We show a device with which, apparently, information (in the form of a "slash-dot" code) is instantly transmitted via Bell state collapse, over arbitrary distance. We discuss some problems and paradoxes arising when this conclusion is viewed in the relativistic framework.
quant-ph0204108.tex

\documentstyle[12pt,epsf]{article}

%\topmargin
%-1.5cm
%\textwidth
%15.5cm
%\textheight
%24cm
%\oddsidemargin
%0.7cm
%\evensidemargin
%1.2cm

\begin{document}


\begin{center}

\vspace{0.5pt}
{\Huge A Bell Telegraph}
\vspace{5pt}\\[5mm]
{Daniel Badagnani \footnote{daniel@cabtep2.cnea.gov.ar}}\\
\vspace{0.5pt}
%{\tiny Instituto Balseiro, Universidad Nacional de Cuyo and
%CONICET}\\[10mm]
\end{center}


\abstract{We show a device with which, apparently, information (in the form
of a "slash-dot" code) is instantly transmitted via Bell state collapse,
over arbitrary distance. We discuss some problems and paradoxes arising when
this conclusion is viewed in the relativistic framework.}



\section{Introduction}

Bell states \cite{Bell-y-Cia} are a direct consecuence of quantum mechanics,
which have been profusely seen in experiments \cite{Aspect-y-Cia} Both
theory and experiment tell that measurements at one place causes quantum
state collapse of parts arbitrarily far away, "instantly". But it has been
argued that no information can be carried in such processes.
If this were not the case, there would be a clash with
relativity, since simultaneity is not an invariant concept so one should
wonder what is the frame in wich the collapse is instantaneous.

Here we show a device in wich, via Bell states, information seems to travel
instantly between distant points. We haven't been able to find why it should
not work, although we find that such a device would cause serious conceptual
problems and even paradoxes.

In the next section we describe the device and how it works. Then, in the
last section, we show some problems and paradoxes occurring at the
relativistic realm.

\newpage

\section{The device}

\begin{picture}(330,100)(0,0)

% Tubo de abajo
\put(30,0){\line(1,0){250}}
\put(90,8){\large \bf c}

% Detector de abajo
\put(290,-5){\line(0,1){10}}
\put(290,5){\line(1,0){20}}
\put(290,-5){\line(1,0){20}}
\put(310,-5){\line(0,1){10}}

% Haz incidente
\put(175,50){\line(0,1){50}}
\put(180,70){\large \bf a}

% Barrera de potencial
\put(170,50){\line(1,0){10}}
\put(185,48){\large \bf b}

% haces divididos
\put(162.5,0){\line(1,4){12.5}}
\put(185,20){\line(-1,3){10}}

% Tubo de arriba
\put(50,20){\line(1,0){250}}

% Detector de arriba
\put(310,15){\line(0,1){10}}
\put(310,25){\line(1,0){20}}
\put(330,15){\line(0,1){10}}
\put(310,15){\line(1,0){20}}
\put(320,30){\large \bf e}

% pantalla
\put(15,-5){\line(4,3){30}}
\put(15,15){\line(4,3){30}}
\put(15,-5){\line(0,1){20}}
\put(45,17){\line(0,1){20}}
\put(20,30){\large \bf d}

\end{picture}

\begin{center}
{\scriptsize Scheme of the telegraph. A beam of excited atoms (a) splits
at a potential barrer (b). Then each atom decay at any of two pipes (c)
emitting two correlated photons. At one end (d) they are set to interfere
with themselves at a screen. At the other end (e), two detectors are
placed, which can be turned on or off} \\[10mm]
\end{center}

A sketch of the device is shown in the figure above. It is inspired
in Feynman's discussion on quantum interference \cite{Feynman}. A beam of
excited atoms (wich will emit a two photon Bell state) is divided in two by
a potential barreer in such a way that a given atom has the same probability
of following each path, wich is itself a Bell state. At the decay, the
resulting photons are collected by some kind of pipes (for instance, two
optic fabrics), so every pair of photons is in any of those, forming a kind
of doubly entangled state. If no one collapses this system, the photons at
one end of the pipes can be set to interfere at a screen. But one could
'see' where each pair is just looking at the second photon at the other end,
destroying the interference pattern. So, turning on and off detectors at one
end sets the other end at two observably different states (random arrival
and interference respectively), wich can obviously be used as a telegraph.

% Ser\'{\i}a bueno escribir unos vectorcitos de estado
% para descoloquializar el asunto...

Still we have to show that this can indeed be used to send information in a
time as short as necessary to be considered instantaneous. We need several
photon pairs (say M) to conclude that we are before an interference or not,
with a given confidence interval. One solution is to use many uncorrelated
pairs simultaneously, and invoke superposition principle. But in order not
to obscure the conclusions by adding hypothesis, we will give an alternative
proof using single pairs. Suppose that for a given telegraph we need a time
separation T for producing each pair being sure that we deal with a single
pair at a given instant. So we need a time MT for sending a "byte". Now take
N such telegraphs, in which the first pair in each is produced in an instant
at random between 0 and T. With this ensemble we build an improved
telegraph, turning on and off all detectors simultaneously for sending
signals. Now the time needed reduces to MT/N, and can be made as little as
we wish. Thus we can send information instantly (at the large N limit) using
(lots of) single pair states.

\section{Troubles}

Let's suppose for the moment that we haven't done any mistakes; if so,
quantum mechanics imply we can send information instantly. What do we mean
by "instantly" in a relativistic context? Or, put differently, instantly in
what reference frame?  This is a difficulty with the very
concept of quantum collapse. Even if it turns that no information could
be transmitted via Bell states, this is still a conceptual puzzle.
Whatever the answer is, fits in any of the following two posibilities:

\begin{itemize}
\item  {{\bf Deny relativity:} There is a privileged frame F in which
quantum collapse occur instantly. This possibility is not inconsistent but
deeply nasty.}

\item  {{\bf Preserve relativity:} The frame F in which the collapse is
instantaneous depends on the state (for instance, it could be the one in
which the center of mass is at rest). This possibility seems more
acceptable, but a closer look shows it leads to inconsistencies, which can
be seen as paradoxes. Consider the setting shown in the figure below: two
identical telegraphs A and B with F(A) and F(B) moving in opposite
directions results in sending a signal to the past. As F(A) moves to the
left, A reception happens before A emmision in this frame. The message is
instantly retransmitted trough B (B emmision) and again, as F(B) moves to
the right, B reception happens before B emission, and at the same space location
than A emmision. In the setting, the
automaton located there transmit $m_1$ if and only if it transmit $m_2$ and
vice versa, wich is absolutely inconsistent.}

\newpage

\end{itemize}

\begin{picture}(300,100)(0,0)

% Telegraph
\put(50,50){\line(4,1){150}}
\put(0,60){\bf A reception}
\put(0,40){\bf B emission}
\put(50,50){\line(4,-1){150}}
\put(210,90){\bf A emission}
\put(210,10){\bf B reception}

% Axes
\put(180,30){\line(1,0){50}}
\put(230,30){\line(-2,1){10}}
\put(230,30){\line(-2,-1){10}}
\put(235,30){\bf x}
\put(180,30){\line(0,1){30}}
\put(180,60){\line(1,-2){5}}
\put(180,60){\line(-1,-2){5}}
\put(185,55){\bf t}

\end{picture}

% caption
\begin{center}
{\scriptsize Setting for the paradox: two identical and opposely oriented
tellegraphs A and B has F(A) and F(B) respectively as frames where
communication is instantaneous. F(A) moves toward the left at some
speed v, while F(B) is set to move towards the right at speed v, and we
produce the A emission in a moment such that A reception and B emission
coincides. The message received from A is retransmitted through B. An
automaton able to send either message $m_1$ or $m_2$ stay still at the
position of A emission, wich is the same than B reception, and we set it to
send $m_1$ throug A if it reads $m_2$ from B and vice versa.}\\[10mm]
\end{center}


Of course, there remain the possibility that we have done some mistake and
quantum mechanics really forbids such a device to work. Hopefully this work
will call someone's attention in order to find it out.

\section{Aknowledgements}
I am gratefull to Alejandro Daleo for very usefull comments and discussions

\begin{thebibliography}{9}
\bibitem{Bell-y-Cia}
 Einstein, Podolsky and Rosen, Phys Rev 47(1935)777\\
 Bohm and Aharonov, Phys rev 108(1957)1070\\
 Bell, Phys 1(1964)195

\bibitem{Aspect-y-Cia}
 Aspect, Grangier and Roger, Phys Rev Lett 49(1982)91\\
 For a modern review, see Galindo and Martin-Delgado,
quant-ph/0112105 and references therein

\bibitem{Feynman}  The Feynmann Lectures on Physics, vol. 3, chapter 1.

\end{thebibliography}

\end{document}

quant-ph0204108.extracted_bib
\begin{thebibliography}{9}
\bibitem{Bell-y-Cia}
 Einstein, Podolsky and Rosen, Phys Rev 47(1935)777\\
 Bohm and Aharonov, Phys rev 108(1957)1070\\
 Bell, Phys 1(1964)195

\bibitem{Aspect-y-Cia}
 Aspect, Grangier and Roger, Phys Rev Lett 49(1982)91\\
 For a modern review, see Galindo and Martin-Delgado,
quant-ph/0112105 and references therein

\bibitem{Feynman}  The Feynmann Lectures on Physics, vol. 3, chapter 1.

\end{thebibliography}