Related papers: Kochen-Specker theorem for a single qubit using po…
It will be shown that the Peres-Mermin square admits value-definite noncontextual hidden-variable models if the observables associated with the operators can be measured only sequentially but not simultaneously. Namely, sequential…
A new simple proof of the adiabatic theorem is given in the finite dimensional case for nondegenerate as well as degenerate states. The explicitly integrable two level system is considered as an example. It is demonstrated that the error…
Quantum measurements are important tools in quantum information, represented by positive, operator-valued measures. A wide class of symmetric measurements is given via generalized equiangular measurements that form conical 2-designs. We…
We introduce a procedure based on quantum expectation values of measurement observables to characterize quantum coherence. Our measure allows one to quantify coherence without having to perform tomography of the quantum state, and can be…
It is proven that any hidden variable theory of the type proposed by Meyer [Phys. Rev. Lett. {\bf 83}, 3751 (1999)], Kent [{\em ibid.} {\bf 83}, 3755 (1999)], and Clifton and Kent [Proc. R. Soc. London, Ser. A {\bf 456}, 2101 (2000)] leads…
The accessible information of general signal states is obtained by performing a generalized measurement. In the case that the signal alphabet consists of two states of a qubit system, it is proved that a von Neumann (orthogonal) measurement…
For a compact convex subset $K $ of a locally convex Hausdorff space, a measurement on $A(K)$ is a finite family of positive elements in $A(K)$ normalized to the unit constant $1_K$, where $A(K)$ denotes the set of continuous real affine…
Classical realism demands that system properties exist independently of whether they are measured, while noncontextuality demands that the results of measurements do not depend on what other measurements are performed in conjunction with…
This paper consists of two prongs. Firstly, we prove that any Specht module labelled by a 2-separated partition is semisimple and we completely determine its decomposition as a direct sum of graded simple modules. Secondly, we apply these…
Quantum mechanics implies that not all physical properties can be simultaneously well defined, such as the momentum and position due to Heisenberg uncertainty principle. Some alternative theories have been explored, notably the…
Interrelation of the Coleman's representabilty theory for 1-density operators and abstract algebraic form of the Hohenberg-Kohn theorem is studied in detail. Convenient realization of the Hohenberg-Kohn set of classes of 1-electron…
In this paper we attempt to physically interpret the Modal Kochen- Specker (MKS) theorem. In order to do so, we analyze the features of the possible properties of quantum systems arising from the elements in an orthomodular lattice and…
We show that some sets of quantum observables are unique up to an isometry and have a contextuality witness that attains the same value for any initial state. We prove that these two properties make it possible to certify any of these sets…
Just as any state of a single qubit or 2-level system can be obtained from any other state by a rotation operator parametrized by three real Euler angles, we show how any state of an n-qubit or 2^n-level system can be obtained from any…
A key ingredient of the Kochen-Specker theorem is the so-called functional composition principle, which asserts that hidden states must ascribe values to observables in a way that is consistent with all functional relations between them.…
The concept of individuality in quantum mechanics shows radical differences from the one used in classical physics. In particular, it is not possible to consider the fundamental particles described by quantum theory as individual…
The Kochen-Specker theorem shows that it is impossible to assign sharp values to all dynamical variables in quantum mechanics in such a way that the algebraic relations among the values of dynamical variables whose self-adjoint operators…
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, and therefore provide an isomorphic proof of the theorem.…
Klyachko and coworkers consider an orthogonality graph in the form of a pentagram, and in this way derive a Kochen-Specker inequality for spin 1 systems. In some low-dimensional situations Hilbert spaces are naturally organised, by a…
We consider a two-level quantum system (qubit) which is continuously measured by a detector. The information provided by the detector is taken into account to describe the evolution during a particular realization of measurement process. We…