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The quantum multiparameter estimation is very different from the classical multiparameter estimation due to Heisenberg's uncertainty principle in quantum mechanics. When the optimal measurements for different parameters are incompatible,…
Uncertainty principle is one of the cornerstones of quantum theory. In the literature, there are two types of uncertainty relations, the operator form concerning the variances of physical observables and the entropy form related to entropic…
Recently, Brukner and Zeilinger (2001) have claimed that the Shannon information is not well defined as a measure of information in quantum mechanics, adducing arguments that seek to show that it is inextricably tied to classical notions of…
The geometric form of standard quantum mechanics is compatible with the two postulates: 1) The laws of physics are invariant under the choice of experimental setup and 2) Every quantum observation or event is intrinsically statistical.…
The quantum measurement problem is formulated in the form of an insolubility theorem that states the impossibility of obtaining, for all available object preparations, a mixture of states of the compound object and apparatus system that…
The fundamental physical theories that interpret and explain behaviour of matter in nature are dependent on several unobservables and insensibles in their construction. While a rigorous natural philosophy cannot take them for granted, there…
Since the particles such as molecules, atoms and nuclei are composite particles, it is important to recognize that physics must be invariant for the composite particles and their constituent particles, this requirement is called particle…
Einstein`s equivalence principle states the complete physical equivalence of a gravitational field and corresponding inertial field in an accelerated reference frame. However, to what extent the equivalence principle remains valid in…
Current physics is faced with the fundamental problem of unifying quantum theory and general relativity, which would have resulted in quantum gravity. The main effort to construct the latter has been bent on quantizing spacetime structure,…
Measurement outcomes of a quantum state can be genuinely random (unpredictable) according to the basic laws of quantum mechanics. The Heisenberg-Robertson uncertainty relation puts constrains on the accuracy of two noncommuting observables.…
A persistent focus on the concept of emergence as a core element of the scientific method allows a clean separation, insofar as this is possible, of the physical and philosophical aspects of the problem of outcomes in quantum mechanics. The…
This chapter acknowledges a gap between the ``non-individuals'' interpretation of quantum mechanics and our world of experience, and begins to bridge it. Section 1 states the problem with Abner Shimony's ``Phenomenological principle'';…
Quantum Mechanics lacks an intuitive interpretation, which is the cause of a generally formalistic approach to its use. This in turn has led to a certain insensitivity to the actual meaning of many words used in its description and…
We define the Wigner entropy of a quantum state as the differential Shannon entropy of the Wigner function of the state. This quantity is properly defined only for states that possess a positive Wigner function, which we name…
The distinction between pure states and mixed states is a kernel ingredient of what is considered to be the standard formulation of quantum mechanics and plays today a kernel role in foundational debates about the meaning of quantum…
Complementarity was originally introduced as a qualitative concept for the discussion of properties of quantum mechanical objects that are classically incompatible. More recently, complementarity has become a \emph{quantitative} relation…
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…
There are four reasons why our present knowledge and understanding of quantum mechanics could be regarded as incomplete. Firstly, the principle of linear superposition has not been experimentally tested for position eigenstates of objects…
A framework for a quantum mechanical information theory is introduced that is based entirely on density operators, and gives rise to a unified description of classical correlation and quantum entanglement. Unlike in classical (Shannon)…
One of quantum theory's salient features is its apparent indeterminism, i.e. measurement outcomes are typically probabilistic. We formally define and address whether this uncertainty is unavoidable or whether post-quantum theories can offer…