We numerically investigate entropic Bell inequalities for a pair of entangled qutrits using information-theoretic distances. We show that for this class of inequalities Tsallis entropy is more suitable than Shannon as it reveals non-classicality for a larger set of quantum states. Finally, we find that like probability based inequalities, entropic ones are maximally violated by the non-maximally entangled qutrit state.Comment: 5 pages, 4 figures, comments welcom
Quantum nonlocality and contextuality are two phenomena stemming from nonclassical correlations. Whereas the former requires entanglement that is consumed in the measurement process the latter can occur for any state if one chooses a proper set of measurements. Despite this stark differences experimental tests of both phenomena were similar so far. For each run of the experiment one had to use a different copy of a physical system prepared according to the same procedure, or the system had to be brought to its initial state. Here we show that this is not necessary and that the state-independent contextuality can be manifested in a scenario in which each measurement round is done on an output state from the previous round.Introduction. In a standard Bell scenario a pair of observers share a bipartite system on which they perform local measurements [1,2]. The results of these measurements may not be explainable by local realistic theories, however to observe it one needs a quantum system prepared in an entangled state. The entanglement contained in this state is consumed during the measurement and the resulting post-measurement state is local and useless for further Bell tests. A similar effect, although more subtle, takes place in the state-dependent contextuality scenarios. For example, in the Klyachko-Can-BiniciogluShumovski (KCBS) test [3] an initial state of the system can exhibit contextuality with respect to a specific set of measurements, but all the post-measurement states are noncontextual if tested in the same KCBS test.It is therefore natural to think of states exhibiting nonlocality or contextuality as some resourceful states, whereas the remaining states can be considered as resourceless. In this sense, the resourceful states can pass the test at the cost of becoming resourceless. Since every such test requires a sufficient amount of data to statistically determine its outcome, more than one measurement has to be performed. This requires an ensemble of resourceful states from which one draws a system in each measurement round, or a resetting procedure in which one brings back resourcefulness to the post-measurement state.The above interpretation makes the state-independent contextuality a different phenomenon. Every quantum state of a more than two-level system can exhibit contextuality if one prepares a special set of measurements [4][5][6][7][8]. Due to this fact one cannot divide the set of all states into resourceful and resourceless since there is no resource consumption. Therefore, one is inclined to ask: How to reuse post-measurement states in some state-independent contextuality scenario? * cqtpkk@nus.edu.sg † phykd@nus.edu.sgThere are two additional motivations behind this question. First of all, if there were an efficient method of state-recycling it would radically simplify any experimental implementations of contextuality tests in which measurements are non-destructive (e.g. trapped ion experiments [9]). Moreover, from the fundamental point of view it is still unclear what kind of resourc...
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