Let\u2019s denote the (unknown but pure) input state of the electrons in the<\/p>\n\n\n\n
beam by |ii and the output state by |oi. The probability of obtaining this<\/p>\n\n\n\n
particular output is given by<\/p>\n\n\n\n
P(|ii \u2192 |oi) =<\/p>\n\n\n\n
no. of electrons in state |oi<\/p>\n\n\n\n
Total number of electrons in input beam<\/p>\n\n\n\n
. (2.2)<\/p>\n\n\n\n
We are going to use this information to build a mathematical picture of the<\/p>\n\n\n\n
spin states of the electron. Let\u2019s introduce a notation for this probability (in<\/p>\n\n\n\n
anticipation of the next chapter). In quantum mechanics, a process such as<\/p>\n\n\n\n
just described, is associated with a probability amplitude, which is in general<\/p>\n\n\n\n
complex, denoted by ho|ii. Following the lead of optics, where the intensity of<\/p>\n\n\n\n
a beam of light is the square of the amplitude of the resultant electric \ufb01eld,<\/p>\n\n\n\n
the probability of getting output |oi from input |ii is represented by<\/p>\n\n\n\n
P(|ii \u2192 |oi) = |ho|ii|<\/p>\n\n\n\n
2<\/p>\n\n\n\n
. (2.3)<\/p>\n\n\n\n
The reason for amplitudes taking possibly complex values will be seen when we<\/p>\n\n\n\n
look at the phenomenon of interference between amplitudes in a later section.<\/p>\n\n\n\n
The importance of basis states is that when an experiment is performed<\/p>\n\n\n\n
to measure the state of an electron, the result is invariably one of the basis<\/p>\n\n\n\n
states. For quantum computation, these basis states represent the bits 0 and<\/p>\n\n\n\n
1. They are quantum states and we write them as<\/p>\n\n\n\n
|0i \u2261 |\u2191i; |1i \u2261 |\u2193i. (2.4)<\/p>\n\n\n\n
This representation is called the computational basis. We can think of these<\/p>\n\n\n\n
basis states as analogous to the classical bits 0 and 1.<\/p>\n","protected":false},"excerpt":{"rendered":"
Let\u2019s denote the (unknown but pure) input state of the electrons in the beam by |ii and the output state by |oi. The probability of obtaining this particular output is given by P(|ii \u2192 |oi) = no. of electrons in state |oi Total number of electrons in input beam . (2.2) We are going to […]<\/p>\n","protected":false},"author":1,"featured_media":3940,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[488],"tags":[],"class_list":["post-3961","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-3-the-quantum-postulates"],"jetpack_featured_media_url":"https:\/\/workhouse.sweetdishy.com\/wp-content\/uploads\/2024\/09\/science-1.png","_links":{"self":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/3961","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/comments?post=3961"}],"version-history":[{"count":1,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/3961\/revisions"}],"predecessor-version":[{"id":3962,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/3961\/revisions\/3962"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/media\/3940"}],"wp:attachment":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/media?parent=3961"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/categories?post=3961"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/tags?post=3961"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}