Related papers: Compressing the hidden variable space of a qubit
Perhaps the quantum state represents information about reality, and not reality directly. Wave function collapse is then possibly no more mysterious than a Bayesian update of a probability distribution given new data. We consider models for…
Every quantum physical system can be considered the ''shadow'' of a special kind of classical system. The system proposed here is classical mainly because each observable function has a well precise value on each state of the system: an…
An arbitrarily dense discretisation of the Bloch sphere of complex Hilbert states is constructed, where points correspond to bit strings of fixed finite length. Number-theoretic properties of trigonometric functions (not part of the…
Focusing particularly on one-qubit and two-qubit systems, I explain how the quantum state of a system of n qubits can be expressed as a real function--a generalized Wigner function--on a discrete 2^n x 2^n phase space. The phase space is…
We report on experimental measurement of the Hilbert-Schmidt distance between two two-qubit states by many-particle interference. We demonstrate that our three-step method for measuring distances in Hilbert space is far less complex than…
We develop an approach where the quantum system states and quantum observables are described as in classical statistical mechanics -- the states are identified with probability distributions and observables, with random variables. An…
Quantum communication is often investigated in scenarios where only the dimension of Hilbert space is known. However, assigning a precise dimension is often an approximation of what is actually a higher-dimensional process. Here, we…
Constructing local hidden variable (LHV) models for entangled quantum states is challenging, as the model should reproduce quantum predictions for all possible local measurements. Here we present a simple method for building LHV models,…
A model for two entangled systems in an EPR setting is shown to reproduce the quantum-mechanical outcomes and expectation values. Each system is represented by a small sphere containing a point-like particle embedded in a field. A quantum…
Multiplying a likelihood function with a positive number makes no difference in Bayesian statistical inference, therefore after normalization the likelihood function in many cases can be considered as probability distribution. This idea led…
We study the quantization of geometry in the presence of a cosmological constant, using a discretiza- tion with constant-curvature simplices. Phase space turns out to be compact and the Hilbert space finite dimensional for each link. Not…
We consider a very natural generalization of quantum theory by letting the dimension of the Bloch ball be not necessarily three. We analyze bipartite state spaces where each of the components has a d-dimensional Euclidean ball as state…
Assuming that quantum mechanics is obeyed exactly after averaging over hidden variables, and considering models that obey both the hypotheses of free will and locality, we establish the form of all possible hidden-variable models that…
The extended Bloch representation of quantum mechanics was recently derived to offer a (hidden-measurement) solution to the measurement problem. In this article we use it to investigate the geometry of superposition and entangled states,…
Most states in the Hilbert space are maximally entangled. This fact has proven useful to investigate - among other things - the foundations of statistical mechanics. Unfortunately, most states in the Hilbert space of a quantum many body…
The necessary and sufficient conditions for minimization of the generalized rate error for discriminating among $N$ pure qubit states are reformulated in terms of Bloch vectors representing the states. For the direct optimization problem an…
It is sometimes pointed out as a curiosity that the state space of quantum two-level systems, i.e. the qubit, and actual physical space are both three-dimensional and Euclidean. In this paper, we suggest an information-theoretic analysis of…
The paper describes an algorithm for semantic representation of behavioral contexts relative to a dichotomic decision alternative. The contexts are represented as quantum qubit states in two-dimensional Hilbert space visualized as points on…
We study the nonlocality of arbitrary dimensional bipartite quantum states. By computing the maximal violation of a set of multi-setting Bell inequalities, an analytical and computable lower bound has been derived for general two-qubit…
Randomly repeated measurements during the evolution of a closed quantum system create a sequence of probabilities for the first detection of a certain quantum state. The related discrete monitored evolution for the return of the quantum…