When we manipulate physical systems for various purposes, we are essentially<\/p>\n\n\n\n
encoding and decoding the information content in those systems in precisely<\/p>\n\n\n\n
de\ufb01ned terms tailored to our purpose. Conversationally speaking of informa-<\/p>\n\n\n\n
tion, one thinks of the \u201cnew knowledge\u201d gained when a particular physical<\/p>\n\n\n\n
process is completed, such as watching television, reading an article, or mea-<\/p>\n\n\n\n
suring the output voltage at the end of a circuit. When we get used to the idea<\/p>\n\n\n\n
that information is not something abstract that is a result of cognition, but is<\/p>\n\n\n\n
actually physically carried by the system that\u2019s being observed or measured,<\/p>\n\n\n\n
we are closer to a scienti\ufb01c understanding of information.<\/p>\n\n\n\n
Classically, information theory gained respectability when Claude Shannon<\/p>\n\n\n\n
[63] quanti\ufb01ed the information content in a physical system or communica-<\/p>\n\n\n\n
tion channel. He was working at Bell Labs at that time and was interested in<\/p>\n\n\n\n
optimizing telephonic communication. He also realized the importance of in-<\/p>\n\n\n\n
formation in the context of data compression and cryptography. We will start<\/p>\n\n\n\n
with his theory, and see how it can be adapted to describing the information<\/p>\n\n\n\n
content of a quantum system. For a more in-depth treatment of the subject,<\/p>\n\n\n\n
you can refer to the excellent book by Barnett [4]. Matters regarding quantum<\/p>\n\n\n\n
information are beautifully discussed in the work by Mark Wilde [73], and in<\/p>\n\n\n\n
Chapter 5 of Preskill\u2019s lecture notes [57].<\/p>\n\n\n\n
11.1 Measures of Information<\/p>\n\n\n\n
We would like to develop a measure for the rather abstract concept of<\/p>\n\n\n\n
information, so that e\ufb03ciencies of di\ufb00erent protocols or physical systems of<\/p>\n\n\n\n
communication can be compared, and more e\ufb03cient systems designed.<\/p>\n\n\n\n
We need to \ufb01rst have a model for the process we are describing, and Shan-<\/p>\n\n\n\n
non\u2019s proposed model has stuck (Figure 11.1). We start with a source of<\/p>\n\n\n\n
information, which, like a talking person or a buzzing telephone receiver, gen-<\/p>\n\n\n\n
erates messages using some prede\ufb01ned language consisting of symbols we<\/p>\n\n\n\n
will call the alphabet. The alphabet could, for example, be the set of English<\/p>\n","protected":false},"excerpt":{"rendered":"
When we manipulate physical systems for various purposes, we are essentially encoding and decoding the information content in those systems in precisely de\ufb01ned terms tailored to our purpose. Conversationally speaking of informa- tion, one thinks of the \u201cnew knowledge\u201d gained when a particular physical process is completed, such as watching television, reading an article, or […]<\/p>\n","protected":false},"author":1,"featured_media":4045,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[500],"tags":[],"class_list":["post-4134","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-characterization-of-quantum-information"],"jetpack_featured_media_url":"https:\/\/workhouse.sweetdishy.com\/wp-content\/uploads\/2024\/09\/quantum-computing-2.png","_links":{"self":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/4134","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=4134"}],"version-history":[{"count":1,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/4134\/revisions"}],"predecessor-version":[{"id":4135,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/4134\/revisions\/4135"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/media\/4045"}],"wp:attachment":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/media?parent=4134"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/categories?post=4134"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/tags?post=4134"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}