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View Full Version : Bell state measurements, entanglement and degrees of confidence


Hayden McGuinness
Aug12-04, 08:29 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\n\nSay you have two people each storing one particle of an entangled\npair, particles A and B, who are arbitrarily far away with the state\nof this system being initially phi+ = [|A:0&gt;|B:1&gt; + |B:0&gt;|A:1&gt;] where\n|0&gt; or |1&gt; are orthogonal quantitative of some particular parameter\nlike spin, polarization, etc. Now say the person storing A performs a\nunitary operation on A so that the system is in one of the equally\nprobable four bell states\n\n1. phi+ = [|A:0&gt;|B:1&gt; + |B:0&gt;|A:1&gt;]\n2. phi- = [|A:0&gt;|B:1&gt; - |B:0&gt;|A:1&gt;]\n3. theta+ = [|A:0&gt;|B:0&gt; + |B:1&gt;|A:1&gt;]\n4. theta- = [|A:0&gt;|B:0&gt; - |B:1&gt;|A:1&gt;]\n\nwhich is known to the performer of the operation (i.e. they know what\nthey did) but of course not known to the keeper of B. Is there *any*\nway (by interacting particle B with other particles, performing\nunitary or otherwise operations on it, measuring it (collapse), etc)\nthe keeper of particle B can deduce the state the system with a degree\nof confidence higher than 25% , i.e. better than a random guess,\n*without* interacting B with A (hence the separation)? Is it easier to\npredict if the system happens to be in one of these states rather than\nthe others? The answer can be of any kind of particle with any\nparameter, although photons and polarization would be preferred.\n\nThanks,\nHayden\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">&nbsp;&nbsp;View this Usenet post in original ASCII form </a></div><P></jabberwocky>Say you have two people each storing one particle of an entangled
pair, particles A and B, who are arbitrarily far away with the state
of this system being initially \phi+ = [|A:0>|B:1> + |B:0>|A:1>] where
|0> or |1> are orthogonal quantitative of some particular parameter
like spin, polarization, etc. Now say the person storing A performs a
unitary operation on A so that the system is in one of the equally
probable four bell states

1. \phi+ = [|A:0>|B:1> + |B:0>|A:1>]2. \phi- = [|A:0>|B:1> - |B:0>|A:1>]3. \theta+ = [|A:0>|B:0> + |B:1>|A:1>]4. \theta- = [|A:0>|B:0> - |B:1>|A:1>]

which is known to the performer of the operation (i.e. they know what
they did) but of course not known to the keeper of B. Is there *any*
way (by interacting particle B with other particles, performing
unitary or otherwise operations on it, measuring it (collapse), etc)
the keeper of particle B can deduce the state the system with a degree
of confidence higher than 25% , i.e. better than a random guess,
*without* interacting B with A (hence the separation)? Is it easier to
predict if the system happens to be in one of these states rather than
the others? The answer can be of any kind of particle with any
parameter, although photons and polarization would be preferred.

Thanks,
Hayden

scerir
Aug12-04, 10:15 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\n"Hayden McGuinness" wrote:\n\n&gt; Is there *any* way [...] the keeper of particle B\n&gt; can deduce the state the system with a degree\n&gt; of confidence higher than 25% [?]\n\nAs far as I remember Yurtsever wrote\nsomething about it, maybe here\nhttp://www.arxiv.org/abs/quant-ph/9806059\nIn MWI, imo, there is a world, out of\nfour, in which particle B has the "right"\nstate. But the keeper of this particle\nmaybe does not know he is in the "right"\nworld.\ns.\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">&nbsp;&nbsp;View this Usenet post in original ASCII form </a></div><P></jabberwocky>"Hayden McGuinness" wrote:

> Is there *any* way [...] the keeper of particle B
> can deduce the state the system with a degree
> of confidence higher than 25% [?]

As far as I remember Yurtsever wrote
something about it, maybe here
http://www.arxiv.org/abs/http://www.arxiv.org/abs/quant-ph/9806059
In MWI, imo, there is a world, out of
four, in which particle B has the "right"
state. But the keeper of this particle
maybe does not know he is in the "right"
world.
s.

Nick Maclaren
Aug12-04, 11:00 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\nIn article &lt;LiLSc.40531\\$OH4.1197813@twister1.libero.it&gt;,\n" scerir" &lt;scerir@libero.it&gt; writes:\n|&gt; "Hayden McGuinness" wrote:\n|&gt;\n|&gt; &gt; Is there *any* way [...] the keeper of particle B\n|&gt; &gt; can deduce the state the system with a degree\n|&gt; &gt; of confidence higher than 25% [?]\n|&gt;\n|&gt; As far as I remember Yurtsever wrote\n|&gt; something about it, maybe here\n|&gt; http://www.arxiv.org/abs/quant-ph/9806059\n|&gt; In MWI, imo, there is a world, out of\n|&gt; four, in which particle B has the "right"\n|&gt; state. But the keeper of this particle\n|&gt; maybe does not know he is in the "right"\n|&gt; world.\n\nGlancing at that paper, it looks to be another one that\nuses causality to prove such information transfers are\nimpossible. As I understand it, some people are unhappy\nthat assuming causality seems to be necessary, given the\napparent arbitrariness of the principle. If anyone has\nresolved this, I should be interested to hear how and\nwhat the resolution was.\n\nI have no difficulty in working with acausality in\nmathematics, but find it hard to get my head around an\nacausal universe as a place to live! Other people may\nhave a more flexible mind than mine :-)\n\nThis is, of course, related to the tachyon question and\nmany others.\n\n\nRegards,\nNick Maclaren.\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">&nbsp;&nbsp;View this Usenet post in original ASCII form </a></div><P></jabberwocky>In article <LiLSc.40531$OH4.1197813@twister1.libero.it>,
"scerir" <scerir@libero.it> writes:
|> "Hayden McGuinness" wrote:
|>
|> > Is there *any* way [...] the keeper of particle B
|> > can deduce the state the system with a degree
|> > of confidence higher than 25% [?]
|>
|> As far as I remember Yurtsever wrote
|> something about it, maybe here
|> http://www.arxiv.org/abs/http://www.arxiv.org/abs/quant-ph/9806059
|> In MWI, imo, there is a world, out of
|> four, in which particle B has the "right"
|> state. But the keeper of this particle
|> maybe does not know he is in the "right"
|> world.

Glancing at that paper, it looks to be another one that
uses causality to prove such information transfers are
impossible. As I understand it, some people are unhappy
that assuming causality seems to be necessary, given the
apparent arbitrariness of the principle. If anyone has
resolved this, I should be interested to hear how and
what the resolution was.

I have no difficulty in working with acausality in
mathematics, but find it hard to get my head around an
acausal universe as a place to live! Other people may
have a more flexible mind than mine :-)

This is, of course, related to the tachyon question and
many others.


Regards,
Nick Maclaren.