Transcript Document

Quantum Entanglement
David Badger
Danah Albaum
Some thoughts on entanglement...
“Spooky action at a distance.”
-Albert Einstein
“It is a problem that will drive you absolutely
crazy.”
-Pratim sen-Gupta, PhD student in physics
“I don’t understand.”
-David Badger, student in physics
A brief history of entanglement
• 1935: Einstein, Podolsky, and Rosen publish
a paper attacking the Copenhagen interpretation
of quantum mechanics
• The mathematics of QM allow for the violation
of relativistic locality; the measurement of
some quantity in one quantum system determines
the same quantity in another quantum system, no
matter how far away the two systems may be
• Einstein: Particles should have a definite state,
independent of observation
• 1936: Schrodinger publishes an extension of
the EPR paper, coining the term “entanglement”
to describe the phenomenon
• Particles that are arbitrary distances apart can
influence one another instantaneously
• Quantum states are NOT independent of
observation; impossible to observe a quantum
state without changing it
How observation changes the state of a system
We want to measure the spin on a neutron
B
spin “up”
detector 1
neutron
detector 2
spin “down”
A neutron has equal probability of being detected in either 1 or 2
B
spin “up”
detector 1
neutron
detector 2
spin “down”
wave function:
ψ(s ↑) + ψ(s ↓)
superposition of
both spin states
wave function:
wave function:
now, the
ψ(s ↑) * Ψ(deflected up) +
detectors’ wave
ψ(s ↓) * Ψ(deflected down)
functions will
become
the spin and position parts
entangled with
of the wave function have
the neutron’s
become entangled
So now we have a problem:
What are the wave functions of the detectors?
• The detectors are macroscopic devices used
to measure microscopic quantities
• Macroscopic measuring devices have an
enormous number of quantum states
• We lose some information about the
wave function of the neutron in the detector;
this is called decoherence
• The only information we are left with are the
relative probabilities that a detector will register
An illustration of non-locality
We prepare two protons in a singlet state;
one has spin up, the other has spin down
along the y-axis
proton 1
ψ1(s ↑) + ψ1(s ↓)
proton 2
ψ2(s ↑) + ψ2(s ↓)
An illustration of non-locality
proton 1
proton 2
arbitrary distance
First we measure the spin of
proton 1 along the y direction
We will get ψ1(s ↑)
or ψ1(s ↓) with equal prob.
Let’s say we get ψ1(s ↑)
Then, the wave function of
proton 2 instantaneously
collapses to ψ2(s ↓)
and we will measure the spin
to be “down”.
Our observation of
system 1 changes the state
of system 2.
What does this mean?
• We “steered” wave function 2 into a certain
form simply by making an observation about
system 1
• Neither of the protons was ever in a definite
spin state, but both of them collapsed to one
once we made an observation; the information
about spin states is “encoded” in both of the
protons
• Particles in an entangled system like this are
called “qubits”, and are the theoretical basis for
quantum computers
Quantum information and computing
• Superposition: a quantum system can take on
two states at once
• Each qubit can encode both a 1 and a 0 at the
same time
• The qubits are “linked” together through
entanglement; measuring the state of one qubit
affects the state of another
Quantum information and computing
classical register
3 bits encodes one symbol
of eight combinations
000
001
010
011
100 1 3-bit register ->
101 1 3-bit symbol
110
111
quantum register
3 qubits can encode
all eight combinations
at once
2^N symbols
1 3-qubit register ->
8 3-bit symbols
Quantum information and computing
• The big problem: decoherence
• Decoherence increases with the number of
quantum logic gates (qubits)
• Many physicists believe that decoherence will
never be limited to an amount that allows more
than a few quantum computations at once
• Research is going into decreasing decoherence
by limiting the amount of macroscopic devices
involved in the process
Recent advances in entanglement research
• Quantum cryptography: any eavesdropper
changes the state of the system by observing it
• In 2004 physicists showed the transmission of
a quantum cryptographic key over a 730 meter
distance at 1 Mbps
• In 2003 three electrons were entangled using an
ultrafast laser pulse and a magnetic quantum well.
Previously, only two particles have been entangled
at once in the laboratory
• Quantum synchronization of atomic clocks over
long distances with unprecedented accuracy
Recent advances in entanglement research
• Entangled Quantum Interferometry: “dramatic
noise reduction and sensitivity improvements
in quantum measurements of tiny inertial
motions”
• Quantum teleportation: destroying an unknown
physical entity and recreating it in another
location (a team at Innsbruck successfully
recreated the polarization state of a photon
across the room)
For more information
Prof. Anton Zeilinger
http://www.quantum.univie.ac.at/research/photonentangle/CQC Introductions
Qubits
http://www.qubit.org
Stanford Encyclopedia of Philosophy
http://plato.stanford.edu/entries/qt-entangle/
Hidden Unity in Nature’s Laws by John C. Taylor