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Quantum incompatibility, referred as the phenomenon that some quantum measurements cannot be performed simultaneously, is necessary for various quantum information processing tasks, such as nonlocality and steering. When these applications…
The Kochen-Specker theorem shows the impossibility for a hidden variable theory to consistently assign values to certain (finite) sets of observables in a way that is non-contextual and consistent with quantum mechanics. If we require…
The best mathematical arguments against a realistic interpretation of quantum mechanics - that gives definite but partially unknown values to all observables - are analysed and shown to be based on reasoning that is not compelling. This…
Wave-particle duality, superposition and entanglement are among the most counterintuitive features of quantum theory. Their clash with our classical expectations motivated hidden-variable (HV) theories. With the emergence of quantum…
A common objective for quantum control is to force a quantum system, initially in an unknown state, into a particular target subspace. We show that if the subspace is required to be a decoherence-free subspace of dimension greater than 1,…
Complementarity, the incomplete nature of a quantum measurement - a core concept in quantum mechanics - stems from the choice of the measurement apparatus. The notion of complementarity is closely related to Heisenberg's uncertainty…
The problem of how to interpret quantum mechanics has persisted for a century. The disconnect between the wavefunction state vector and what is observed in experimental apparati has had no shortage of explanations. But all explanations so…
We show that the protocol known as quantum state separation can be used to transfer information between the phase and path of a particle in an interferometer. When applied to a quantum eraser, this allows us to erase some, but not all, of…
Quantum mechanics has irked physicists ever since its conception more than 100 years ago. While some of the misgivings, such as it being unintuitive, are merely aesthetic, quantum mechanics has one serious shortcoming: it lacks a physical…
We analyse a proposition which considers quantum theory as a mere tool for calculating probabilities for sequences of outcomes of observations made by an Observer, who him/herself remains outside the scope of the theory. Predictions are…
The new interpretation of Quantum Mechanics is based on a complex probability theory. An interpretation postulate specifies events which can be observed and it follows that the complex probability of such event is, in fact, a real positive…
The existence of observables that are incompatible or not jointly measurable is a characteristic feature of quantum mechanics, which lies at the root of a number of nonclassical phenomena, such as uncertainty relations, wave--particle dual…
The question whether quantum measurements reflect some underlying objective reality has no generally accepted answer. We show that description of such reality is possible under natural conditions such as linearity and causality, although in…
I. This paper is devoted to the problem of error detection with quantum codes. In the first part we examine possible problem settings for quantum error detection. Our goal is to derive a functional that describes the probability of…
Spontaneous emission and the inelastic scattering of photons are two natural processes usually associated with decoherence and the reduction in the capacity to process quantum information. Here we show that when suitably detected, these…
A quantum system can behave as a wave or as a particle, depending on the experimental arrangement. When for example measuring a photon using a Mach-Zehnder interferometer, the photon acts as a wave if the second beam-splitter is inserted,…
The decay of an unstable system is usually described by an exponential law. Quantum mechanics predicts strong deviations of the survival probability from the exponential: indeed, the decay is initially quadratic, while at very large times…
Recent theoretical results confirm that quantum theory provides the possibility of new ways of performing efficient calculations. The most striking example is the factoring problem. It has recently been shown that computers that exploit…
This paper clarifies the picture about Dense-choice Counter Machines, which have been less studied than (discrete) Counter Machines. We revisit the definition of "Dense Counter Machines" so that it now extends (discrete) Counter Machines,…
Whenever a mathematical proposition to be proved requires more information than it is contained in an axiomatic system, it can neither be proved nor disproved, i.e. it is undecidable, or logically undetermined, within this axiomatic system.…