Two Unpublished Sculptures from Amarāvatī

Barrett, Douglas

doi:10.2307/4422533

Cited by 6 publications

(7 citation statements)

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“…It has been shown that for every inequality on correlations between pairs of separated measurements that is implied by the assumption of a local ontological model, an equivalent inequality for the correlations between preparations and measurements is implied by the assumption of a preparation-noncontextual ontological model[51].…”

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confidence: 99%

Specker’s parable of the overprotective seer: A road to contextuality, nonlocality and complementarity

2011

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In 1960, the mathematician Ernst Specker described a simple example of nonclassical correlations, the counterintuitive features of which he dramatized using a parable about a seer who sets an impossible prediction task to his daughter's suitors. We revisit this example here, using it as an entrée to three central concepts in quantum foundations: contextuality, Bell-nonlocality, and complementarity. Specifically, we show that Specker's parable offers a narrative thread that weaves together a large number of results, including: the impossibility of measurement-noncontextual and outcome-deterministic ontological models of quantum theory (the 1967 Kochen-Specker theorem), in particular the recent state-specific pentagram proof of Klyachko; the impossibility of Bell-local models of quantum theory (Bell's theorem), especially the proofs by Mermin and Hardy and extensions thereof; the impossibility of a preparation-noncontextual ontological model of quantum theory; and the existence of triples of positive operator valued measures (POVMs) that can be measured jointly pairwise but not triplewise. Along the way, several novel results are presented, including: a generalization of a theorem by Fine connecting the existence of a joint distribution over outcomes of counterfactual measurements to the existence of a measurement-noncontextual and outcome-deterministic ontological model; a generalization of Klyachko's proof of the Kochen-Specker theorem from pentagrams to a family of star polygons; a proof of the Kochen-Specker theorem in the style of Hardy's proof of Bell's theorem (i.e., one that makes use of the failure of the transitivity of implication for counterfactual statements); a categorization of contextual and Bell-nonlocal correlations in terms of frustrated networks; a derivation of a new inequality testing preparation noncontextuality; and lastly, some novel results on the joint measurability of POVMs and the question of whether these can be modeled noncontextually. Finally, we emphasize that Specker's parable of the over-protective seer provides a novel type of foil to quantum theory, challenging us to explain why the particular sort of contextuality and complementarity embodied therein does not arise in a quantum world.

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confidence: 99%

Specker’s parable of the overprotective seer: A road to contextuality, nonlocality and complementarity

2011

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“…To verify the nonlocal character of teleportation, two conditions must be satisfied in any experiment. On the one hand, one has to demonstrate that a genuinely unknown state (in the optimal case, a qubit which itself is still entangled to another one) is teleported [12], on the other hand a high experimental visibility is necessary in order to exclude local hidden variable models (LHV) [13][14][15][16]. The so-called entanglement swapping experiment [10] is the only one to date that demonstrates the teleportation of a genuinely unknown state.…”

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Experimental Demonstration of Four-Photon Entanglement and High-Fidelity Teleportation

et al. 2001

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We experimentally demonstrate observation of highly pure four-photon GHZ entanglement produced by parametric down-conversion and a projective measurement. At the same time this also demonstrates teleportation of entanglement with very high purity. Not only does the achieved high visibility enable various novel tests of quantum nonlocality, it also opens the possibility to experimentally investigate various quantum computation and communication schemes with linear optics. Our technique can in principle be used to produce entanglement of arbitrarily high order or, equivalently, teleportation and entanglement swapping over multiple stages.Entanglement is not only the essence of quantum mechanics as suggested by Erwin Schrödinger [1], but is also at the basis of nearly all quantum information protocols such as quantum cryptography, quantum teleportation and quantum computation [2]. While entanglement of two qubits is routine in the laboratory, entanglement of three photons [3] with high quality has only recently been experimentally realized [4] and used to experimentally demonstrate the extreme contradiction between local realism and quantum mechanics [5] in so-called GHZ states. In a parallel development entanglement of the quantum states of three atoms [6] or four qubits in ions [7] has been demonstrated, yet in all these cases the quality of the entangled states still needs to be significantly improved in order to be useful for tests of quantum mechanics or in quantum information schemes.A similar situation is found in the recent teleportation experiments [8][9][10][11]. To verify the nonlocal character of teleportation, two conditions must be satisfied in any experiment. On the one hand, one has to demonstrate that a genuinely unknown state (in the optimal case, a qubit which itself is still entangled to another one) is teleported [12], on the other hand a high experimental visibility is necessary in order to exclude local hidden variable models (LHV) [13][14][15][16]. The so-called entanglement swapping experiment [10] is the only one to date that demonstrates the teleportation of a genuinely unknown state. However, since its observed visibility was lower than 71%, one could in principle still doubt the nonlocal feature of teleportation [13].In this letter we report on an experiment that not only demonstrates the observation of four-photon entanglement but also shows high-fidelity entanglement swapping, thus proving the nonlocal character of quantum teleportation. Both features are not only important for performing novel fundamental experiments to test quantum mechanics or to demonstrate its counter-intuitive features, but also to expand our toolbox for quantum computation and quantum communication.Our technique of observing four-photon GHZ entanglement uses two independently created photon pairs (Fig. 1). Suppose that the two pairs are in the statewhich is a tensor product of two polarization entangled photon pairs. Here |H (|V ) indicates the state of a horizontally (vertically) polarized photon. Principle fo...

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“…In two-party, two-outcome Bell scenario, the assumption of preparation non-contextuality is equivalent to locality [27]. In such a case, (β 3,3 ) local ≤ 5 and (P 3,3 ) local = 7/9 ≈ 0.777.…”

Section: A Communication Game In (33) Scenariomentioning

confidence: 99%

Revealing universal quantum contextuality through communication games

Pan

2019

Sci Rep

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An ontological model of an operational theory is considered to be universally noncontextual if both preparation and measurement noncontextuality assumptions are satisfied in that model. In this report, we first generalize the logical proofs of quantum preparation and measurement contextuality for qubit system for any odd number of preparations and measurements. Based on the logical proof, we derive testable universally non-contextual inequalities violated by quantum theory. We then propose a class of two-party communication games and show that the average success probability of winning such games is solely linked to suitable Bell expression whose local bound is greater than universal non-contextual bound. Thus, for a given state, even if quantum theory does not exhibit non-locality, it may still reveal non-classicality by violating the universal non-contextual bound. Further, we consider a different communication game to demonstrate that for a given choices of observables in quantum theory, even if there is no logical proof of preparation and measurement contextuality exist, the universal quantum contextuality can be revealed through that communication game. Such a game thus test a weaker form of universal non-contextuality with minimal assumption.

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Two Unpublished Sculptures from Amarāvatī

Cited by 6 publications

References 0 publications

Specker’s parable of the overprotective seer: A road to contextuality, nonlocality and complementarity

Specker’s parable of the overprotective seer: A road to contextuality, nonlocality and complementarity

Experimental Demonstration of Four-Photon Entanglement and High-Fidelity Teleportation

Revealing universal quantum contextuality through communication games

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