Quantifying Contextuality

Grudka, Andrzej; Horodecki, Karol; Horodecki, Michał; Horodecki, Paweł; Horodecki, Ryszard; Joshi, Pankaj S.; Kłobus, Waldemar; Wójcik, Antoni

doi:10.1103/physrevlett.112.120401

Cited by 115 publications

(159 citation statements)

References 73 publications

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“…Therefore, we use an object introduced in [12], called RAC-box. It is a non-classical probability distribution which, when augmented with a log d bits of classical communication, can be used to create an EARAC according to the recipe from Figure 2.…”

mentioning

confidence: 99%

“…Quantum RACs are important for a broad range of applications including finite automata [3], network coding [4], quantum state tomography [5], device independent dimension witnessing [6,7], semi-device independent cryptography [8] and randomness expansion [9], nonlocal games [10], tests of contextuality [11], studies of no-signaling resources [12] and characterization of quantum correlations from information theory [13].…”

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confidence: 99%

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Spatial versus sequential correlations for random access coding

et al. 2016

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Random access codes are important for a wide range of applications in quantum information. However, their implementation with quantum theory can be made in two very different ways: (i) by distributing data with strong spatial correlations violating a Bell inequality, or (ii) using quantum communication channels to create stronger-than-classical sequential correlations between state preparation and measurement outcome. Here, we study this duality of the quantum realization. We present a family of Bell inequalities tailored to the task at hand and study their quantum violations. Remarkably, we show that the use of spatial and sequential quantum correlations imposes different limitations on the performance of quantum random access codes: sequential correlations can outperform spatial correlations. We discuss the physics behind the observed discrepancy between spatial and sequential quantum correlations.

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confidence: 99%

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confidence: 99%

Spatial versus sequential correlations for random access coding

et al. 2016

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“…Now, in [8] it is shown, that if Alice and Bob share a PR box, they can implement random access code by means of just one bit of communication. In [3] a converse question was answered: Namely, an object was defined called racbox. It is a box that implements RAC if supported by one bit of communication from Alice to Bob (see Fig.…”

Section: Random Access Code and "Racbox"mentioning

confidence: 99%

“…This peculiar feature was used to formulate the principle of information causality [2]. In this context in [3] the notion of a racbox was introduced. It is a box which can implement a random access code with the support of one bit of communication.…”

Section: Introductionmentioning

confidence: 99%

Nonsignaling quantum random access-code boxes

Grudka

Horodecki

et al. 2015

Phys. Rev. A

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A well known cryptographic primitive is so called random access code. Namely, Alice is to send to Bob one of two bits, so that Bob has the choice which bit he wants to learn about. However at any time Alice should not learn Bob's choice, and Bob should learn only the bit of his choice. The task is impossible to accomplish by means of either classical or quantum communication. On the other hand, a concept of correlations stronger than quantum ones, exhibited by so called PopescuRohrlich box, was introduced and widely studied. In particular, it is known that Popescu-Rohrlich box enables simulation of the random access code with the support of one bit of communication.Here, we propose a quantum analogue of this phenomenon. Namely, we define an analogue of a random access code, where instead of classical bits, one encodes qubits. We provide a quantum non-signaling box that if supported with two classical bits, allows to simulate a quantum version of random access code. We point out that two bits are necessary. We also show that a quantum random access code cannot be fully quantum: when Bob inputs superposition of two choices, the output will be in a mixed state rather than in a superposition of required states.

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“…trapped ion experiments [9]). Moreover, from the fundamental point of view it is still unclear what kind of resource contextuality is and how to quantify it with respect to some meaningful tasks [10]. Showing that post-measurement states can be efficiently reused in state-independent contextuality tests would suggest that in order to look for resourcefulness of contextuality one should not associate it to nonlocality and entanglement.…”

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confidence: 99%

State-recycling method for testing quantum contextuality

et al. 2016

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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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Quantifying Contextuality

Cited by 115 publications

References 73 publications

Spatial versus sequential correlations for random access coding

Spatial versus sequential correlations for random access coding

Nonsignaling quantum random access-code boxes

State-recycling method for testing quantum contextuality

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