TY - JOUR
T1 - The cohomological and the resource-theoretic perspective on quantum contextuality
T2 - Common ground through the contextual fraction
AU - Okay, Cihan
AU - Tyhurst, Emily
AU - Raussendorf, Robert
N1 - Funding Information:
This work is funded by NSERC (CO, RR), the Stewart Blusson Quantum Matter Institute (CO), and Cifar (RR).
PY - 2018/12
Y1 - 2018/12
N2 - We unify the resource-theoretic and the cohomological perspective on quantum contextuality. At the center of this unification stands the notion of the contextual fraction. For both symmetry and parity based contextuality proofs, we establish cohomological invariants which are witnesses of state-dependent contextuality. We provide two results invoking the contextual fraction, namely (i) refinements of logical contextuality inequalities, and (ii) upper bounds on the classical cost of Boolean function evaluation, given the contextual fraction of the corresponding measurement-based quantum computation.
AB - We unify the resource-theoretic and the cohomological perspective on quantum contextuality. At the center of this unification stands the notion of the contextual fraction. For both symmetry and parity based contextuality proofs, we establish cohomological invariants which are witnesses of state-dependent contextuality. We provide two results invoking the contextual fraction, namely (i) refinements of logical contextuality inequalities, and (ii) upper bounds on the classical cost of Boolean function evaluation, given the contextual fraction of the corresponding measurement-based quantum computation.
KW - Bell inequalities
KW - Cohomology
KW - Contextuality
KW - Measurement-based quantum computation
UR - http://www.scopus.com/inward/record.url?scp=85064767221&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:85064767221
VL - 18
SP - 1272
EP - 1294
JO - Quantum Information and Computation
JF - Quantum Information and Computation
SN - 1533-7146
IS - 15-16
ER -