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```“Anyone who can contemplate
quantum mechanics without getting
dizzy hasn’t understood it.”
--Niels Bohr
The Quantum Information Revolution
Paul Kwiat
Kwiat’s Quantum
Clan (2012)
Rebecca Holmes
Trent Graham
Kevin Zielnicki
Mike Wayne
Courtney Byard
Daniel Kumor
David Schmid
Jia Jun (“JJ”) Wong
Cory Alford
Joseph Nash
David Rhodes
Visit Prof: Hee Su Park
Post-Doc: Jian Wang
A New Science!
Quantum
Mechanics
Information
Science
20th Century
Quantum Information Science
21st Century
Quantum cryptography
Secure key distribution
(even between
non-speaking parties)
Fundamental physics
Entanglement
Decoherence
Ultimate control over
“large” systems
Quantumclassical
Quantum
Information
Quantum metrology
Measurements beyond
the classical limit
Non-invasive measurements
Measurements on quantum
systems
Quantum communciation
Teleportation
quantum systems
(“q. network”)
Quantum computation
Factoring
Simulating other quantum
systems (>30bits)
Error correction
Quantum
Metrology
Quantum
Cryptography
Quantum
Computing
“Things should
simple as
possible, but not
any simpler.”
What I do…
Unravel the mysteries
of the universe…
Quantum Optics
???
Light
Quantum…
a. very small
b. very big (e.g., “quantum leap”)
c. an unsplittable parcel/bundle of
energy
d. a cool buzzword to get more
funding, more papers, more
people at your Sat. am physics
lecture, etc.
e. all of the above
leap’ and proposed that light
with tiny energy given by
E = h f = h c/l
wavelength
6.6 x 10-34J-s
frequency
Physics 214: Lect. 7
Example: “Counting photons”
How do we reconcile this notion that light comes in ‘packets’ with
our view of an electromagnetic wave, e.g., from a laser??
Visible light
Partially transmitting
mirror
Power input
How many photons per second are emitted from a 1-mW laser (l=635nm)?
E photon 
hc
l

1240 eV -nm
 2 eV
635 nm
Power output: P = (# photons/sec) x Ephoton
(# photons/sec) 
P
E photon

10
3
s
J

1 eV
1.6  10
-19

J
1 photon
2 eV
 3.1  10 s
15
1
1 mW red laser
3 x 1015 photons/sec =
3,000,000,000,000,000/sec
This is an incredibly huge number – your eye basically
cannot resolve this many individual photons (though
the rods can detect single photons!).
And you MAY be able to see just one photon!!
Formation of Optical Images
For large light intensities, image
formation by an optical system can be
described by classical optics.
l
l
However, for very low light intensities, one can see the
statistical and random nature of image formation.
l
Use an extremely sensitive CCD camera that can detect single photons.
A. Rose, J. Opt. Sci. Am. 43, 715 (1953)
Exposure time
But how do we *know* there’s
only ONE photon…
A beamsplitter…
“1”
“0”
Photon only detected in one output.
Equally likely to be transmitted or
reflected – cannot tell which.
"God
does not
play dice with the
universe."
Quantum
random-number
generator!
“It •seems
to me that the
idea of a personal God is an
completely
unpredictable
anthropological concept which I cannot take seriously.”
• patented
• commercially available
“The important thing is
not to stop questioning.”
-A. Einstein
Quantum
Interrogation
The problem…
Measure
-film
-absorber
-atom
without
-exposing
-heating
-exciting it
There is film in the camera!”
WHY was Einstein’s 1905
proposal that light was made of
particles such a profound leap
that almost no one believed him?
Because everyone KNEW that light
was really waves.
One of the strangest features of QM:
all particles can behave like waves…
Interference of waves (e.g.,
water, sound, …)
“Constructive interference”
Waves cancel:
“Destructive interference”
Light: Particle or Wave?
1675: Newton “proved” the light was made
of “corpuscles”
l
l
Fresnel proposed interference of light.
Judge Poisson knew light was made of
particles: “Fresnel’s ideas ridiculous” If
Fresnel ideas were correct, one would
see a bright spot in the middle of the
Judge Arago decided to
actually do the experiment…
Conclusion (at the time): Light
must be a wave, since
particles don’t interfere!
Only, now we know
that they must!
Single-Photon Interference:
Question: what if we reduce the
source intensity so that at most
one particle (photon) is in the
apparatus at a time?
?
Photons
l
Answer: Just like in the “optical
image formation”, given enough time,
the classical interference pattern
will gradually build up from a huge #
of seemingly random “events”!
Exposure time
l
Optical Interferometers
l
l
l
Interference arises when there are two (or more) ways
for something to happen, e.g., sound from two speakers
An interferometer is a device using mirrors and “beam
splitters” (half light is transmitted, half is reflected) to
give two separate paths for light to get from the source
to the detector.
Two common types:
Mach-Zehnder:
beamsplitter
Michelson :
mirror
mirror
beamsplitter
Quantum
Interrogation
The problem…
Measure
-film
-absorber
-atom
without
-exposing
-heating
-exciting it
There is film in the camera!”
The solution… (Elitzur & Vaidman, 1993)
Use dual wave-particle nature of quantum
objects (“wavicles”)
Single photon always shows up at D1
(complete destructive interference to D2)
Now place an absorbing object in one arm…
50% chance that photon is absorbed by object
50% chance it isn’t  25% chance D2 fires 
“interaction-free measurement” of object
Quantum Interrogation
•
•
•
Optimizing reflectivities  50% efficiency
By combining these techniques with the
“quantum Zeno effect” (making repeated very
weak interactions), the efficiency can in
principle be pushed to 100%: no photons
absorbed by the absorbing object!
[85% demonstrated to date]
Imaging semi-transparent objects does not
Quantum
Metrology
Wpdrval
Quantum
Cryptography
L&wz;xcuymnzx
Quantum
Computing
Cryptography:
Make messages so that only the
intended recipient can understand
them…
1.
public key encryption: Standard, but
not provably secure; relies on
difficulty of factoring (e.g., 15 = 3x5)
2. secret key encryption: PROVABLY
secure as long as
a. no one else has the key
b. the key is never reused
Quantum Cryptography = Quantum Key Distribution
Quantum Cryptography
ALICE
BOB
KEY:
…010001010011101001…
Cipher:
…0110010110100010…
XOR(Cipher,Key)
XOR(Message,Key)
Message
Cipher
EVE
Quantum Cryptography:
Use a different property of light–
polarization!
Polarization:
--the oscillation direction of the light
--property of each photon
--can measure with polarizers, calcite, etc.
Prob(horizontally polarized photon pass horizontal polarizer): 1
Prob(horizontally polarized photon pass vertical polarizer): 0
Prob(diagonally pol. photon pass horizontal polarizer): 1/2
Prob(diagonally pol. photon pass vertical polarizer): 1/2
How to Make “Entangled” Coins
“Spontaneous
DownConversion”:
high energy
parent photon can
split into two
daughter photons
(with same
polarization)
We don’t know WHICH crystal created the pair of
photons, but we know they both came from the same
crystal  they MUST have the same polarization.
• Eve cannot “tap” the line  photons that don’t
make it to Bob are not part of the key
• Eve cannot “clone” the photon  forbidden by
basic quantum mechanics
• Measurements by Eve necessarily have a
chance (25%) to disturb the quantum state
 Alice and Bob can detect errors in the key!
If the bit error rate is too high, they simply discard
the key. No message is ever compromised.
Current Free-Space QKD Distance Record:
144 km between LaPalma and Tenerife
Last week news item: they used the
entangled photons to teleport the
state of a photon between the
islands – world distance record for
quantum teleportation!
QKD Goes Commercial…
Quantum Interrogation vs.
Quantum Cryptography
Since we can seemingly “see” without “looking”
using quantum interrogation, does this mean an
eavesdropper could use it to defeat quantum
cryptography?
No! It turns out that even making the gentlest
measurement possible, if the eavesdropper gains
any information, she disturbs the state.
Or if she is so gentle so as not to disturb the state,
then she gets no information.
Quantum key distribution is secure against any
attack allowed by the laws of physics!
Imagination is more
important than knowledge
Moore’s Law
Source: Intel
The first solid-state transistor
(Bardeen, Brattain & Shockley, 1947)
The Ant and
the Pentium
~100 million transistors
INTEL
Pentium 4
transistor
Size of an atom
~ 0.1nm
Binary digit
Quantum bit
“bit”
“qubit”
0, 1
0101
Physical realization of qubits  any 2 level system
2-level atom:
ge
spin-1/2:

polarization:
HV
All 2-level systems are created equal, but some are
more equal than others!
Quantum communication  photons
Quantum storage  atoms, spins
Scaleable circuits  superconducting systems
“Quantum”
phenomena
Superposition Interference
Waveparticle
duality
Intrinsic
Entanglement
randomness in
measurement
“Entanglement”, and the scaling that results, is the
key to the power of quantum computing.
• Classically , information is stored in a bit register: a 3-bit
register can store one number, from 0 – 7. 1 0 1
• Quantum Mechanically, a register of 3 entangled qubits
can store all of these numbers in superposition:
a|000 + b|001 + c|010 + d|011  + e|100 + f|101  + g|110  + h|111 
• Result:
-- Classical: one N-bit number
-- Quantum: 2N (all possible) N-bit numbers
•N.B.: A 300-qubit register can simultaneously store
2300 ~ 1090 numbers
That’s a BIG number
1090 = 1,000,000,000,000,000,000,
000,000,000,000,000,000,
000,000,000,000,000,000,
000,000,000,000,000,000,
000,000,000,000,000,000
This is more than the total number of particles
in the Universe!
Some important problems benefit from this
exponential scaling, enabling solutions of
otherwise insoluble problems.
A hard problem: factoring large integers:
For example, it is hard to factor 167,659
But an elementary school student can
easily multiply 389 x 431 = 167,659
This asymmetry in the difficulty of factoring
vs. multiplying is the basis of public key
encryption, on which everything from on-line
transaction security to ensuring diplomatic
secrecy depends.
Quantum Computing’s “killer app.”
Quantum algorithms enable one to factor numbers
into their prime constituents MUCH faster:
RSA digits
PC
(1 GHz)
Blue
Waters
(10PF)
Quantum
Computer
(1 GHz)
129
4 months
1 sec
10 sec
225
300,000 yr
12 days
100 sec
300
1016 yr
20 million yr
(>> universe)
200 sec
The difficulty (impossibility) of factoring large numbers
(and the ease of creating a large number from its
factors) is the basis of public key encryption (which
nearly everyone uses for secure transmission today).
Atom in different energy states:
energy states:
state labels
“ ”, “ ”
atom in
state
atom in
state
atom
atom in
superposition state
shorthand “wave function”
representation
 =   + 
Probability of measuring
, P = ||2
Probability of measuring
, P = ||2
Collective motion: the “quantum data bus”
state of motion
|rest
|0
|0 + |1
|0
|0
|1
laser
|rest + |moving
|0
|0
|0
|0
|1
Science News
Quantum Computing Explored
Sep 12 2001 @ 08:10
American computer scientists are studying the possibility to
build a super fast computer based on quantum physics.
Why it might not work…
Technology requirements
•Set of qubits isolated from environment.
•“Quantum information bus” to connect qubits.
Essential Dichotomy
Need WEAK coupling to
environment to avoid
decoherence, but you also
need STRONG coupling to at
least some external modes in
order to ensure high speed and
reliability.
Quantum Information Timeline
Difficulty/Complexity
Quantum
Computation
The expected
The unlikely – impossible?
Quantum
Widgets
The known
Quantum
Sensors?
Quantum
Engineered
Photocells?
The as yet unimagined!!!
Quantum
Communication
0
5
Quantum
Measurement
10
~15
Time (years)
Quantum
Games & Toys
20?
25??
“Why is it that nobody
understands me, and
everybody likes me?”
– A.E.
Multiplexed Ion Trap
Architecture
control electrodes
• Interconnected multi-trap
structure
• Route ions by controlling
electrode potentials
• Processor sympathetically
cooled
• No individual optical
gates (can do gates in strong
trap  fast)
• One-qubit gates in subtrap
Quantum factoring and cryptography
# of instructions
the RSA cryptosystem:
• polynomial work to
encrypt/decrypt
• exponential work to
break = factoring
• BUT quantum factoring is
only polynomial work
24
1 10
23
1 10
22
1 10
21
1 10
20
1 10
19
1 10
18
1 10
17
1 10
16
1 10
15
1 10
14
1 10
13
1 10
12
1 10
11
1 10
10
1 10
9
1 10
8
1 10
7
1 10
6
1 10
5
1 10
4
1 10
1000
100
10
1
Classical ~ eAL
~ 1017 instructions: 8 months
Quantum~ L3
~ 109 operations: seconds
0
200
400
RSA129
•“latency”: will information
encrypted today be secure
against future quantum
computers?
600
800
1000
# of bits, L, factored
```