TY - JOUR
T1 - Quantifying non-classical and beyond-quantum correlations in the unified operator formalism
AU - Geller, Joshua
AU - Piani, Marco
N1 -
Geller. J. and Piani. M. (2014). Quantifying non-classical and beyond-quantum correlations in the unified operator formalism., Journal of Physics A: Mathematical and Theoretical., 47(42), 424030
PY - 2014/10/8
Y1 - 2014/10/8
N2 - Acin et al (2010 Phys. Rev. Lett. 104 140404) introduced a unified framework for the study of no-signalling correlations. Such a framework is based on the notion of local quantum measurements, but, in order to account for beyond quantum correlations, global pseudo-states that are not positive semidefinite are allowed. After a short review of the formalism, we consider its use in the quantification of both general non-local and beyond-quantum correlations. We argue that the unified framework for correlations provides a simple approach to such a quantification, in particular when the quantification is meant to be operational and meaningful in a resource-theory scenario, i.e., when considering the processing of resources by means of non-resources. We relate different notions of robustness of correlations, both at the level of (pseudo-)states and abstract probability distributions, with particular focus on the beyond-quantum robustness of correlations and pseudo-states. We revisit known results and argue that, within the unified framework, the relation between the two levels—that of operators and that of probability distributions—is very strict. We point out how the consideration of robustness at the two levels leads to a natural framework for the quantification of entanglement in a device independent way. Finally, we show that the beyond-quantum robustness of the non-positive operators needed to achieve beyond-quantum correlations coincides with their negativity and their distance from the set of quantum states. As an example, we calculate the beyond-quantum robustness for the case of a noisy Popescu–Rohrlich box.
AB - Acin et al (2010 Phys. Rev. Lett. 104 140404) introduced a unified framework for the study of no-signalling correlations. Such a framework is based on the notion of local quantum measurements, but, in order to account for beyond quantum correlations, global pseudo-states that are not positive semidefinite are allowed. After a short review of the formalism, we consider its use in the quantification of both general non-local and beyond-quantum correlations. We argue that the unified framework for correlations provides a simple approach to such a quantification, in particular when the quantification is meant to be operational and meaningful in a resource-theory scenario, i.e., when considering the processing of resources by means of non-resources. We relate different notions of robustness of correlations, both at the level of (pseudo-)states and abstract probability distributions, with particular focus on the beyond-quantum robustness of correlations and pseudo-states. We revisit known results and argue that, within the unified framework, the relation between the two levels—that of operators and that of probability distributions—is very strict. We point out how the consideration of robustness at the two levels leads to a natural framework for the quantification of entanglement in a device independent way. Finally, we show that the beyond-quantum robustness of the non-positive operators needed to achieve beyond-quantum correlations coincides with their negativity and their distance from the set of quantum states. As an example, we calculate the beyond-quantum robustness for the case of a noisy Popescu–Rohrlich box.
KW - quantum nonlocality
KW - robustness of correlations
KW - entanglement
KW - Popescu–Rohrlich box
KW - pseudo-state
KW - device-independent
UR - http://iopscience.iop.org/1751-8121/
U2 - 10.1088/1751-8113/47/42/424030
DO - 10.1088/1751-8113/47/42/424030
M3 - Special issue
SN - 1751-8113
VL - 47
JO - Journal of Physics A: Mathematical and Theoretical
JF - Journal of Physics A: Mathematical and Theoretical
IS - 42
M1 - 424030
ER -