Abstract
| Language | English |
|---|---|
| Article number | 083040 |
| Number of pages | 17 |
| Journal | New Journal of Physics |
| Volume | 20 |
| DOIs | |
| Publication status | Published - 28 Aug 2018 |
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Keywords
- quantum measurements
- quantum state
- non-decomposable positive maps
- unextendible product bases
- steering
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A formalism for steering with local quantum measurements. / Sainz, A B; Aolita, L; Piani, M; Hoban, M J; Skrzypczyk, P.
In: New Journal of Physics, Vol. 20, 083040, 28.08.2018.Research output: Contribution to journal › Article
TY - JOUR
T1 - A formalism for steering with local quantum measurements
AU - Sainz, A B
AU - Aolita, L
AU - Piani, M
AU - Hoban, M J
AU - Skrzypczyk, P
PY - 2018/8/28
Y1 - 2018/8/28
N2 - We develop a unified approach to classical, quantum and post-quantum steering. The framework is based on uncharacterised (black-box) parties performing quantum measurements on their share of a (possibly unphysical) quantum state, and its starting point is the characterisation of general no-signalling assemblages via non-positive local hidden-state models. By developing a connection to entanglement witnesses, this formalism allows for new definitions of families of assemblages, in particular via (i) non-decomposable positive maps and (ii) unextendible product bases. The former proves to be useful for constructing post-quantum assemblages with the built-in feature of yielding only quantum correlations in Bell experiments, while the latter always gives certifiably post-quantum assemblages. Finally, our framework is equipped with an inherent quantifier of post-quantum steering, which we call the negativity of post-quantum steering. We postulate that post-quantum steering should not increase under one-way quantum operations from the steered parties to the steering parties, and we show that, in this sense, the negativity of post-quantum steering is a convex post-quantum-steering monotone.
AB - We develop a unified approach to classical, quantum and post-quantum steering. The framework is based on uncharacterised (black-box) parties performing quantum measurements on their share of a (possibly unphysical) quantum state, and its starting point is the characterisation of general no-signalling assemblages via non-positive local hidden-state models. By developing a connection to entanglement witnesses, this formalism allows for new definitions of families of assemblages, in particular via (i) non-decomposable positive maps and (ii) unextendible product bases. The former proves to be useful for constructing post-quantum assemblages with the built-in feature of yielding only quantum correlations in Bell experiments, while the latter always gives certifiably post-quantum assemblages. Finally, our framework is equipped with an inherent quantifier of post-quantum steering, which we call the negativity of post-quantum steering. We postulate that post-quantum steering should not increase under one-way quantum operations from the steered parties to the steering parties, and we show that, in this sense, the negativity of post-quantum steering is a convex post-quantum-steering monotone.
KW - quantum measurements
KW - quantum state
KW - non-decomposable positive maps
KW - unextendible product bases
KW - steering
UR - http://iopscience.iop.org/journal/1367-2630
U2 - 10.1088/1367-2630/aad8df
DO - 10.1088/1367-2630/aad8df
M3 - Article
VL - 20
JO - New Journal of Physics
T2 - New Journal of Physics
JF - New Journal of Physics
SN - 1367-2630
M1 - 083040
ER -