89 | 0.08 | asserted 0.98 |
| s7 | This makes it one of the simpler contextual inequalities to analyse. | interpretation 0.93 | 0.59 | 0.07 | asserted 0.97 |
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The paper
Original abstract
In this work we analyse the notion of measurement non-contextuality (MNC) and identify contextual scenarios which involve sequential measurements of only a single measurement device. We show that any non-contextual ontological model fails to explain the statistics of outcomes of a single carefully constructed positive operator valued measure (POVM) executed sequentially on a quantum system. The context of measurement arises from the different configurations in which the device can be used. We develop an inequality from the non-contextual (NC) ontic model, and construct a quantum situation involving measurements from the KCBS inequality. We show that the resultant statistics arising from this device violate our NC inequality. This device can be generalised by incorporating measurements from arbitrary $n$-cycle contextuality inequalities of which $n = 5$ corresponds to the KCBS inequality. We show that the NC and quantum bounds for various scenarios can be derived more easily using only the functional relationships between the outcomes for larger values $n$. This makes it one of the simpler contextual inequalities to analyse.
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2 arXiv papers cite this in 7 sentences
Papers citing it · 6 sentences without a confident label
Contests it 1 paper
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This assumption was not shown to follow from noncontextuality, so Ref. [ref] does not establish our result.[ Additionally, we were not able to show that this assumption follows from noncontextuality.
Contextuality without incompatibility · Introduction · contest 0.85
What it cites
Cites as background 2 papers
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The graph theoretic approach has been successful in identifying new contextual scenarios [ref] , simplifying formulations of contextuality monogamy [ref] , contextuality non-locality relationship [ref] , developing robust self tests [ref] and information theoretic applications of contextuality [ref] .
A Contextuality Based Quantum Key Distribution Protocol · Introduction · 0.84
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Although such generalizations have been attempted [ref] , these questions are still not fully resolved.
Unscrambling the omelette of causation and inference: The framework of causal-inferential theories · Introduction · 0.91
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