Density cubes and higher-order interference theories

Dakić, Borivoje; Paterek, Tomasz; Brukner, Časlav

doi:10.1088/1367-2630/16/2/023028

Cited by 67 publications

(100 citation statements)

References 38 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(1) greater than K Lüders 3 is possible has come in the recent work by Dakić et al [20]. There, however, the excess violation was claimed to stem from correlations beyond quantum theory.…”

mentioning

confidence: 95%

Temporal Quantum Correlations and Leggett-Garg Inequalities in Multilevel Systems

2014

View full text Add to dashboard Cite

We show that the quantum bound for temporal correlations in a Leggett-Garg test, analogous to the Tsirelson bound for spatial correlations in a Bell test, strongly depends on the number of levels N that can be accessed by the measurement apparatus via projective measurements. We provide exact bounds for small N , that exceed the known bound for the Leggett-Garg inequality, and show that in the limit N → ∞ the Leggett-Garg inequality can be violated up to its algebraic maximum.PACS numbers: 03.65. Ud, 03.65.Ta Introduction.-Bell inequalities place fundamental bounds on the nature of correlations between spatiallyseparated entities within a local hidden variable framework [1]. Leggett and Garg showed that temporal correlations obey similar inequalities based on assumptions of macroscopic realism and non-invasive measureability [2]. Quantum particles are bound neither by local hidden variables nor macroscopic realism and so can violate both Bell and Leggett-Garg inequalities (LGIs).The maximum degree to which a quantum system can violate a Bell inequality is known as the Tsirelson bound [3], significantly less than the largest-conceivable value, the algebraic bound [4]. Violations of a Bell inequality beyond the Tsirelson bound would be evidence of a new physics beyond quantum theory [6].With interest in the LGIs growing (see Ref.[7] for a review), we ask here whether there is such a thing as a temporal Tsirelson bound for the LGIs. In the light of some recent results [8,9] and given the formal symmetry between the two types of inequality [10,11] and the general trend towards unification between temporal and spatial correlations [12][13][14][15], one would expect that the Tsirelson bound for the LGIs holds analogously to the spatial case. Surprisingly, and as we show here, this is not the case. By considering a broader class of projective measurements than hitherto considered, we show that the maximum quantum violation of the LGIs can exceed the Tsirelson value, and increases with increasing system size, even up to the algebraic bound in the asymptotic limit.Let us now be more concrete and consider the simplest LGI which, for dichotomous observable Q = ±1, readswhere C βα = Q(t β )Q(t α ) is the correlation function of variable Q at the two times t β ≥ t α . For a two-level system, the maximum quantum value of K 3 is K max 3 = 3 2 [2], which we shall refer to as the Lüders bound, K Lüders 3 = 3 2 , for reasons to become clear shortly. It has been proven rigorously that for measurements given by just two projectors, Π + and Π − , onto eigenspaces associated with results Q = +1 and Q = −1, the maximum quantum value of K 3 is the same as for the qubit, irrespective of system size [9]. This has been reflected in several studies: the experiment of Ref.[16] on a three-level system obtained a maximum value less than 3 2 ; on the theory side, multi-level quantum systems such as a large spin [17], optoelectromechanical systems [18] and photosynthetic complexes [19] have also been observed to obey. From this, one might co...

show abstract

mentioning

confidence: 95%

Temporal Quantum Correlations and Leggett-Garg Inequalities in Multilevel Systems

2014

View full text Add to dashboard Cite

show abstract

“…To prove such a conjecture however, a concrete example of such a theory is needed. While there are partial examples in the literature [24,25], none of these are complete [26]. Answering such a conjecture in the affirmative is thus not yet possible, although some evidence was provided in [26].…”

Section: Computational Oraclesmentioning

confidence: 99%

Generalised phase kick-back: the structure of computational algorithms from physical principles

Lee

Selby

2016

New J. Phys.

View full text Add to dashboard Cite

The advent of quantum computing has challenged classical conceptions of which problems are efficiently solvable in our physical world. This motivates the general study of how physical principles bound computational power. In this paper we show that some of the essential machinery of quantum computation-namely reversible controlled transformations and the phase kick-back mechanismexist in any operational-defined theory with a consistent notion of information. These results provide the tools for an exploration of the physics underpinning the structure of computational algorithms. We investigate the relationship between interference behaviour and computational power, demonstrating that non-trivial interference behaviour is a general resource for post-classical computation. In proving the above, we connect higher-order interference to the existence of postquantum particle types, potentially providing a novel experimental test for higher-order interference. Finally, we conjecture that theories with post-quantum interference-the higher-order interference of Sorkin-can solve problems intractable even on a quantum computer.

show abstract

“…Other than in an invasive scenario (where the algebraic maximum is trivially achieved, e.g., a classical device with memory or its quantum realization via POVMs [23]), the only hint that a violation of (5.17) greater than K Lüders 3 is possible has come in the recent work by Dakić et al [141]. There, however, the excess violation was claimed to stem from correlations beyond quantum theory.…”

Section: Sequential Measurements and Leggett-garg Inequalitymentioning

confidence: 99%

Temporal Quantum Correlations and Hidden Variable Models

Budroni

2016

Springer Theses

View full text Add to dashboard Cite

This thesis is devoted to the investigation of the differences between the predictions of classical and quantum theory. More precisely, we shall analyze such differences starting from their consequences on quantities with a clear empirical meaning, such as probabilities, or relative frequencies, that can be directly observed in experiments.Different kind of classical probability theories, or hidden variable theories, corresponding to different physical constraints imposed on the measurement scenario are discussed, namely, locality, noncontextuality and macroscopic realism. Each of these theories predicts bounds on the strength of correlations among different variables, and quantum mechanical predictions violate such bounds, thus revealing a stark contrast with our classical intuition.Our work starts with the investigation of the set of classical probabilities by means of the correlation polytope approach, which provides a minimal and optimal set of bounds for classical correlations. In order to overcome some of the computational difficulties associated with it, we develop an alternative method that avoid the direct computation of the polytope and we apply it to Bell and noncontextuality scenarios showing its advantages both for analytical and numerical computations.A different notion of optimality is then discussed for noncontextuality scenarios that provide a state-independent violation: Optimal expression are those maximizing the ratio between the quantum and the classical value. We show that this problem can be formulated as a linear program and solved with standard numerical techniques. Moreover, optimal inequalities for the cases analyzed are also proven to be part of the minimal set described above.Subsequently, we provide a general method to analyze quantum correlations in the sequential measurement scenario, which allows us to compute the maximal correlations. Such a method has a direct application for computation of maximal quantum violations of Leggett-Garg inequalities, i.e., the bounds for correlation in a macroscopic realist theories, and it is relevant in the analysis of noncontextuality tests, where sequential measurements are usually employed.Finally, we discuss a possible application of the above results for the construction of dimension witnesses, i.e., as a certification of the minimal dimension of the Hilbert spaces needed to explain the arising of certain quantum correlations. Anschließend stellen wir eine allgemeine Methode vor mit der man Quantenkorrelationen bei sequentiellen Messungen analysieren kann und die maximalen Korrelationen berechnen kann.

show abstract

Density cubes and higher-order interference theories

Cited by 67 publications

References 38 publications

Temporal Quantum Correlations and Leggett-Garg Inequalities in Multilevel Systems

Temporal Quantum Correlations and Leggett-Garg Inequalities in Multilevel Systems

Generalised phase kick-back: the structure of computational algorithms from physical principles

Temporal Quantum Correlations and Hidden Variable Models

Contact Info

Product

Resources

About