Related papers: Realistic interpretation of a superposition state …
In this survey we discuss the notion of combinatorial interpretation in the context of Algebraic Combinatorics and related areas. We approach the subject from the Computational Complexity perspective. We review many examples, state a…
The state $\rho$ of a quantum system can be represented by a vector $\mathbf{P}_{\mathcal{M}}(\rho)$ of outcome probabilities for a set of measurements $\mathcal{M}$. Such representations appear throughout physics, for example, in quantum…
In a recent paper Sanpera et al. have shown, that for the simplest binary composite systems any density matrix can be described in terms of only product vectors. The purpose of this note is to show that posibillity of decomposing any state…
The measurement problem is to explain why a system which is in a linear combination of states appears, upon measurement, to be in just one of those states. The solution given here is to first show that if one assumes linear, unitary, no…
The assumption that the system Hamiltonian for entangled states is additive is widely used in orthodox quantum no-signalling arguments. It is shown that additivity implies a contradiction with the assumption that the system being studied is…
The most general mathematical law for summing bounded quantities is not the arithmetic law, but a composition law of which the summation law for velocities in special relativity is only one particular example. We believe that this…
There is a longstanding debate on the metaphysical relation between quantum states and the systems they describe. A series of relatively recent {\psi}-ontology theorems have been taken to show that, provided one accepts certain assumptions,…
We modify the Relative State Interpretation (RSI) of Quantum Mechanics so that it does not imply many worlds and parallel realities. We drop the assumption that probability amplitudes correspond one-to-one with reality: Not all information…
The distinction between proper and improper mixtures is a staple of the discussion of foundational questions in quantum mechanics. Here we note an analogous distinction in the context of the theory of entanglement. The terminology of…
In modern physics only relative quantities are considered to have physical significance. For example, position assigned to a system depends on the choice of coordinates, and only relative distances between different systems have physical…
I show a situation of multiparticle entanglement which cannot be explained in the framework of an interpretation of quantum mechanics recently proposed by Mermin. This interpretation is based on the assumption that correlations between…
This paper proposes a new framework for learning a rule ensemble model that is both accurate and interpretable. A rule ensemble is an interpretable model based on the linear combination of weighted rules. In practice, we often face the…
Adding interpretability to multivariate methods creates a powerful synergy for exploring complex physical systems with higher order correlations while bringing about a degree of clarity in the underlying dynamics of the system.
The superposition principle of two qubit states is formulated as nonlinear addition rule of mean spinprojection onto three perpendicular directions. The explicit expression for the mean value determining the superposition state in term of…
All compositions of a mixed-state density operator are equivalent for the prediction of the probabilities of future outcomes of measurements. For retrodiction, however, this is not the case. The retrodictive formalism of quantum mechanics…
The superposition principle lies at the heart of many non-classical properties of quantum mechanics. Motivated by this, we introduce a rigorous resource theory framework for the quantification of superposition of a finite number of linear…
It is shown that different distinguishability measures impose different orderings on ensembles of $N$ pure quantum states. This is demonstrated using ensembles of equally-probable, linearly independent, symmetrical pure states, with the…
There is a natural equivalence relation on representations of the states of a given quantum system in a Hilbert space, two representations being equivalent iff they are related by a unitary transformation. There are two equivalence classes,…
Ensemble models are widely recognized in the ML community for their limited interpretability. For instance, while a single decision tree is considered interpretable, ensembles of trees (e.g., boosted trees) are often treated as black-boxes.…
In this short paper, we show that the solution set of a combination of equilibrium problems is not necessary contained in the intersection of a finite family of solution sets of equilibrium problems. As a corollary, we deduce that…