Dear Dr. Vedral,

I'm reading your recent paper [Ref. 1] with great interest. You and your colleagues wrote:

"It is clear from our work, however, that it is very difficult to extend the tensor product structure beyond the two neighbouring instances in time without altering the basic principles of quantum mechanics."

I have to confess that I couldn't comprehend your notion of 'two neighbouring instances in time'. Is it possible to adopt a geometric formulation of QM,

http://members.aon.at/chakalov/Fearns.html#3

and provide a *measure* on 'two neighboring instances in time'? Perhaps Dorje Brody could be of help. See also John Fearns

http://members.aon.at/chakalov/Fearns.html#inbetween

and Chris Isham,

http://members.aon.at/chakalov/McGuire.html#note

Regards,

Dimi Chakalov
http://members.aon.at/chakalov
http://members.aon.at/chakalov/white_paper.html
--
Aoccdrnig to a rscheearch at Cmabrigde Uinervtisy, it deosn't mttaer in waht oredr the ltteers in a wrod are, the olny iprmoetnt tihng is taht the frist and lsat ltteer be at the rghit pclae.  The rset can be a total mses and you can sitll raed it wouthit a porbelm. Tihs is bcuseae the huamn mnid deos not raed ervey lteter by istlef, but the wrod as a wlohe,

http://members.aon.at/chakalov/faq.html

Pritie amzanig huh?
 

Reference

[Ref. 1] Caslav Brukner, Samuel Taylor, Sancho Cheung, and Vlatko Vedral, Quantum Entanglement in Time, quant-ph/0402127 v1

"Because of different roles time and space play in quantum theory one could be tempted to assume that the notion of "entanglement in time" cannot be introduced in quantum physics. In this letter we will investigate this question and we will find that this is not the case.

"It is clear from our work, however, that it is very difficult to extend the tensor product structure beyond the two neighbouring instances in time without altering the basic principles of quantum mechanics. In fact, one of the features of entanglement in time is exactly a consequence of this difficulty: two maximally entangled events can still be maximally entangled to two other events in time (a principle we may call "polygamy" of entanglement in time). This is in contrast to the spatial entanglement which can only be "monogamous" [19]. The diffeerence between the spatial and temporal structure may ultimately be fundamental, or it may be an indication that we need a deeper theory in which the two need to be treated on a more equal footing (quantum field theory does not suffice in this sense). Either way, it appears that the next step should lie in exploring the consequences of combining entanglement in space and time in order to study how they relate to each other."