dorsal/arxiv
View SchemaExtending Heisenberg's measurement--disturbance relation to the twin-slit case
| Authors | H. M. Wiseman |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0210065 |
| URL | https://arxiv.org/abs/quant-ph/0210065 |
| Journal | Found. Phys. vol. 28, 1619 (1998) |
Abstract
Heisenberg's position-measurement--momentum-disturbance relation is derivable from the uncertainty relation $\sigma(q)\sigma(p) \geq \hbar/2$ only for the case when the particle is initially in a momentum eigenstate. Here I derive a new measurement--disturbance relation which applies when the particle is prepared in a twin-slit superposition and the measurement can determine at which slit the particle is present. The relation is $d \times \Delta p \geq 2\hbar/\pi$, where $d$ is the slit separation and $\Delta p=D_{M}(P_{f},P_{i})$ is the Monge distance between the initial $P_{i}(p)$ and final $P_{f}(p)$ momentum distributions.
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"abstract": "Heisenberg\u0027s position-measurement--momentum-disturbance relation is derivable\nfrom the uncertainty relation $\\sigma(q)\\sigma(p) \\geq \\hbar/2$ only for the\ncase when the particle is initially in a momentum eigenstate. Here I derive a\nnew measurement--disturbance relation which applies when the particle is\nprepared in a twin-slit superposition and the measurement can determine at\nwhich slit the particle is present. The relation is $d \\times \\Delta p \\geq\n2\\hbar/\\pi$, where $d$ is the slit separation and $\\Delta p=D_{M}(P_{f},P_{i})$\nis the Monge distance between the initial $P_{i}(p)$ and final $P_{f}(p)$\nmomentum distributions.",
"arxiv_id": "quant-ph/0210065",
"authors": [
"H. M. Wiseman"
],
"categories": [
"quant-ph"
],
"journal_ref": "Found. Phys. vol. 28, 1619 (1998)",
"title": "Extending Heisenberg\u0027s measurement--disturbance relation to the twin-slit case",
"url": "https://arxiv.org/abs/quant-ph/0210065"
},
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