What are kets?
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866911878649741312 |
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| author | Gurevich, Yuri Blass, Andreas |
| author_facet | Gurevich, Yuri Blass, Andreas |
| contents | According to Dirac's bra-ket notation, in an inner-product space, the inner product $\langle x\,|\,y\rangle$ of vectors $x,y$ can be viewed as an application of the bra $\langle x|$ to the ket $|y\rangle$. Here $\langle x|$ is the linear functional $|y\rangle \mapsto \langle x\,|\,y\rangle$ and $|y\rangle$ is the vector $y$. But often -- though not always -- there are advantages in seeing $|y\rangle$ as the function $a \mapsto a\cdot y$ where $a$ ranges over the scalars. For example, the outer product $|y\rangle\langle x|$ becomes simply the composition $|y\rangle \circ \langle x|$. It would be most convenient to view kets sometimes as vectors and sometimes as functions, depending on the context. This turns out to be possible. While the bra-ket notation arose in quantum mechanics, this note presupposes no familiarity with quantum mechanics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_10055 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | What are kets? Gurevich, Yuri Blass, Andreas Quantum Physics Logic in Computer Science According to Dirac's bra-ket notation, in an inner-product space, the inner product $\langle x\,|\,y\rangle$ of vectors $x,y$ can be viewed as an application of the bra $\langle x|$ to the ket $|y\rangle$. Here $\langle x|$ is the linear functional $|y\rangle \mapsto \langle x\,|\,y\rangle$ and $|y\rangle$ is the vector $y$. But often -- though not always -- there are advantages in seeing $|y\rangle$ as the function $a \mapsto a\cdot y$ where $a$ ranges over the scalars. For example, the outer product $|y\rangle\langle x|$ becomes simply the composition $|y\rangle \circ \langle x|$. It would be most convenient to view kets sometimes as vectors and sometimes as functions, depending on the context. This turns out to be possible. While the bra-ket notation arose in quantum mechanics, this note presupposes no familiarity with quantum mechanics. |
| title | What are kets? |
| topic | Quantum Physics Logic in Computer Science |
| url | https://arxiv.org/abs/2405.10055 |