lecture 27616 : quantum communication - uni-jena.de · register for the exam by 24.12.2018....

Lecture 27616 : Quantum Communication Falk Eilenberger, Fabian Steinlechner, Andreas Tünnermann

winter semester 2018-2019

Organisational

Lectures every Tuesday @ 12.15 – 13:45, ACP Auditorium

Falk Eilenberger

Institute of Applied Physics, Abbe Center of Photonics

e‐mail: Falk.Eilenberger@uni‐jena.de

Fabian Steinlechner

Fraunhofer Institute for Applied Optics and Precision Engineering

e‐mail: Fabian.Steinlechner@uni‐jena.de

Seminar (#27617) : bi-weekly Tuesday, 14:15-15:45, ACP SR1, starting 24.11.2018

Schedule

date lecture lecturer seminar

17.10.2018 Overview of Quantum Information Processing Steinlechner

24.10.2018 Quantum Information with Photons Eilenberger X

07.11.2018 Quantum Information with Photons, Figures of Merit Eilenberger

14.11.2018 Generation an characterization of photons Steinlechner X

21.11.2018 Generation an characterization of photons Steinlechner

28.11.2018 Physical implementation of light sources Eilenberger X

5.12.2018 Physical implementation of light sources Steinlechner

12.12.2018 Quantum Communication Protocols I Steinlechner X

15.12.2018 Quantum Cryptography Steinlechner

09.01.2019 Quantum Communication Protocols II Eilenberger X

16.01.2019 Quantum Communication Networks Eilenberger

23.01.2019 Quantum Metrology Eilenberger X

30.01.2019 Quantum Imaging Steinlechner

06.02.2019 Lab Tour

Seminars / Exam

practical application of concepts explained in lecture

technical realization of quantum communication protocols

Exam: 90 min written examDate: 13.02.2019 or 20.02.2019 (TBD)Place: TBDTime: 12:15-13:45

Register for the exam by 24.12.2018

Syllabus

Basic introduction to quantum optics

Properties and realizations of quantum light sources

Encoding, transmission and detection of information with quantum states

Nonlocal properties of entangled photons (Bell‘s inequality)

Quantum communication and cryptography

Quantum communication networks

Outlook on Quantum metrology and Quantum imaging

Supporting Literature

G. Grynberg, A. Aspect, C. Fabre „Introduction to Quantum Optics“

M. Fox, “Quantum Optics –An introduction”

S. Barnett, “Quantum Information”

R. Boyd ”Nonlinear Optics”

J. Ou ”Multi-Photon Quantum Interference”

P. Kok, B.Lovett ”Introduction to Optical Quantum Information Processing”

G. Leuchs ”Lectures on Quantum Information”

A. Sergienko ”Quantum Communications and Cryptography”

• Schedule etc.

• Information and Communication

• Photons as information carriers

• Quantum Key Distribution

• Quantum Entanglement

• Quantum Teleportation

Outline for today

What‘s so Quantum about Quantum Technology?

Classical Information Processing

Components in many information processingdevices exploit quantum effects (computer, lasersfor fiber-based communication,…)

quantum effects not used toactually process the information

Quantum Information Processing (QIP)

Exploitation of quantum effects, such asentanglement & superpostion at processing level

can accomplish classically impossible tasks

Quantum Information Processing

Quantum Communication

Quantum Computation

Quantum Sensing

Quantum CryptographyQuantum Teleportation

DenseCoding

Quantum Networks

Quantum MetrologyQuantum Imaging

ClockSynchronization

Blind Cloud Computing

Quantum Simulation Prime FactoringDatabase search

MachineLearning

Ranging

Communication

Shannon’s model of a communication channel.

Signal

Noise

Communication Channel

Transmitter

receivedsignal

Destination

Receiver

Information Source

Alice Bob

PhysicalEncoding

Decoding

Communication

QuantumState

Noise


Transmitter

receivedstate

Destination

Receiver

QuantumInformation

Source

Alice Bob

Quantum State

Encoding

Quantum Measurement

Quantum communication:

signal is encoded in a quantum system

new applications and communication protocols

modified Sources, Transmitters, Receivers

How these may be realized will be discussed over the course

Information is physical

Fundamental units of information:

2-level system –> BIT

10

0

01

1

“Computational basis”



2-level system –> QuBIT

10

0


01

1



2-level system –> QuBIT

QuBit can be prepared in superposition state

0 1

22

0)0( P

2 21

22

1)1( P

10

0


01

1

Probabilistic Measurement Outcomes with updated Post-Measurement State:

Wavefunction represents all relevant knowledgeabout the preparation procedure

0 1 1 / 0??

01

1

10

0

The quantum state of a system cannot be copied…

Classical bit string:

0 0 0 0

0 1 1 0 0 1 1 0

0 1 1 0

CNOT

CNOT

0 1

Blank space for Copy:

10

0

Ideal quantumXerox machine: 0 1

10

0

0 1 0 1

?

Generlization: No Cloning Theorem (Wooters, Zurek)

• Schedule etc.






Outline for today

Light is composed of discrete quanta of energy

hEphoton kg/sm1062.6 234h

Planck’s constant:

frequency:

Quantum-ness not relevant in every-day scenarios

1 mW Power (@650nm) : photons/s103 15n

Individual photons can be detected with commercial Si SPAD detectors:

< 1 ns timing resolution

< 50 ns dead time

> 60% detection efficiency

< 100 cps dark counts

10 Mcps saturation rate

Typical specs

Single-photons at balanced beam-splitter

20

inEE

inE

classical wave-packet split at 50:50 beam-splitter

5.0R

Transmitted path

Reflected path

single-photon cannot be split - probabilistic behavior

5.0)0( P 5.0)1( P

5.0T

21

inEE

Interference observed even when only one photon is in the interferometer at the time

…each “particle” interferes with itself (Paul Dirac)

balanced Mach-Zehnder interferometer

cos12

1)0( P

cos12

1)1( P

1101 ii ee Wave-particle duality

… but that’s not the whole story Multi-photon Interference

Photons have many properties that can be used to encode quantum states

Example: Polarization of a photon

0H1V

12

sin02

cos ie

Polarization QuBit can also be prepared in general state

Poincaré sphere:

qubit:encoding a qubit in polarization via half-wave plate (HWP) with rotatable optical axis:

HWP @ 0º

HWP @ 45º

HWP @ 22.5º

HWP @ -22.5º

D

A

Encoding information in polarization of single photons

0H

V

HWP angle:

HWPPBS

HWP @ 0º :

H or V ?

Detection of polarization-encoded qubits

PBS

Polarization analyzer (Bob-module):

T

R

“click”

HWP

D

A

H

V

Detection of polarization-encoded qubits

HWP @ 22.5º :

D or A ?

PBS

impossible to distinguish H/V and D/A using the same measurement setting

T

R

“click”

HWP

D

A

H

V

Certain properties cannot be known simultaneously

Polarization analyzer (Bob-module):

• Schedule etc.






Outline for today

The history of communication is a history of secure communication

Signal


Transmitter

Information Source

receivedsignal

Destination

Receiver

Alice Bob

The history of communication is a history of secure communication

Skytale

transposition cipher

Enigma

Shannon defined the notion of perfect security


Plaintext: “Hello World”

“Hello Wprld”

Cyphertext: “Yw3sdasd32vy”

Information theoretic security: discovering or intercepting the ciphertext does not provide any information on the plaintext

Secret Key

“Yw3sdasd32vy”

Vernam Cypher

simplest perfectly secure cipher is the Vernam cipher

Gilbert Stanford VernamSECRET SIGNALING SYSTEM. Patented July 22, 1919.

One-time Pad Encryption

Plaintext⊕ Key = Ciphertext

Ciphertext⊕ Key = Plaintext

Only use the one-time pad once:

Ciphertext1 ⊕ Ciphertext2 = Plaintext1 ⊕ Plaintext2

Quantum Key Distribution

Alice and Bob can have an unbreakable code if theyshare newly created identical strings of random bits (one time pad)

101100

101100

Polarization-based BB84 protocol

Quantum Key Distribution

Alice and Bob can have an unbreakable code if theyshare newly created identical strings of random bits (one time pad)

Eavesdropper can be detected via

Errors introduced in the measurement process

101100

101000

Polarization-based BB84 protocol

• Schedule etc.






Outline for today

Entanglement: Multi-partite superposition states

The whole is more than

the sum of its parts (it’s the tensor product) :

General bi-partite states

Only when

Bell- state in not a product (correlation)

Bell States

Maximally Entangled

All information shifted to correlations

We can produce (very good approximations) of maximally-entangled Bell states in the Laboratory

Quizzing Entangled Photons

AB |

? ?

1 or 0 ?

+ or - ?

1 or 0 ?

+ or - ?


A B

1 or 0 ?

+ or - ?

1 or 0 ?

+ or - ?


AB |

1 or 0 ?

+ or - ?

1 or 0 ?

+ or - ?


A B

1 or 0 ?

+ or - ?

1 or 0 ?

+ or - ?

A


A B

1 or 0 ?

+ or - ?

1 or 0 ?

+ or - ?


A B

1 or 0 ?

+ or - ?

1 or 0 ?

+ or - ?

A


AB |

1 or 0 ?

+ or - ?

1 or 0 ?

+ or - ?


A B

1 or 0 ?

+ or - ?

1 or 0 ?

+ or - ?

A

Nope. The quantum correlation of entangled systems is stronger than any correlation local realistic theory would permit…

John S. Bell

correlation + uncertainty = EPR Paradox

Can we resolve the paradox, and “complete” the quantum theory by adding some hidden variables?

And we can show this experimentally!

Quantum Dense Coding

Bob performs one of 4 transformations on his photon

encoded 2 bits of information by the

manipulation of only one bit.

Alice and Bob share Bell – state

Sends photon to Alice who performs Bell – state - measurement

Quantum Dense Coding

Goal: transfer Quantum State from A to B

Quantum Teleportation

A and B share ancillary entangled bits 2,3


Combined quantum state of 1,2,3:

Output


Machine

Input .

EPR Source

U(i)i=1…4

BSMi=1..4

Alice Bob

Input

state

2 Bit of

Classical

information

1 2 3entangled

pair

teleported

state

3

“Teleportation of Entanglement”

Transmission distance / a.u.

Quantum state quality

1

0

Loss and noise limit the maximum transmission distance in fiber



Bell State Measurement

A global “Quantum Internet”

Long-distance satellite links + local fiber networks + quantum repeaters

DelinghaLijiang

Next week: Quantum Information and Photons

Same time, different placeLecture+Seminar

lecture 27616 : quantum communication - uni-jena.de · register for the exam by 24.12.2018....

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