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A discrete Schrodinger model that describes the quantum measurement process

April 2021

April 2021

DOI:10.13140/RG.2.2.30387.55843

Authors:

Hiroki Yagisita

Kyoto Sangyo University

We propose a discrete Schrodinger mathematical model that describes the quantummeasurement process. ------ continuous spontaneous localization, objective-collapse theory, quantum decoherence, quantum entanglement, quantum information, Anderson localization, CHSH inequality, Einstein-Podolsky-Rosen paradox.

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A discrete Schrodinger model that describes

the quantum measurement process

Hiroki Yagisita (Kyoto Sangyo University)

We propose a discrete Schrodinger model that describes the quantum

measurement process.

Let Xbe the Hilbert space of state vectors of a one-particle system of

spin 1

2on the one-dimensional discrete grid Z. That is, X=L2(Z;C2). Let

natural numbers L0and N0be very large. Put I={n∈Z|L0≤ |n| ≤

L0+N0}. We assume that Iis the place where two detectors exist.

Suppose that for n∈I,V(n)isa2×2 Hermitian random matrix.

Suppose that for n∈I, if Uis a 2 ×2 unitary matrix, then the distributions

of (U−1)(V(n))Uand V(n) are the same. Suppose that for n∈I, the den-

sity function of V(n), roughly speaking, is smooth and compact supported.

Suppose that {V(n)}n∈Iis independent and identically distributed.

Suppose that for n∈Z\I,V(n) is the 2 ×2zero matrix.

Then, we propose a discrete Schrodinger model

√−1du

dt (n) = −1

2m((u(n−1) −u(n)) + (u(n+ 1) −u(n))) + V(n)u(n)

on the Hilbert space X(= L2(Z;C2)).

continuous spontaneous localization, objective-collapse theory, quantum

decoherence, quantum entanglement, quantum information, Anderson

localization, CHSH inequality, Einstein-Podolsky-Rosen paradox.

https://arxiv.org/abs/0807.3612

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