{"id":405,"date":"2008-05-23T08:41:06","date_gmt":"2008-05-23T12:41:06","guid":{"rendered":"http:\/\/michaelnielsen.org\/blog\/?p=405"},"modified":"2008-05-23T08:41:50","modified_gmt":"2008-05-23T12:41:50","slug":"an-underappreciated-gem-probability-backflow","status":"publish","type":"post","link":"https:\/\/michaelnielsen.org\/blog\/an-underappreciated-gem-probability-backflow\/","title":{"rendered":"An underappreciated gem: probability backflow"},"content":{"rendered":"

I was recently reminded of a beautiful paper by Tony Bracken and Geoff Melloy, Probability Backflow and a New Dimensionless Quantum Number<\/a> (publisher subscription required, alas). What they describe is a marvellous (and too little known) quantum phenomenon that they dub “probability backflow”.<\/p>\n

The basic idea is simple, although counterintuitive. Imagine a quantum particle moving in free space. It’s easiest if you imagine space is one-dimensional, i.e., the particle can only move left or right on a line. The discussion also works in three dimensions, but is a bit trickier to describe.<\/p>\n

What Bracken and Melloy show is that it’s possible to prepare the particle in a state such that both the following are true:<\/p>\n

(1) If you measure the velocity<\/em> of the particle, you’re guaranteed to find that the particle is moving rightwards along the line.<\/p>\n

(2) Suppose you fix a co-ordinate origin on the line, i.e., a “zero” of position. They prove that if you measure position then the probability of finding the particle to the right of the origin actually decreases<\/em> in time, not increases, as one might naively expect from point (1).<\/p>\n

So far as I know, this has never been experimentally demonstrated.<\/p>\n

Bracken and Melloy also give a beautiful explanation of probability backflow in terms of “quasi-probabilities”. It’s been known for a long time, at least since Wigner, that you can reformulate quantum mechanics as something very much like a classical theory, but one with negative probabilities. Using this reformulation, Bracken and Melloy explain the phenomenon: sure, the particle is moving right, but it’s actually negative<\/em> probability that is flowing to the right of the origin, and so the probability of being to the right of the origin decreases in time.<\/p>\n

Inspired by the power of this intuitive explanation, I once worked for a while trying to use quasi-probability formulations to find new algorithms for quantum computers. Despite my lack of success, I still think this is a promising approach, not just to algorithms, but more generally to quantum information.<\/p>\n","protected":false},"excerpt":{"rendered":"

I was recently reminded of a beautiful paper by Tony Bracken and Geoff Melloy, Probability Backflow and a New Dimensionless Quantum Number (publisher subscription required, alas). What they describe is a marvellous (and too little known) quantum phenomenon that they dub “probability backflow”. The basic idea is simple, although counterintuitive. Imagine a quantum particle moving… Continue reading An underappreciated gem: probability backflow<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[],"tags":[],"class_list":["post-405","post","type-post","status-publish","format-standard","hentry","entry"],"_links":{"self":[{"href":"https:\/\/michaelnielsen.org\/blog\/wp-json\/wp\/v2\/posts\/405","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/michaelnielsen.org\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/michaelnielsen.org\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/michaelnielsen.org\/blog\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/michaelnielsen.org\/blog\/wp-json\/wp\/v2\/comments?post=405"}],"version-history":[{"count":0,"href":"https:\/\/michaelnielsen.org\/blog\/wp-json\/wp\/v2\/posts\/405\/revisions"}],"wp:attachment":[{"href":"https:\/\/michaelnielsen.org\/blog\/wp-json\/wp\/v2\/media?parent=405"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/michaelnielsen.org\/blog\/wp-json\/wp\/v2\/categories?post=405"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/michaelnielsen.org\/blog\/wp-json\/wp\/v2\/tags?post=405"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}