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M1L7a.txt
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M1L7a.txt
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#
# File: content-mit-8422-1x-captions/M1L7a.txt
#
# Captions for 8.422x module
#
# This file has 104 caption lines.
#
# Do not add or delete any lines. If there is text missing at the end, please add it to the last line.
#
#----------------------------------------
Let me start by presenting something
I learned today during lunch.
I had lunch with three colleagues,
and we discussed entanglement.
And well, I'm telling this story a little bit differently.
But the question which came up is
you have two harmonic oscillators.
One harmonic oscillator is in the ground state.
One is in the excited state.
And then you have the harmonic oscillators,
where the excitation is here and there.
Is that an entangled state or not?
It's a real question.
They're just--
[INAUDIBLE]
I want you to think about it.
What's the [INAUDIBLE]?
Can you distinguish it?
OK.
OK.
Who's working with ion traps?
Yes, a few people, I know.
We have a few ion traps here at MIT.
If this is an ion-- what is a good ion, ytterbium plus?
Strontium [INAUDIBLE].
Strontium plus, OK.
So if it's strontium plus, which can be in the quantum state v
equals 1 or v equals 0, and you have another strontium
plus-- you have another strontium
plus ion in a second ion trap, and it
can be in the ground state or first excited state,
isn't it wonderfully entangled?
Two systems far away.
You can manipulate them.
You have two particles, and they're in two quantum states.
It fulfills, with flying colors, all the qualities you want
to see with entangled state.
OK.
But now I can say, if I call this harmonic oscillator,
I have two optical fibers.
And you know a single-mode fiber defines an harmonic oscillator,
namely the electromagnetic field in the single mode.
And if I put one excitation into this fiber,
I have a photon here, and here I have zero photon.
Or here, I have one photon, and I have zero photons.
So if you look at the fiber, you would
say the fiber has two states.
It can have an excitation or not.
And if you use now that approach, you would say,
well, I have an entangled state between two fibers.
However, I can realize exactly that state
by having a beam splitter-- by having one photon coming
on the beam splitter, and then the photon
is coupled into one of the fibers.
So in other words, there is an ambiguity,
which I want to point out, between whether you have
a state of one particle, one photon, into two fibers
or whether you have two fibers, which
can be in two different states.
So there is often an ambiguity.
What do you call the state, and what do you call the particle?
So at our lunch conversation, it came up in a, well,
in a somewhat different context.
But people would actually say that spitting
a photon-- sending one photon across the beam splitter
fulfills, if you interpret it in that way,
fulfills the definition of entanglement.
I know our wiki page and Professor Chuang
will probably not agree.
But well, welcome to the frontier of research,
where different people have different opinions,
and certain definitions are still being worked out.
But there is one thing which is real.
These two different-- we have here two different harmonic
oscillators-- ions oscillating in a harmonic oscillator
potential or photons in a single mode.
I remember from 15 years ago, there
were papers which show if you put
the ion in a cavity or such, you can really transfer the quantum
state from the single photon, from this harmonic
oscillator, the harmonic oscillator
of the electromagnetic field, to the harmonic
oscillator of the ion.
So if we want to hold onto the definition,
which I'm not sure if we should, that this is a single photon,
a single particle cannot be entangled, well, I know,
and people reminded me at lunch, that there is a protocol
to adiabatically map the single photon in the two modes after
the beam splitter onto an entangled state of ions.
So if you focus here on the photon and say a single
particle cannot be entangled, you are facing the problem that
there is a protocol which would transfer something which you
call not entangled to something which is entangled.
I hope you enjoy that.
It's not clear what is the particle
and what is the excitation.