Related papers: Minimal Bell-Kochen-Specker proofs with POVMs on q…

We present two geometric proofs of the Kochen-Specker theorem. A quite similar argument has been used by Cooke, Keane, and Moran, as well as by Kalmbach in her book to derive the Gleason theorem.

Kochen-Specker (KS) vector systems are sets of vectors in R^3 with the property that it is impossible to assign 0s and 1s to the vectors in such a way that no two orthogonal vectors are assigned 0 and no three mutually orthogonal vectors…

We discuss the dependence of the Shannon entropy of normalized finite rank-1 POVMs on the choice of the input state, looking for the states that minimize this quantity. To distinguish the class of measurements where the problem can be…

Self-testing represents the strongest form of certification of a quantum system. Here we investigate theoretically and experimentally the question of self-testing non-projective quantum measurements. That is, how can one certify, from…

In quantum estimation for a $d$-parameter family of density operators on a finite-dimensional Hilbert space $\mathcal{H}$, an estimator is specified by a pair $\left(M,\hat{\theta}\right)$, where $M$ is a POVM with a finite outcome set…

We examine the possible states of subsystems of a system of bits or qubits. In the classical case (bits), this means the possible marginal distributions of a probability distribution on a finite number of binary variables; we give necessary…

Quantum labeling tasks ask one to recover the missing associations between classical outcome labels and the effects forming the POVM. We study labeling in the multiple-shot regime, allowing a finite number of uses of the device and the most…

We introduce a logic modelling some aspects of the behaviour of the measurement process, in such a way that no direct mention of quantum states is made, thus avoiding the problems associated to this rather evasive notion. We then study some…

Hidden variables theories for quantum mechanics are usually assumed to satisfy the KS condition. The Bell-Kochen-Specker theorem then shows that these theories are necessarily contextual. But the KS condition can be criticized from an…

One of the fundamental results in quantum foundations is the Kochen-Specker (KS) theorem, which states that any theory whose predictions agree with quantum mechanics must be contextual, i.e., a quantum observation cannot be understood as…

In [1] it was shown that the Kochen Specker theorem can be written in terms of the non-existence of global elements of a certain varying set over the partially ordered set of boolean subalgebras of projection operators on some Hilbert…

In this work, we provide a complete analysis to minimum-error discrimination of mixed four qubit states with arbitrary prior probabilities. For the complete anaysis, the most important work to do is to find the necessary and sufficient…

In the device-independent scenario, positive operator-valued measurements (POVMs) can certify more randomness than projective measurements. This paper self-tests a three-outcome extremal qubit POVM in the X-Z plane of the Bloch sphere by…

Various forms of optimality for quantum observables described as normalized positive operator valued measures (POVMs) are studied in this paper. We give characterizations for observables that determine the values of the measured quantity…

I give a first characterization of the class of generalized measurements that can be exactly realized on a pair of qudits encoded in indistinguishable particles, by using only linear elements and particle detectors. Two immediate results…

Certain concrete "ontological models" for quantum mechanics (models in which measurement outcomes are deterministic and quantum states are equivalent to classical probability distributions over some space of `hidden variables') are…

We formulate minimum-error and unambiguous discrimination problems for quantum processes in the language of process positive operator valued measures (PPOVM). In this framework we present the known solution for minimum-error discrimination…

A proof of Bell's theorem without inequalities and involving only two observers is given by suitably extending a proof of the Bell-Kochen-Specker theorem due to Mermin. This proof is generalized to obtain an inequality-free proof of Bell's…

Quantum hypothesis testing (QHT) provides an effective method to discriminate between two quantum states using a two-outcome positive operator-valued measure (POVM). Two types of decision errors in a QHT can occur. In this paper we focus on…

We investigate two aspects of the elementary example of POVMs on the Euclidean plane, namely their status as quantum observables and their role as quantizers in the integral quantization procedure. The compatibility of POVMs in the ensuing…