(1) Background: Over a dozen constructions have been proposed to untangle the foundations of quantum mechanics (QM). So many irreconcilable schemes raise the suspect that methodological requisites should be discussed before beginning a theoretical construction in QM. In particular, we identify the ensuing issues of methods: formal definitions of particles and waves; incompatible probability theories and the single case problem. (2) Methods of the present inquiry: We tackle the second and third issue with a novel and comprehensive probability theory. Next it applies the theoretical results to quantum physics. (3) Results of the present inquiry: The new probability theory proves how some effects - the impossibility of measuring, the collapse of outcomes, non-locality and counterfactual definiteness - are not exclusive to quantum mechanics but can be observed also in classical context. (4) Conclusions: A probability-based interpretation of quantum mechanics is derived; innovative answers are put forward about quantum dualism, the measurement problem, collapse and the relations between classical and quantum physics.(1) Background: Over a dozen constructions have been proposed to untangle the foundations of quantum mechanics (QM). So many irreconcilable schemes raise the suspect that methodological requisites should be discussed before beginning a theoretical construction in QM. In particular, we identify the ensuing issues of methods: formal definitions of particles and waves; incompatible probability theories and the single case problem. (2) Methods of the present inquiry: We tackle the second and third issue with a novel and comprehensive probability theory. Next it applies the theoretical results to quantum physics. (3) Results of the present inquiry: The new probability theory proves how some effects - the impossibility of measuring, the collapse of outcomes, non-locality and counterfactual definiteness - are not exclusive to quantum mechanics but can be observed also in classical context. (4) Conclusions: A probability-based interpretation of quantum mechanics is derived; innovative answers are put forward about quantum dualism, the measurement problem, collapse and the relations between classical and quantum physics.

Jul 23, 20250 citations

Single-qubit measurement of Heisenberg uncertainty lower bounds for three incompatible observables

Rehan, K., Tian‐Jian Xiong, L.-L. Yan +6 more

Being one of the centroidal concepts in quantum theory, the fundamental constraint imposed by Heisenberg uncertainty relations has always been a subject of immense attention and challenging in the context of joint measurements of general quantum mechanical observables. In particular, the recent extension of the original uncertainty relations has grabbed a distinct research focus and set a new ascendent target in quantum mechanics and quantum information processing. In the present work we explore the joint measurements of three incompatible observables, following the basic idea of a newly proposed error trade-off relation. In comparison to the counterpart of two incompatible observables, the joint measurements of three incompatible observables are more complex and of more primal interest in understanding quantum mechanical measurements. Attributed to the pristine idea proposed by Heisenberg in 1927, we develop the error trade-off relations for compatible observables to categorically approximate the three incompatible observables. Implementing these relations we demonstrate the first experimental witness of the joint measurements for three incompatible observables using a single ultracold $^{40}Ca^{+}$ ion in a harmonic potential. We anticipate that our inquisition would be of vital importance for quantum precision measurement and other allied quantum information technologies.Being one of the centroidal concepts in quantum theory, the fundamental constraint imposed by Heisenberg uncertainty relations has always been a subject of immense attention and challenging in the context of joint measurements of general quantum mechanical observables. In particular, the recent extension of the original uncertainty relations has grabbed a distinct research focus and set a new ascendent target in quantum mechanics and quantum information processing. In the present work we explore the joint measurements of three incompatible observables, following the basic idea of a newly proposed error trade-off relation. In comparison to the counterpart of two incompatible observables, the joint measurements of three incompatible observables are more complex and of more primal interest in understanding quantum mechanical measurements. Attributed to the pristine idea proposed by Heisenberg in 1927, we develop the error trade-off relations for compatible observables to categorically approximate the three incompatible observables. Implementing these relations we demonstrate the first experimental witness of the joint measurements for three incompatible observables using a single ultracold $^{40}Ca^{+}$ ion in a harmonic potential. We anticipate that our inquisition would be of vital importance for quantum precision measurement and other allied quantum information technologies.

arXiv:1909.09337Sep 20, 20190 citations

The measurement problem and interpretations of quantum mechanics

Badis Ydri

Institute of Physics eBooksOct 1, 202118 citations

Decoherence, measurement and interpretation of quantum mechanics

Juan Sebastián Ardenghi, Mario Castagnino, Sebastián Fortín +1 more

According to our modal-Hamiltonian interpretation (MHI) of quantum mechanics, the Hamiltonian of the closed system defines the set of its definite-valued observables. This definition seems to be incompatible with the pointer basis selected by the environment-induced decoherence (EID) of the open system. In this paper we argue that decoherence can be understood from a closed system perspective which (i) shows that the incompatibility between MHI and EID is only apparent, and (ii) solves certain conceptual challenges that the EID program still has to face.According to our modal-Hamiltonian interpretation (MHI) of quantum mechanics, the Hamiltonian of the closed system defines the set of its definite-valued observables. This definition seems to be incompatible with the pointer basis selected by the environment-induced decoherence (EID) of the open system. In this paper we argue that decoherence can be understood from a closed system perspective which (i) shows that the incompatibility between MHI and EID is only apparent, and (ii) solves certain conceptual challenges that the EID program still has to face.

arXiv:0908.4069Aug 27, 20091 citation

^{40}Ca^{+}

ion in a harmonic potential. We anticipate that our inquisition would be of vital importance for quantum precision measurement and other allied quantum information technologies.