Related papers: On the reality of the quantum state once again: A …
We interpret ontological models for finite-dimensional quantum theory as functors from the category of finite-dimensional Hilbert spaces and bounded linear maps to the category of measurable spaces and Markov kernels. This uniformises…
Following the argument of Pusey, Barrett and Rudolph (Nature Phys. 8:476, 2012), new interest has been raised on whether one can interpret state-vectors (pure states) in a statistical way ($\psi$-epistemic theories), or if each of them…
In spite of the very common opinion we show that QM is not complete and that it is possible to create prequantum models providing finer description of physical reality than QM. There exists (at least in theoretical models) dispersion free…
The most irreducible way to represent information is a sequence of two symbols. In this paper, we construct quantum states using this basic building block. Specifically, we show that the probabilities that arise in quantum theory can be…
During the recent developments of quantum theory it has been clarified that the observable quantities (like energy or position) may be represented by operators (with real spectra) which are manifestly non-Hermitian. The mathematical…
Standard quantum theory represents a composite system at a given time by a joint state, but it does not prescribe a joint state for a composite of systems at different times. If a more even-handed treatment of space and time is possible,…
We analyze the recent no go theorem by Pusey, Barrett and Rudolph (PBR) concerning ontic and epistemic hidden variables. We define two fundamental requirements for the validity of the result. We finally compare the models satisfying the…
If the system is known to be in one of two non-orthogonal quantum states, $|\psi_1\rangle$ or $|\psi_2\rangle$, it is not possible to discriminate them by a single measurement due to the unitarity constraint. In a regular Hermitian quantum…
We discuss how to reconstruct quantum theory from operational postulates. In particular, the following postulates are consistent only with for classical probability theory and quantum theory. Logical Sharpness: There is a one-to-one map…
When it isn't possible to tell two distinct experimental procedures apart purely from their input/output statistics, then it seems a plausible hypothesis that the two procedures must be physically identical. We call such a hypothesis…
The non-Hermitian Schr\"odinger equation is re-expressed generally in the form of Hamilton's canonical equation without any approximation. Its quantization called non-Hermitian quantum field theory is discussed. By virtue of the canonical…
Pusey, Barrett, and Rudolph introduce a new no-go theorem for hidden-variables models of quantum theory. We make precise the class of models targeted and construct equivalent models that evade the theorem. The theorem requires assumptions…
One of the postulates of quantum mechanics is that the Hamiltonian is Hermitian, as this guarantees that the eigenvalues are real. Recently there has been an interest in asking if $H^\dagger = H$ is a necessary condition, and has lead to…
PT-symmetric quantum theory was originally proposed with the aim of extending standard quantum theory by relaxing the Hermiticity constraint on Hamiltonians. However, no such extension has been formulated that consistently describes states,…
In a recent work, authors prove a yet another no-go theorem that forbids the existence of a universal probabilistic quantum protocol producing a superposition of two unknown quantum states. In this short note, we show that in the presence…
In quantum foundations, there is growing interest in the program of reconstructing the quantum formalism from clear physical principles. These reconstructions are formulated in an operational framework, deriving the formalism from…
The physical states of matter and fields are represented in the quantum theory with complex valued wavefunctions, or more generally by quantum states in an abstract linear vector space. Determining the physical nature of wavefunctions…
It is shown how to introduce a geometric description of the algebraic approach to the non-relativistic quantum mechanics. It turns out that the GNS representation provides not only symplectic but also Hermitian realization of a `quantum…
Recently, it has been argued that no extension of quantum theory can have improved predictive power under a strong assumption of free choice of the experimental settings and validity of quantum mechanics. Here, under a different free choice…
Quantum states are the key mathematical objects in quantum theory. It is therefore surprising that physicists have been unable to agree on what a quantum state truly represents. One possibility is that a pure quantum state corresponds…