The document discusses quantum entanglement and its applications. It begins by describing early experiments that demonstrated quantum entanglement, such as the Stern-Gerlach experiment and photon polarization. It then discusses Bell's theorem and how entanglement violates local realism. Applications of entanglement discussed include quantum cryptography, random number generation, and quantum teleportation. Recent experiments have demonstrated entanglement over long distances, including ground-to-satellite and intercontinental quantum communication.

1. Quantum Entanglement and
its applications
Prashanth Adhikari

2. Bertlmann’s Socks
“The philosopher on the street who has not suffered a course
in quantum mechanics, is quite unimpressed by EPR correlations.
He can point to many examples of similar correlations in everyday life.
The case of Bertlmann’s socks is often sited.”
- John Bell
What’s the big deal with EPR?

3. Example: Spin quantization
By Tatoute - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=34095239
1: furnace.
2: beam of silver atoms.
3: inhomogeneous magnetic
field.
4: expected result.
5: observed result
The Stern Gerlach Experiment
Expected
Observed
Rotated

4. Stern-Gerlach Sequential Experiments
• You cannot measure any
two components of
angular momentum
simultaneously (they are
complementary).
• Measurement along one
axis modifies the
observed state of the
system.

5. Photon Polarization

6. The Copenhagen Interpretation
• “There is no quantum world. There is only an abstract quantum
mechanical description. It is wrong to think that the task of physics is
to find out how Nature is. Physics concerns itself with what we can say
about Nature.” - Bohr
• ”In the experiments about atomic events we have to do with things
and facts , with phenomena that are just as real as any phenomena in
daily life. But the atoms or the elementary particles are not as real;
they form a world of potentialities or possibilities rather than one of
things or facts.” - Heisenberg
• ”Observations not only disturb what has to be measured, they
produce it.” - Jordan

7. The EPR Objection: Entanglement
• You can in fact measure complementary observables simultaneously by
simply making measurements on an entangled pair of particles.
• Quantum indeterminacy implies a “spooky action at a distance”.
• To avoid such action at a distance, we have to attribute to the space-time
regions in question real correlated properties in advance of observation,
which predetermine the outcomes of these observations (Local Realism).
• QM is incomplete because its formalism does not include those properties.
EPR Bohm Setup using Stern-Gerlach Analyzers

8. Photon Entanglement
• A UV Laser strikes a crystal of beta barium borate.
• A small probability of decay into two photons of longer wavelengths.
• Type II Parametric Down Conversion:
• One is polarized horizontally
• Other is polarized vertically
• The polarizations states are entangled.

9. Is the moon there when nobody looks?
Mermin’s Local Reality Machine
Bell’s Theorem:
E(a, b) – E(b, c) <= 1 + E(a, c)
E(a,b) is expectation value of product
of outcomes of measurements at two
locations – A and B with configuration
a and b respectively..

10. Is the moon there when nobody looks?
Mermin’s Local Reality Machine
1. Whenever the switch
positions are the same
in the boxes (say 11, 22,
33) the light colors are
always the same (RR,
GG).
2. If the switch positions
are ignored then the
light bulb colors are
random with 50% of
same color (RR, GG).
Bell’s Theorem:
E(a, b) – E(b, c) <= 1 + E(a, c) In a local realistic scheme you can get same colors only 5/9 times, except in
the trivial case (when you get will get a match 100% of the time).

11. Quantum Strategy to achieve Mermin’s result
E(a, b) = -a.b = - cos <a, b>
Map the switches to Stern-
Gerlach analyzers at 120
degrees from each other (0,
120, 240 degrees).
E(a, b) = 1/2

12. The CHSH Nonlocal Game
To win the game, Alice and Bob must make winning moves more than ¾ =75% of times.
No classical strategy can do it!
Classical Deterministic Strategy

13. Entangled Qubits
Single Qubit
Bell States
GHZ Tripartite State

14. Quantum Strategy for Winning CHSH
Tsirelson’s Bound
Alice and Bob share an entangled state.
(22.5 and -22.5 degrees).

15. Application: Quantum Randomness
• “God does not play dice with the universe.” – Einstein
• “Local causality implies determinism.” – EPR
• Bell’s Theorem + No Signalling Theorem  measurement outcomes
have to be random.
• Application: True Random Number Generators (no more PRNG)!

16. Two Channel Bell Test Experiment
By George Stamatiou based on png file of C.Thompson - http://commons.wikimedia.org/wiki/File:Two_channel.png, CC BY-SA 3.0,
https://commons.wikimedia.org/w/index.php?curid=21149883
CHSH Two-Channel Bell Test
Bell Test Statistic
CHSH Inequality (for Local Realism)
Tsirelson’s Bound (for Quantum Strategy)
a, a’ are detector settings at A and b, b’ are detector settings at B.
E(a, b) is the “quantum” correlation, i.e. expectation value of product
of outcomes of experiment.

17. Application: Quantum Cryptography
• Single Photons (BB84 Protocol):
• Entangled Particles (E91 Protocol):
• Uses maximally entangled pair of photons.
• Same setup as CHSH – use basis states rotated by 0, 45,
22.5 and 67.5 degrees.
• Alice measures using one of 0, 45 and 22.5 basis states.
• Bob Measures using one of 0, 22.5 and -22.5 basis states
• Calculate Bell test statistic.
• Should hit Tsirelson’s bound of
• Else Eve has eavesdropped and introduced local realism.

18. Applications: Quantum Teleportation
Qubit to be teleported from A (Alice) to B (Bob):
4 Bell States:
• Alice expressed the states of the two particles as a superposition of
Bell states.
• Then Alice measures A and C in terms of the Bell states.
• This entangles A with C and breaks the entanglement with B.
• Bob’s particle B ends up in a superposition state that is similar to C.
• Alice’s measurement tells her which of the 4 states the system is in.
• She communicates with Bob over a classical channel with state info.
• Bob performs unitary transformations if necessary to recover the state C.
Alice and Bob share a pair of maximally entangled qubits in one of

19. Joint Measurement
3. Alice measures in Bell basis states
4. 3-particle state collapses to one of
6. Based on Alice’s message Bob performs a standard unitary transformation (Pauli gate) on B to get the desired state.
Bell identities
1. Assume Alice and Bob share
2. Alice uses the Bell identities to express the joint state of 3 particles in terms of Bell states.
5. Alice tells Bob the Bell state she is in.

20. Ground based entanglement experiments
• Non-local interferometer experiment performed over a distance of 10 km under Lake Geneva.
• Showed that collapse of wave function occurs at 10,000 times faster than the speed of light.

21. Space based quantum entanglement
http://www.sciencemag.org/news/2017/06/china-s-quantum-satellite-achieves-spooky-action-record-distance

22. Ground-Satellite Quantum Communication
Ground-to-Satellite Quantum Teleportation Satellite-To-Ground Quantum Key Distribution
Micius QKD Satellite
Three payloads:
• a decoy-state QKD transmitter,
• an entangled-photon source, and
• a quantum teleportation receiver and analyzer.

23. Inter-continental Quantum Communication
• https://phys.org/news/2017-07-physicists-
transmit-earth-to-space-quantum-
entanglement.html
• https://phys.org/news/2017-08-chinese-team-
quantum-keys-ground.html#nRlv
• https://phys.org/news/2017-09-team-world-space-
ground-quantum-network.html