60 citations · 386 across the 22 of their papers we have counts for
22 papers
Triacontagonal proofs of the Bell-Kochen-Specker theorem
P. K. Aravind, Justin Y. J. Burton, Guillermo Núñez Ponasso +1
Coxeter pointed out that a number of polytopes can be projected orthogonally into two dimensions in such a way that their vertices lie on a number of concentric regular triacontago…
The Golay codes and Quantum Contextuality
Mordecai Waegell, P. K. Aravind
It is shown that the codewords of the binary and ternary Golay codes can be converted into rays in RP(23) and RP(11) that provide proofs of the Kochen-Specker theorem in real state…
Automated generation of Kochen-Specker sets
Mladen Pavicic, Mordecai Waegell, Norman D. Megill +1
Quantum contextuality turns out to be a necessary resource for universal quantum computation and also has applications in quantum communication. Thus it becomes important to genera…
MUBs and SIC-POVMs of a spin-1 system from the Majorana approach
P. K. Aravind
In the Majorana or stellar representation of quantum states, an arbitrary (pure) state of a spin-1 system is represented by a pair of points on the unit sphere or, equivalently, by…
The Minimum Complexity of Kochen-Specker Sets Does Not Scale with Dimension
Mordecai Waegell, P. K. Aravind
A Kochen-Specker (KS) set is a specific set of projectors and measurement contexts that prove the Bell-Kochen-Specker contextuality theorem. The simplest known KS sets in Hilbert s…
The Penrose dodecahedron and the Witting polytope are identical in CP(3)
M. Waegell, P. K. Aravind
It is demonstrated that the set of 40 states of a spin-3/2 particle used by Zimba and Penrose to give proofs of the Kochen-Specker and Bell theorems is identical (i.e., unitarily e…
Parity proofs of the Kochen-Specker theorem based on the Lie algebra E8
Mordecai Waegell, P. K. Aravind
The 240 root vectors of the Lie algebra E8 lead to a system of 120 rays in a real 8-dimensional Hilbert space that contains a large number of parity proofs of the Kochen-Specker th…
Parity proofs of the Kochen-Specker theorem based on the 120-cell
Mordecai Waegell, P. K. Aravind
It is shown how the 300 rays associated with the antipodal pairs of vertices of a 120-cell (a four-dimensional regular polytope) can be used to give numerous "parity proofs" of the…
Proofs of the Kochen-Specker theorem based on the N-qubit Pauli group
Mordecai Waegell, P. K. Aravind
We present a number of observables-based proofs of the Kochen-Specker (KS) theorem based on the N-qubit Pauli group for N >= 4, thus adding to the proofs that have been presented e…
GHZ paradoxes based on an even number of qubits
Mordecai Waegell, P. K. Aravind
GHZ paradoxes are presented for all even numbers of qubits from four up. They are obtained from proofs of the Kochen-Specker (KS) theorem by showing how the assumption of noncontex…
Proofs of the Kochen-Specker theorem based on a system of three qubits
Mordecai Waegell, P. K. Aravind
A number of new proofs of the Kochen-Specker theorem are given based on the observables of the three-qubit Pauli group. Each proof is presented in the form of a diagram from which…
Universal violation of pentagon inequalities in four-state systems
Mordecai Waegell, P. K. Aravind
The 60 real vectors derived from the vertices of a 600-cell are shown to yield a number of pentagon inequalities that are satisfied by realistic noncontextual theories but violated…
Parity proofs of the Kochen-Specker theorem based on 60 complex rays in four dimensions
Mordecai Waegell, P. K. Aravind
It is pointed out that the 60 complex rays in four dimensions associated with a system of two qubits yield over 10^9 critical parity proofs of the Kochen-Specker theorem. The geome…
Probabilistic Generation of Quantum Contextual Sets
Norman D. Megill, Kresimir Fresl, Mordecai Waegell +2
We give a method for exhaustive generation of a huge number of Kochen-Specker contextual sets, based on the 600-cell, for possible experiments and quantum gates. The method is comp…
Parity proofs of the Kochen-Specker theorem based on the 24 rays of Peres
Mordecai Waegell, P. K. Aravind
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…
Parity proofs of the Bell-Kochen-Specker theorem based on the 600-cell
Mordecai Waegell, P. K. Aravind, Norman D. Megill +1
The set of 60 real rays in four dimensions derived from the vertices of a 600-cell is shown to possess numerous subsets of rays and bases that provide basis-critical parity proofs…
New Class of 4-Dim Kochen-Specker Sets
Mladen Pavicic, Norman D. Megill, P. K. Aravind +1
We find a new highly symmetrical and very numerous class (millions of non-isomorphic sets) of 4-dim Kochen-Specker (KS) vector sets. Due to the nature of their geometrical symmetri…
Critical noncolorings of the 600-cell proving the Bell-Kochen-Specker theorem
Mordecai Waegell, P. K. Aravind
Aravind and Lee-Elkin (1997) gave a proof of the Bell-Kochen-Specker theorem by showing that it is impossible to color the 60 directions from the center of a 600-cell to its vertic…
Isomorphism between the Peres and Penrose proofs of the BKS theorem in three dimensions
Elizabeth Gould, P. K. Aravind
It is shown that the 33 complex rays in three dimensions used by Penrose to prove the Bell-Kochen-Specker theorem have the same orthogonality relations as the 33 real rays of Peres…
Decoherence of a Measure of Entanglement
D. Tolkunov, V. Privman, P. K. Aravind
We demonstrate by an explicit model calculation that the decay of entanglement of two two-state systems (two qubits) is governed by the product of the factors that measure the degr…
Best conventional solutions to the King's Problem
P. K. Aravind
In the King's Problem, a physicist is asked to prepare a d-state quantum system in any state of her choosing and give it to a king who measures one of (d+1) sets of mutually unbias…
Solution to the King's Problem in prime power dimensions
P. K. Aravind
It is shown how to ascertain the values of a complete set of mutually complementary observables of a prime power degree of freedom by generalizing the solution in prime dimensions…