Quantum Entanglement

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Quantum Entanglement
David Badger Danah Albaum
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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 dont understand. -David Badger, student in
physics
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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

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• 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

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How observation changes the state of a system
We want to measure the spin on a neutron
A neutron has equal probability of being detected
in either 1 or 2
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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

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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
?1(s ?) ?1(s ?)
?2(s ?) ?2(s ?)
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An illustration of non-locality
First we measure the spin of proton 1 along the
y direction
We will get ?1(s ?) or ?1(s ?) with equal prob.
Our observation of system 1 changes the state of
system 2.
Lets say we get ?1(s ?)
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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

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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

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Quantum information and computing
classical register
quantum register
1 3-qubit register -gt 8 3-bit symbols
1 3-bit register -gt 1 3-bit symbol
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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

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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

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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)

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For more information
Prof. Anton Zeilinger http//www.quantum.univie.ac
.at/research/photonentangle/CQC
Introductions Qubits http//www.qubit.org Stanfo
rd Encyclopedia of Philosophy http//plato.stanfor
d.edu/entries/qt-entangle/ Hidden Unity in
Natures Laws by John C. Taylor