Rethinking Collapse: Coupling Quantum States to Classical Bits with quasi-probabilities
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866911300628512768 |
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| author | Kaszlikowski, Dagomir Kurzynski, Pawel |
| author_facet | Kaszlikowski, Dagomir Kurzynski, Pawel |
| contents | We propose a formulation of quantum measurement within a modified framework of frames, in which a quantum system - a single qubit - is directly coupled to a classical measurement bit. The qubit is represented as a positive probability distribution over two classical bits, a and a', denoted by p(aa'). The measurement apparatus is described by a classical bit $α= \pm 1$, initialized in the pure distribution $p(α) = \frac{1}{2}(1 + α)$. The measurement interaction is modeled by a quasi-bistochastic process $ S(bb'β\mid aa'α)$ - a bistochastic map that may include negative transition probabilities, while acting on an entirely positive state space. When this process acts on the joint initial state $p(aa')p(α)$, it produces a collapsed state $p(bb'\midβ)$, yielding the measurement outcome $β$ with the correct quantum-mechanical probability $p(β)$. This approach bypasses the von Neumann chain of infinite couplings by treating the measurement register classically, while capturing the nonclassical nature of measurement through the quasi-bistochastic structure of the interaction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_03929 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rethinking Collapse: Coupling Quantum States to Classical Bits with quasi-probabilities Kaszlikowski, Dagomir Kurzynski, Pawel Quantum Physics We propose a formulation of quantum measurement within a modified framework of frames, in which a quantum system - a single qubit - is directly coupled to a classical measurement bit. The qubit is represented as a positive probability distribution over two classical bits, a and a', denoted by p(aa'). The measurement apparatus is described by a classical bit $α= \pm 1$, initialized in the pure distribution $p(α) = \frac{1}{2}(1 + α)$. The measurement interaction is modeled by a quasi-bistochastic process $ S(bb'β\mid aa'α)$ - a bistochastic map that may include negative transition probabilities, while acting on an entirely positive state space. When this process acts on the joint initial state $p(aa')p(α)$, it produces a collapsed state $p(bb'\midβ)$, yielding the measurement outcome $β$ with the correct quantum-mechanical probability $p(β)$. This approach bypasses the von Neumann chain of infinite couplings by treating the measurement register classically, while capturing the nonclassical nature of measurement through the quasi-bistochastic structure of the interaction. |
| title | Rethinking Collapse: Coupling Quantum States to Classical Bits with quasi-probabilities |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2512.03929 |