Contextuality, a generalization of non-locality, has been proposed as the resource that provides the computational speed-up for quantum computation. For universal quantum computation using qudits, of odd-prime dimension, contextuality has been shown to be a necessary and possibly sufficient resource. However, the role of contextuality in quantum computation with qubits remains open. The $n$ -qubit stabilizer formalism, which by itself cannot provide a quantum computer super-polynomial computational advantage over a classical counterpart, is contextual. Therefore contextuality cannot be identified as a sufficient resource for quantum computation. However it can be identified as a necessary resource. In this paper we construct a contextual $ψ$ -epistemic ontological model of the $n$ -qubit stabilizer formalism, to investigate the contextuality present in the formalism. We demonstrate it is possible for such a model to be outcome deterministic, and therefore have a value assignment to all Pauli observables. In our model the value assignment must be updated after a measurement of any stabilizer observable. Remarkably, this includes the value assignments for observables that commute with the measurement. A stronger manifestation of contextuality than is required by known no-go theorems.Contextuality, a generalization of non-locality, has been proposed as the resource that provides the computational speed-up for quantum computation. For universal quantum computation using qudits, of odd-prime dimension, contextuality has been shown to be a necessary and possibly sufficient resource. However, the role of contextuality in quantum computation with qubits remains open. The $n$-qubit stabilizer formalism, which by itself cannot provide a quantum computer super-polynomial computational advantage over a classical counterpart, is contextual. Therefore contextuality cannot be identified as a sufficient resource for quantum computation. However it can be identified as a necessary resource. In this paper we construct a contextual $ψ$-epistemic ontological model of the $n$-qubit stabilizer formalism, to investigate the contextuality present in the formalism. We demonstrate it is possible for such a model to be outcome deterministic, and therefore have a value assignment to all Pauli observables. In our model the value assignment must be updated after a measurement of any stabilizer observable. Remarkably, this includes the value assignments for observables that commute with the measurement. A stronger manifestation of contextuality than is required by known no-go theorems.

arXiv:1904.04268Apr 8, 20194 citations

Emergence of non-contextuality in macroscopic systems

Paweł Kurzyński, Akihito Soeda, Ravishankar Ramanathan +3 more

Nov 11, 20110 citations

Hypercyclic systems of measurements and patterns of contextuality

Victor Hernando Cervantes, Ehtibar N. Dzhafarov

arXiv:2304.01155The European Physical Journal Special TopicsSep 1, 20233 citations

Spekkens' toy model and contextuality as a resource in quantum computation

Lorenzo Catani, Dan E. Browne, Nadish de Silva

Spekkens’ toy model (SM) is a non-contextual hidden-variable model made to support the epistemic view of quantum theory, where quantum states are states of partial knowledge about a deeper underlying reality. Despite being a classical model, it has reproduced many features of quantum theory (entanglement, teleportation, . . .): (almost) everything but contextuality, which therefore seems to be the inherent quantum feature. In addition to the importance in foundation of quantum theory, the notion of contextuality seems to be a crucial resource for quantum computation. In particular it has been proven that, in the case of odd prime discrete dimensional systems, contextuality is necessary for universal quantum computation in state-injection schemes of computation based on stabilizer quantum mechanics (SQM). The latter is a subtheory of quantum mechanics which is very popular in the field of quantum computation and quantum error correction. State-injection schemes consist of a classically-simulable part (like SQM) and a resource state that boosts the computation to a quantum improvement. In the odd-dimensional case, SM is operationally equivalent to SQM. In the even-dimensional case, the equivalence only holds in terms of structure, not in terms of statistical predictions. This because qubit-SQM shows contextuality, while qudit(odd dimensions)-SQM does not. We believe that SM can be a valid tool to study contextuality as a resource in the field of quantum computation. Restricted versions of SM compatible with quantum mechanics (QM) can be used as the non-contextual classically-simulable part of state-injection schemes thus opening other scenarios where studying if contextuality is necessary for quantum computational speed-up.Spekkens’ toy model (SM) is a non-contextual hidden-variable model made to support the epistemic view of quantum theory, where quantum states are states of partial knowledge about a deeper underlying reality. Despite being a classical model, it has reproduced many features of quantum theory (entanglement, teleportation, . . .): (almost) everything but contextuality, which therefore seems to be the inherent quantum feature. In addition to the importance in foundation of quantum theory, the notion of contextuality seems to be a crucial resource for quantum computation. In particular it has been proven that, in the case of odd prime discrete dimensional systems, contextuality is necessary for universal quantum computation in state-injection schemes of computation based on stabilizer quantum mechanics (SQM). The latter is a subtheory of quantum mechanics which is very popular in the field of quantum computation and quantum error correction. State-injection schemes consist of a classically-simulable part (like SQM) and a resource state that boosts the computation to a quantum improvement. In the odd-dimensional case, SM is operationally equivalent to SQM. In the even-dimensional case, the equivalence only holds in terms of structure, not in terms of statistical predictions. This because qubit-SQM shows contextuality, while qudit(odd dimensions)-SQM does not. We believe that SM can be a valid tool to study contextuality as a resource in the field of quantum computation. Restricted versions of SM compatible with quantum mechanics (QM) can be used as the non-contextual classically-simulable part of state-injection schemes thus opening other scenarios where studying if contextuality is necessary for quantum computational speed-up.

Jan 1, 20191 citation

A Contextual

ψ

-Epistemic Model of the

n

-Qubit Stabilizer Formalism

n

-qubit stabilizer formalism, which by itself cannot provide a quantum computer super-polynomial computational advantage over a classical counterpart, is contextual. Therefore contextuality cannot be identified as a sufficient resource for quantum computation. However it can be identified as a necessary resource. In this paper we construct a contextual

ψ

-epistemic ontological model of the

n

-qubit stabilizer formalism, to investigate the contextuality present in the formalism. We demonstrate it is possible for such a model to be outcome deterministic, and therefore have a value assignment to all Pauli observables. In our model the value assignment must be updated after a measurement of any stabilizer observable. Remarkably, this includes the value assignments for observables that commute with the measurement. A stronger manifestation of contextuality than is required by known no-go theorems.