اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدCanonical decomposition of quantum correlations in the framework of generalized nonsignaling theories
176
0
0.0
(
0
)
تأليف
C. Jebarathinam
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We introduce the measures, Bell discord (BD) and Mermin discord (MD), to characterize bipartite quantum correlations in the context of nonsignaling (NS) polytopes. These measures divide the full NS polytope into four regions depending on whether BD and/or MD is zero. This division of the NS polytope allows us to obtain a 3-decomposition that any bipartite box with two binary inputs and two binary outputs can be decomposed into Popescu-Rohrlich (PR) box, a maximally local box, and a local box with BD and MD equal to zero. BD and MD quantify two types of nonclassicality of correlations arising from all quantum correlated states which are neither classical-quantum states nor quantum-classical states. BD and MD serve us the semi-device-independent witnesses of nonclassicality of local boxes in that nonzero value of these measures imply incompatible measurements and nonzero quantum discord only when the dimension of the measured states is fixed. The 3-decomposition serves us to isolate the origin of the two types of nonclassicality into a PR-box and a maximally local box which is related to EPR-steering, respectively. We consider a quantum polytope that has an overlap with all the four regions of the full NS polytope to figure out the constraints of quantum correlations.
قيم البحث
اقرأ أيضاً
To make precise the sense in which the operational predictions of quantum theory conflict with a classical worldview, it is necessary to articulate a notion of classicality within an operational framework. A widely applicable notion of classicality o
f this sort is whether or not the predictions of a given operational theory can be explained by a generalized-noncontextual ontological model. We here explore what notion of classicality this implies for the generalized probabilistic theory (GPT) that arises from a given operational theory, focusing on prepare-measure scenarios. We first show that, when mapping an operational theory to a GPT by quotienting relative to operational equivalences, the constraint of explainability by a generalized-noncontextual ontological model is mapped to the constraint of explainability by an ontological model. We then show that, under the additional assumption that the ontic state space is of finite cardinality, this constraint on the GPT can be expressed as a geometric condition which we term simplex-embeddability. Whereas the traditional notion of classicality for a GPT is that its state space be a simplex and its effect space be the dual of this simplex, simplex-embeddability merely requires that its state space be embeddable in a simplex and its effect space in the dual of that simplex. We argue that simplex-embeddability constitutes an intuitive and freestanding notion of classicality for GPTs. Our result also has applications to witnessing nonclassicality in prepare-measure experiments.
We show that, for any n, there are m-outcome quantum correlations, with m>n, which are stronger than any nonsignaling correlation produced from selecting among n-outcome measurements. As a consequence, for any n, there are m-outcome quantum measureme
nts that cannot be constructed by selecting locally from the set of n-outcome measurements. This is a property of the set of measurements in quantum theory that is not mandatory for general probabilistic theories. We also show that this prediction can be tested through high-precision Bell-type experiments and identify past experiments providing evidence that some of these strong correlations exist in nature. Finally, we provide a modified version of quantum theory restricted to having at most n-outcome quantum measurements.
It is well-known that in a Bell experiment, the observed correlation between measurement outcomes -- as predicted by quantum theory -- can be stronger than that allowed by local causality, yet not fully constrained by the principle of relativistic ca
usality. In practice, the characterization of the set Q of quantum correlations is often carried out through a converging hierarchy of outer approximations. On the other hand, some subsets of Q arising from additional constraints [e.g., originating from quantum states having positive-partial-transposition (PPT) or being finite-dimensional maximally entangled] turn out to be also amenable to similar numerical characterizations. How then, at a quantitative level, are all these naturally restricted subsets of nonsignaling correlations different? Here, we consider several bipartite Bell scenarios and numerically estimate their volume relative to that of the set of nonsignaling correlations. Among others, our findings allow us to (1) gain insight on (i) the effectiveness of the so-called Q1 and the almost quantum set in approximating Q, (ii) the rate of convergence among the first few levels of the aforementioned outer approximations, (iii) the typicality of the phenomenon of more nonlocality with less entanglement, and (2) identify a Bell scenario whose Bell violation by PPT states might be experimentally viable.
This paper presents a systematic method to decompose uncertain linear quantum input-output networks into uncertain and nominal subnetworks, when uncertainties are defined in SLH representation. To this aim, two decomposition theorems are stated, whic
h show how an uncertain quantum network can be decomposed into nominal and uncertain subnetworks in cascaded connection and how uncertainties can be translated from SLH parameters into state-space parameters. As a potential application of the proposed decomposition scheme, robust stability analysis of uncertain quantum networks is briefly introduced. The proposed uncertainty decomposition theorems take account of uncertainties in all three parameters of a quantum network and bridge the gap between SLH modeling and state-space robust analysis theory for linear quantum networks.
Many three-party correlations, including some that are commonly described as genuinely tripartite nonlocal, can be simulated by a network of underlying subsystems that display only bipartite nonsignaling nonlocal behavior. Quantum mechanics predicts
three-party correlations that admit no such simulation, suggesting there a
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
