Publisher’s Note: Proposal of a Two-Qutrit Contextuality Test Free of the Finite Precision and Compatibility Loopholes [Phys. Rev. Lett.<b>106</b>, 190401 (2011)]

Cabello, Adán; Cunha, Marcelo Terra

doi:10.1103/physrevlett.106.209904

Cited by 6 publications

(6 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the reasonings above we have taken into account of condition 2 which demands that linked rays not be assigned simultaneously to value 1 and in a triangle one and only one ray be assigned to value 1. A set of eight rays in each case considered above, e.g., ĥ0,1 , z 2,3 , and y ± 2,3 , constitutes in fact a 3-box paradox [23] which appears also in Cliffton's state-dependent proof of KS theorem [24] and a recent proposal to close the compatibility loopholes [25].…”

Section: +1 +2mentioning

confidence: 99%

State-Independent Proof of Kochen-Specker Theorem with 13 Rays

2012

Phys. Rev. Lett.

203

320

View full text Add to dashboard Cite

Quantum contextuality, as proved by Kochen and Specker, and also by Bell, should manifest itself in any state in any system with more than two distinguishable states and recently has been experimentally verified on various physical systems. However for the simplest system capable of exhibiting contextuality, a qutrit, the quantum contextuality is verified only state-dependently in experiment because too many (at least 31) observables are involved in all the known state-independent tests. Here we report an experimentally testable inequality involving only 13 observables that is satisfied by all non-contextual realistic models while being violated by all qutrit states. Thus our inequality will practically facilitate a state-independent test of the quantum contextuality for an indivisible quantum system. We provide also a record-breaking state-independent proof of the Kochen-Specker theorem with 13 directions determined by 26 points on the surface of a three by three magic cube.It is believed, almost religiously, that every effect has its own cause and the same cause shall lead to the same effect. The predictions of quantum mechanics (QM) are however probabilistic and the effect that different outcomes appear in different runs of a measurement seem to have no definite cause, at least unexplainable using QM alone. Einstein, Podolsky, and Rosen [1] initiated a longlasting quest for a quantum reality by questioning the completeness of quantum mechanics. Hidden variable (HV) models are introduced in order to explain why a certain outcome appears in each run of a measurement, attempting to make QM complete. Years later Kochen, Specker [2], and Bell [3] discovered that quantum mechanics can be completed only by a hidden variable model that is contextual: the outcome of a measurement depends on which compatible observable might be measured alongside. Simply put, Kochen-Specker (KS) theorem states that non-contextual HV models cannot reproduce all the predictions of QM or quantum mechanics is contextual.In any non-contextual HV model all observables have definite values determined only by some HVs λ that are distributed according to a given probability distribution ̺ λ with normalization dλ̺ λ = 1. Two observables are compatible if they can be measured in a single experimental setup and a maximal set of mutually compatible observables defines a context. Non-contextuality is a typical classical property: the value of an observable revealed by a measurement is predetermined by HVs λ only regardless of which compatible observable might be measured alongside. Local realism is a form of non-contextuality enforced by the locality and thus Bell's inequalities [4] are a special form of KS inequalities [5][6][7][8][9], experimentally testable inequalities that are satisfied by all noncontextual HV models, some of which have been tested in recent measurements [10][11][12][13][14][15][16][17][18]. In general KS inequalities reveal the nonclassical nature of single systems demanding neither space-like separation nor entanglement, i.e....

show abstract

Section: +1 +2mentioning

confidence: 99%

State-Independent Proof of Kochen-Specker Theorem with 13 Rays

2012

Phys. Rev. Lett.

203

320

View full text Add to dashboard Cite

show abstract

“…A debate still continues about whether finite precision and compatibility loopholes negate experimental tests of the K-S theorem and demonstrations of contextuality [31]. It is possible that newer proofs of the K-S theorem [32] could suggest experiments that plug these loopholes and also find application in such protocols as quantum key distribution [26], random number generation [27] and parity oblivious transfer [28].…”

Section: Relation To Ongoing Workmentioning

confidence: 99%

Parity Proofs of the Kochen-Specker Theorem Based on the 24 Rays of Peres

Waegell

Aravind

2011

Found Phys

View full text Add to dashboard Cite

A diagrammatic representation is given of the 24 rays of Peres that makes it easy to pick out all the 512 parity proofs of the Kochen-Specker theorem contained in them. The origin of this representation in the fourdimensional geometry of the rays is pointed out.Some time back Peres [1] gave a proof of the Kochen-Specker (K-S) theorem [2] using 24 rays in a real four-dimensional Hilbert space. His proof was much simpler than the original proof of Kochen and Specker, which used 117 rays (or unoriented directions) in ordinary three-dimensional space. Peres's proof was simplified by Kernaghan [3] and Cabello et al [4], who showed that the Peres rays contain several subsets of 20 and 18 rays that provide transparent "parity" proofs of the theorem. The existence of further parity proofs involving 22 and 24 rays was pointed out by Pavičić et al [5]. This paper presents a diagram (Fig.1) that permits a simple visualization of the 2 9 = 512 parity proofs in this system. We invite the reader to solve a Sudoku-like puzzle, with easily stated rules, whose solutions yield the parity proofs. This puzzle can be attempted even by non-physicists. We give a solution to the puzzle in the form of a simple set of rules for generating all the parity proofs. We then discuss the four-dimensional geometry of the Peres rays that underlies Fig.1 and helps explain the rules for generating the parity proofs. Although no new results are presented in this paper, we believe it still serves a useful purpose because it gives a unified account of all the parity proofs in this system obtained by many authors over a period of many years. The interest of this demonstration in relation to ongoing work on the Kochen-Specker theorem is discussed in the concluding section of this paper.

show abstract

“…This raises the question of the connection between contextuality and nonlocality. It is known that it is possible to convert some contextuality proofs based on KS sets into Bell inequalities [17][18][19][20]. However, so far only one of them has a violation large enough to allow experimental verification with entangled ququarts [20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Proposed experiments of qutrit state-independent contextuality and two-qutrit contextuality-based nonlocality

et al. 2012

Self Cite

View full text Add to dashboard Cite

Recent experiments have demonstrated ququart state-independent quantum contextuality and qutrit state-dependent quantum contextuality. So far, the most basic form of quantum contextuality pointed out by Kochen and Specker, and Bell, has eluded experimental confirmation. Here we present an experimentally feasible test to observe qutrit state-independent quantum contextuality using single photons in a three-path setup. In addition, we show that if the same measurements are performed on two entangled qutrits, rather than sequentially on the same qutrit, then the noncontextual inequality becomes a Bell inequality. We show that this connection also applies to other recently introduced noncontextual inequalities.

show abstract

Publisher’s Note: Proposal of a Two-Qutrit Contextuality Test Free of the Finite Precision and Compatibility Loopholes [Phys. Rev. Lett.106, 190401 (2011)]

Cited by 6 publications

References 0 publications

State-Independent Proof of Kochen-Specker Theorem with 13 Rays

State-Independent Proof of Kochen-Specker Theorem with 13 Rays

Parity Proofs of the Kochen-Specker Theorem Based on the 24 Rays of Peres

Proposed experiments of qutrit state-independent contextuality and two-qutrit contextuality-based nonlocality

Contact Info

Product

Resources

About