Entanglement swapping and FTL [Archive]

chronon

May13-04, 05:25 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>\nI\'ve been reading about entanglement swapping in\n\nhttp://physicsweb.org/article/world/11/3/9\n\nEssentially two pairs of entangled photons A,B and C,D are produced,\nthen B and C are entangled using a Bell-state analyser. The result is\nthat A and D become entangled although they have never interacted.\nThe point is made elsewhere that A and D may have spacelike\nseparations, but of course this doesn\'t lead to FTL transmission of\ninformation.\nBut what if the pair B,C has a spacelike separation from the pair A,D.\nIf the article is to be taken at face value then I could choose\nwhether or not to entangle B and C and someone having A and D could\nsee whether they have become entangled - instantaneous transmission of\ninformation.\nI don\'t believe in faster than light communication, so what is wrong\nwith this argument.\n\nStephen Lee\nwww.chronon.org\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">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>I've been reading about entanglement swapping in

http://physicsweb.org/article/world/11/3/9

Essentially two pairs of entangled photons A,B and C,D are produced,
then B and C are entangled using a Bell-state analyser. The result is
that A and D become entangled although they have never interacted.
The point is made elsewhere that A and D may have spacelike
separations, but of course this doesn't lead to FTL transmission of
information.
But what if the pair B,C has a spacelike separation from the pair A,D.
If the article is to be taken at face value then I could choose
whether or not to entangle B and C and someone having A and D could
see whether they have become entangled - instantaneous transmission of
information.
I don't believe in faster than light communication, so what is wrong
with this argument.

Stephen Lee
www.chronon.org

Matt Leifer

May14-04, 06:14 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>\nWhen you make the Bell measurement on B and C, each of the four Bell\nstates can occur with probability 1/4. Corresponding to this, A and D\ncollapse into one of the four Bell states with probability 1/4. The\nresulting ensemble at A and D is an equal mixture of the four Bell\nstates, which gives the maximally mixed density matrix. This means\nthat any possible measurement on A and D gives completely random\noutcomes.\n\nIf no measurement is made on B and C, then the density matrix at A and\nD is still the maximally mixed state. This occurs because the state\nof A is maximally mixed since it is maximally entangled with B and\nsimilarly D is maximally mixed due to its entanglement with C. The\ntensor product of two maximally mixed states is the maximally mixed\nstate on the joint system and so the two cases you consider are\nindistinguishable.\n\nThe mistake you have made is to assume that when the entanglement\nswapping measurement is made, A and D collapse to a particular\nmaximally entangled state, rather than having equal probabilities for\nall Bell states. In order to complete the entanglement swapping, the\nmeasurement result must be communicated from BC to either A or D, so\nthey can correct the state to the desired Bell state. It is a special\nproperty of Bell states that the correction can be done by either A or\nD alone, so one of these parties can simply do nothing.\n\nIn fact, many quantum information protocols are pretty resistant to\nthe particular Bell state you have, so often A and D do not have to\nwait for the classical information in order to complete the protocol.\nUsusally, they can instead do some simple classical processing on\ntheir measurement results once they find out what Bell state they were\nusing. This is useful for photons, because they like to travel around\nat the speed of light, so it is difficult to store them while you wait\nfor some classical communication to arrive.\n\nEntanglement swapping itself is an example of a protocol that is not\naffected too much by which Bell state is used. Therefore, is useful\nfor setting up a Bell state over very long distances using equipment\nthat is only capable of distributing Bell states over much shorter\ndistances. Some variant of entanglement swapping might eventually be\nused in long distance quantum cryptography over optical fibres, which\ncurrently only works for distances up to 50km or so.\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">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>When you make the Bell measurement on B and C, each of the four Bell
states can occur with probability 1/4. Corresponding to this, A and D
collapse into one of the four Bell states with probability 1/4. The
resulting ensemble at A and D is an equal mixture of the four Bell
states, which gives the maximally mixed density matrix. This means
that any possible measurement on A and D gives completely random
outcomes.

If no measurement is made on B and C, then the density matrix at A and
D is still the maximally mixed state. This occurs because the state
of A is maximally mixed since it is maximally entangled with B and
similarly D is maximally mixed due to its entanglement with C. The
tensor product of two maximally mixed states is the maximally mixed
state on the joint system and so the two cases you consider are
indistinguishable.

The mistake you have made is to assume that when the entanglement
swapping measurement is made, A and D collapse to a particular
maximally entangled state, rather than having equal probabilities for
all Bell states. In order to complete the entanglement swapping, the
measurement result must be communicated from BC to either A or D, so
they can correct the state to the desired Bell state. It is a special
property of Bell states that the correction can be done by either A or
D alone, so one of these parties can simply do nothing.

In fact, many quantum information protocols are pretty resistant to
the particular Bell state you have, so often A and D do not have to
wait for the classical information in order to complete the protocol.
Ususally, they can instead do some simple classical processing on
their measurement results once they find out what Bell state they were
using. This is useful for photons, because they like to travel around
at the speed of light, so it is difficult to store them while you wait
for some classical communication to arrive.

Entanglement swapping itself is an example of a protocol that is not
affected too much by which Bell state is used. Therefore, is useful
for setting up a Bell state over very long distances using equipment
that is only capable of distributing Bell states over much shorter
distances. Some variant of entanglement swapping might eventually be
used in long distance quantum cryptography over optical fibres, which
currently only works for distances up to 50km or so.

Mike Crowe

May16-04, 12:57 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>"chronon" <stephen@chronon.org> wrote in message\nnews:60b2eda6.0405130042.116ab373@posting .google.com...\n>\n> I\'ve been reading about entanglement swapping in\n>\n> http://physicsweb.org/article/world/11/3/9\n>\n> Essentially two pairs of entangled photons A,B and C,D are produced,\n> then B and C are entangled using a Bell-state analyser. The result is\n> that A and D become entangled although they have never interacted.\n> The point is made elsewhere that A and D may have spacelike\n> separations, but of course this doesn\'t lead to FTL transmission of\n> information.\n> But what if the pair B,C has a spacelike separation from the pair A,D.\n> If the article is to be taken at face value then I could choose\n> whether or not to entangle B and C and someone having A and D could\n> see whether they have become entangled - instantaneous transmission of\n> information.\n> I don\'t believe in faster than light communication, so what is wrong\n> with this argument.\n>\n> Stephen Lee\n> www.chronon.org\n\nAs I understand it you would now be looking at two wavefunctions instead of\nfour, since your operator is "entangle or not?". This operator would only\napply to TWO photons, A and D (and the same operator would have been applied\nto B and C - to entangle them [or not as the case may be]). So the\nwavefunctions are actually AD and BC not A and B and C and D. And you are\nnow back to the case of two entangled states. AD is entangled with BC it is\njust that we are using a two photon system rather than the usual 1 photon.\n\nMike Crowe\n\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">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>"chronon" <stephen@chronon.org> wrote in message
news:60b2eda6.0405130042.116ab373@posting.google.c om...
>
> I've been reading about entanglement swapping in
>
> http://physicsweb.org/article/world/11/3/9
>
> Essentially two pairs of entangled photons A,B and C,D are produced,
> then B and C are entangled using a Bell-state analyser. The result is
> that A and D become entangled although they have never interacted.
> The point is made elsewhere that A and D may have spacelike
> separations, but of course this doesn't lead to FTL transmission of
> information.
> But what if the pair B,C has a spacelike separation from the pair A,D.
> If the article is to be taken at face value then I could choose
> whether or not to entangle B and C and someone having A and D could
> see whether they have become entangled - instantaneous transmission of
> information.
> I don't believe in faster than light communication, so what is wrong
> with this argument.
>
> Stephen Lee
> www.chronon.org

As I understand it you would now be looking at two wavefunctions instead of
four, since your operator is "entangle or not?". This operator would only
apply to TWO photons, A and D (and the same operator would have been applied
to B and C - to entangle them [or not as the case may be]). So the
wavefunctions are actually AD and BC not A and B and C and D. And you are
now back to the case of two entangled states. AD is entangled with BC it is
just that we are using a two photon system rather than the usual 1 photon.

Mike Crowe

Uncle Al

May17-04, 06:18 PM

<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>chronon wrote:\n>\n> I\'ve been reading about entanglement swapping in\n>\n> http://physicsweb.org/article/world/11/3/9\n>\n> Essentially two pairs of entangled photons A,B and C,D are produced,\n> then B and C are entangled using a Bell-state analyser. The result is\n> that A and D become entangled although they have never interacted.\n> The point is made elsewhere that A and D may have spacelike\n> separations, but of course this doesn\'t lead to FTL transmission of\n> information.\n> But what if the pair B,C has a spacelike separation from the pair A,D.\n> If the article is to be taken at face value then I could choose\n> whether or not to entangle B and C and someone having A and D could\n> see whether they have become entangled - instantaneous transmission of\n> information.\n> I don\'t believe in faster than light communication, so what is wrong\n> with this argument.\n\nNo information is transferred superluminally. You couldn\'t send a\nmessage via Morse code, for instance. Look up the difference between\nphase and group velocities - and which one can carry information.\n\nhttp://gregegan.customer.netspace.net.au/APPLETS/20/20.html\n\nEPR experiments don\'t have results (information) until their remote\ndatasets are compared. While the answer is determined\ninstantaneously, it cannot be observed outside lightspeed\nprohibitions.\n\n--\nUncle Al\nhttp://www.mazepath.com/uncleal/qz.pdf\nhttp://www.mazepath.com/uncleal/eotvos.htm\n(Do something naughty to physics)\n\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">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>chronon wrote:
>
> I've been reading about entanglement swapping in
>
> http://physicsweb.org/article/world/11/3/9
>
> Essentially two pairs of entangled photons A,B and C,D are produced,
> then B and C are entangled using a Bell-state analyser. The result is
> that A and D become entangled although they have never interacted.
> The point is made elsewhere that A and D may have spacelike
> separations, but of course this doesn't lead to FTL transmission of
> information.
> But what if the pair B,C has a spacelike separation from the pair A,D.
> If the article is to be taken at face value then I could choose
> whether or not to entangle B and C and someone having A and D could
> see whether they have become entangled - instantaneous transmission of
> information.
> I don't believe in faster than light communication, so what is wrong
> with this argument.

No information is transferred superluminally. You couldn't send a
message via Morse code, for instance. Look up the difference between
phase and group velocities - and which one can carry information.

http://gregegan.customer.netspace.net.au/APPLETS/20/20.html

EPR experiments don't have results (information) until their remote
datasets are compared. While the answer is determined
instantaneously, it cannot be observed outside lightspeed
prohibitions.

--
Uncle Al
http://www.mazepath.com/uncleal/qz.pdf
http://www.mazepath.com/uncleal/eotvos.htm
(Do something naughty to physics)

Mike Crowe

May17-04, 06:19 PM

<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>"chronon" <stephen@chronon.org> wrote in message\nnews:60b2eda6.0405130042.116ab373@posting .google.com...\n>\n> I\'ve been reading about entanglement swapping in\n>\n> http://physicsweb.org/article/world/11/3/9\n>\n> Essentially two pairs of entangled photons A,B and C,D are produced,\n> then B and C are entangled using a Bell-state analyser. The result is\n> that A and D become entangled although they have never interacted.\n> The point is made elsewhere that A and D may have spacelike\n> separations, but of course this doesn\'t lead to FTL transmission of\n> information.\n> But what if the pair B,C has a spacelike separation from the pair A,D.\n> If the article is to be taken at face value then I could choose\n> whether or not to entangle B and C and someone having A and D could\n> see whether they have become entangled - instantaneous transmission of\n> information.\n> I don\'t believe in faster than light communication, so what is wrong\n> with this argument.\n>\n> Stephen Lee\n> www.chronon.org\n\nAs I understand it you would now be looking at two wavefunctions instead of\nfour, since your operator is "entangle or not?". This operator would only\napply to TWO photons, A and D (and the same operator would have been applied\nto B and C - to entangle them [or not as the case may be]). So the\nwavefunctions are actually AD and BC not A and B and C and D. And you are\nnow back to the case of two entangled states. AD is entangled with BC it is\njust that we are using a two photon system rather than the usual 1 photon.\n\nMike Crowe\n\n\n\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">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>"chronon" <stephen@chronon.org> wrote in message
news:60b2eda6.0405130042.116ab373@posting.google.c om...
>
> I've been reading about entanglement swapping in
>
> http://physicsweb.org/article/world/11/3/9
>
> Essentially two pairs of entangled photons A,B and C,D are produced,
> then B and C are entangled using a Bell-state analyser. The result is
> that A and D become entangled although they have never interacted.
> The point is made elsewhere that A and D may have spacelike
> separations, but of course this doesn't lead to FTL transmission of
> information.
> But what if the pair B,C has a spacelike separation from the pair A,D.
> If the article is to be taken at face value then I could choose
> whether or not to entangle B and C and someone having A and D could
> see whether they have become entangled - instantaneous transmission of
> information.
> I don't believe in faster than light communication, so what is wrong
> with this argument.
>
> Stephen Lee
> www.chronon.org

As I understand it you would now be looking at two wavefunctions instead of
four, since your operator is "entangle or not?". This operator would only
apply to TWO photons, A and D (and the same operator would have been applied
to B and C - to entangle them [or not as the case may be]). So the
wavefunctions are actually AD and BC not A and B and C and D. And you are
now back to the case of two entangled states. AD is entangled with BC it is
just that we are using a two photon system rather than the usual 1 photon.

Mike Crowe

Mike Stay

May17-04, 06:20 PM

<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>stephen@chronon.org (chronon) wrote in message news:<60b2eda6.0405130042.116ab373@posting.google. com>...\n> I\'ve been reading about entanglement swapping in\n>\n> http://physicsweb.org/article/world/11/3/9\n>\n> Essentially two pairs of entangled photons A,B and C,D are produced,\n> then B and C are entangled using a Bell-state analyser. The result is\n> that A and D become entangled although they have never interacted.\n> The point is made elsewhere that A and D may have spacelike\n> separations, but of course this doesn\'t lead to FTL transmission of\n> information.\n> But what if the pair B,C has a spacelike separation from the pair A,D.\n> If the article is to be taken at face value then I could choose\n> whether or not to entangle B and C and someone having A and D could\n> see whether they have become entangled - instantaneous transmission of\n> information.\n> I don\'t believe in faster than light communication, so what is wrong\n> with this argument.\n>\n> Stephen Lee\n> www.chronon.org\n\nStart in the state |ABCD> = 1/2(|0000> + |0011> + |1100> + |1111>).\nThe Bell operator B is\n1/sqrt(2)( |00><00| + |00><11| +\n|01><01| + |01><10| +\n|01><01| - |01><10| +\n|00><00| - |00><11| )\n\nApply I_2 x B x I2 to |ABCD> to get\n\n1/sqrt(8)( |0000> + |0011> + |0101> + |0110> +\n|1001> + |1010> - |1100> - |1111> )\n\nNotice that this state has even parity. When you measure B and C, the\nwave function collapses, entangling A and D so they have the same\nparity as B+C.\n\nSo what happens is you get A,D either correlated or anticorrelated\n(depending on the parity of B + C) but you can\'t tell which.\n--\nMike Stay\nhttp://www.cs.auckland.ac.nz/~msta039\n\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">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>stephen@chronon.org (chronon) wrote in message news:<60b2eda6.0405130042.116ab373@posting.google.com>...
> I've been reading about entanglement swapping in
>
> http://physicsweb.org/article/world/11/3/9
>
> Essentially two pairs of entangled photons A,B and C,D are produced,
> then B and C are entangled using a Bell-state analyser. The result is
> that A and D become entangled although they have never interacted.
> The point is made elsewhere that A and D may have spacelike
> separations, but of course this doesn't lead to FTL transmission of
> information.
> But what if the pair B,C has a spacelike separation from the pair A,D.
> If the article is to be taken at face value then I could choose
> whether or not to entangle B and C and someone having A and D could
> see whether they have become entangled - instantaneous transmission of
> information.
> I don't believe in faster than light communication, so what is wrong
> with this argument.
>
> Stephen Lee
> www.chronon.org

Start in the state |ABCD> = 1/2(|0000> + |0011> + |1100> + |1111>).
The Bell operator B is
1/\sqrt(2)( |00><00| + |00><11| +|01><01| + |01><10| +|01><01| - |01><10| +|00><00| - |00><11| )

Apply I_2 x B x I2 to |ABCD> to get

1/\sqrt(8)( |0000> + |0011> + |0101> + |0110> +|1001> + |1010> - |1100> - |1111> )

Notice that this state has even parity. When you measure B and C, the
wave function collapses, entangling A and D so they have the same
parity as B+C.

So what happens is you get A,D either correlated or anticorrelated
(depending on the parity of B + C) but you can't tell which.
--
Mike Stay
http://www.cs.auckland.ac.nz/~msta039