Implementation of QKD BB84

Summary

The video script delves into the implementation of the BB8 protocol for quantum key distribution (QKD), which utilizes the polarization of single photons to encode key bits. It explains the rectilinear and diagonal bases and their respective polarizations. The script outlines the process of QKD, from Alice's random bit string generation to Bob's secure photon measurements, and the subsequent key extraction. It also discusses the security aspect by illustrating how an eavesdropper, Eve, introduces discrepancies by measuring and retransmitting photons, which can be detected by Alice and Bob. The use of Q-Scape simulations on the IBM platform with poly Xcode and Hadamard gates is highlighted to demonstrate the quantum circuit's functionality and security.

Takeaways

• 🔐 Quantum Key Distribution (QKD) BB-8 is the first protocol for secure communication using the polarization state of single photons.
• 🌟 The BB-8 protocol utilizes two bases for encoding: rectilinear (0-degree horizontal and 90-degree vertical polarization) and diagonal (45-degree diagonal and 135-degree anti-diagonal polarization).
• 🛰️ The four possible quantum states for encoding bits are 0, 1, +1, and -1, derived from the two bases.
• 💡 QKD BB-8 is simulated using Q-Scape simulations on the IBM platform, with gates like the Pauli-X gate for bit value creation and the Hadamard gate for superposition.
• 🔬 The security of the key exchange is verified by measuring and comparing the bases; if they match, the exchange is secure.
• 👤 The implementation of BB-8 requires a team consisting of Alice (sender), Bob (receiver), an authenticated public classical channel, and a potentially insecure private quantum channel.
• 🔄 Alice generates a random bit string and encodes it using photons with random polarization from the four possibilities.
• 🔍 Bob randomly decides the measurement basis for each photon and records the results, only announcing his choice of measurement bases through the classical channel.
• 🕵️‍♀️ Eavesdropper Eve's presence is detected if there is inconsistency in the measurement results and the agreed-upon bases between Alice and Bob.
• 🔄 The key is obtained by Alice and Bob agreeing on the measurement results for more than 25% of the bases and discarding the rest.
• 🚫 Eve cannot break the security of BB-8 as her measurements disturb the quantum system, leading to detectable discrepancies in the key exchange.

Q & A

What is the BB8 protocol?

The BB8 protocol is the first quantum key distribution protocol, which uses the polarization state of single photons to encode key bits for secure communication.

What are the two bases used to represent a bit in BB8 protocol?

The two bases used are the rectilinear basis, which consists of 0-degree horizontal and 90-degree vertical polarization, and the diagonal basis, which consists of 45-degree diagonal and 135-degree anti-diagonal polarization.

What are the four possible quantum states in the BB8 protocol?

The four possible quantum states are 0 and 1 from the rectilinear basis, and plus and minus from the diagonal basis.

How does one access the quantum computer for BB8 simulations?

The BB8 simulations are accessed using Q-Scape simulations on the IBM platform.

What are the two main gates used in the BB8 simulation?

The two main gates used are the Pauli-X gate, which allows the conversion of the state of the qubit, and the Hadamard gate, which creates a superposition of 0 and 1.

What does the histogram in the BB8 simulation represent?

The histogram represents the probability of Alice and Bob having the same qubits, indicating a secure key exchange, or Bob receiving different qubits from Alice, indicating a potential eavesdropper.

How does the BB8 protocol ensure the detection of an eavesdropper?

By comparing the bases used for encoding and measurement, if there is an inconsistency or disagreement, it suggests that an eavesdropper has tampered with the key exchange.

What are the roles of Alice and Bob in the BB8 protocol?

Alice is the sender who chooses a random bit string and encodes it using photon polarization. Bob is the receiver who measures the photons in randomly chosen bases and communicates with Alice through a classical channel.

What is the purpose of the authenticated public classical channel in the BB8 protocol?

The authenticated public classical channel is required for Alice and Bob to securely exchange information about their chosen measurement bases without the risk of tampering.

How does the BB8 protocol handle the presence of an eavesdropper?

The BB8 protocol assumes an eavesdropper may intercept and measure the photons. However, due to the nature of quantum measurement, any attempt to measure will disturb the system, leading to detectable discrepancies in the key exchange between Alice and Bob.

What is the process for Alice and Bob to obtain the final key in the BB8 protocol?

Alice and Bob first discard bits where their chosen bases do not match. Then, they discuss a subset of the remaining bits to check for eavesdropping. If no discrepancies are found, the remaining bits become the final key.

Outlines

00:00

🔐 Introduction to Quantum Key Distribution with BB8-4 Protocol

This paragraph introduces the BB8-4 protocol, the first quantum key distribution method, which utilizes the polarization state of single photons to encode key bits. The key bits can be represented using two bases: rectilinear (0-degree horizontal and 90-degree vertical polarization) and diagonal (45-degree and 135-degree polarization). The speaker explains how they accessed a quantum computer via Q-Scape simulations on the IBM platform, using specific quantum gates like the poly Xcode and Hadamard gate to manipulate qubits. The simulation circuit is described, highlighting the process of encoding and measuring qubits to ensure a secure key exchange between Alice and Bob. The presence of an eavesdropper, Eve, is also discussed, with the simulation showing how her interference can be detected, thus proving the security of the BB8-4 protocol.

05:01

🕵️‍♀️ Eavesdropping Detection in Quantum Key Distribution

The second paragraph delves into the scenario where an eavesdropper, Eve, attempts to intercept the quantum communication between Alice and Bob. It outlines the steps taken by Alice to generate and send photons with random polarization, and how Eve's interception and measurement of these photons in randomly chosen bases inevitably disturbs the quantum system. This disturbance results in discrepancies when Bob measures the photons, which he receives from Eve rather than directly from Alice. The protocol involves Alice and Bob comparing their measurement bases through a classical channel, discarding bits where the bases do not match, and then checking a subset of the remaining bits to detect any inconsistencies caused by eavesdropping. The paragraph concludes by emphasizing that Eve's actions, while potentially allowing her to learn some information, also introduce detectable errors, thus maintaining the security of the quantum key distribution process.

Keywords

💡Quantum Key Distribution

Quantum Key Distribution (QKD) is a method for two parties to produce a shared random secret key, which can be used to encrypt and decrypt messages, ensuring secure communication. In the context of the video, BB8 is the first QKD protocol, which uses the quantum properties of photons to encode information for the key. The script explains how QKD works and its significance in maintaining the security of the key exchange.

💡Polarization State

The polarization state of a photon refers to the direction of the photon's electric field oscillation. In the script, it is mentioned that the BB8 protocol encodes key bits using the polarization state of single photons. The two bases used are the rectilinear basis (0-degree horizontal and 90-degree vertical polarization) and the diagonal basis (45-degree diagonal and 135-degree anti-diagonal polarization), which are essential for creating the four possible quantum states for the key bits.

💡Q-Scape Simulations

Q-Scape simulations refer to the use of a quantum computing platform to simulate quantum circuits and algorithms. In the video, the presenter uses Q-Scape simulations on the IBM platform to demonstrate the BB8 protocol. This is an example of how quantum computing can be used to test and understand quantum cryptographic protocols like BB8.

💡Pauli-X Gate

The Pauli-X gate, also known as the bit-flip gate, is a quantum gate that flips the state of a qubit from |0⟩ to |1⟩ and vice versa. In the script, the Pauli-X gate is used to create a bit value of 1 in the quantum circuit simulation, which is crucial for encoding the key bits in the BB8 protocol.

💡Hadamard Gate

The Hadamard gate is a quantum gate that creates a superposition of quantum states. It is used to put a qubit into a state where it has equal probability of being measured in the |0⟩ or |1⟩ state. In the context of the video, the Hadamard gate is applied to create superpositions when the diagonal basis is chosen for encoding the key bits.

💡Alice

In the context of the video, Alice represents the sender in the BB8 protocol. She is responsible for choosing a random bit string and encoding it onto photons using different polarization states. Alice's actions are central to the process of key generation in QKD, as she initiates the secure communication by sending the encoded photons to Bob.

💡Bob

Bob is the receiver in the BB8 protocol. He randomly decides the measurement basis for each photon he receives from Alice. If Bob's choice of measurement basis matches Alice's encoding basis, he can correctly interpret the bit value. The script describes how Bob's measurements and subsequent communication with Alice are crucial for establishing the shared secret key.

💡Eve

Eve represents the eavesdropper in the BB8 protocol. She is assumed to intercept the photons sent by Alice, measure them, and then forward them to Bob. The script explains how Eve's actions can potentially disturb the quantum system, leading to detectable discrepancies in the measurements, which can be used to identify her presence and ensure the security of the key exchange.

💡Rectilinear Basis

The rectilinear basis is one of the two bases used in the BB8 protocol for encoding the key bits onto photons. It consists of 0-degree horizontal and 90-degree vertical polarization states. The script highlights that if Bob measures a photon in the rectilinear basis that was encoded with a 0 or 1, he will correctly interpret the bit value, assuming no eavesdropping has occurred.

💡Diagonal Basis

The diagonal basis is the other basis used in the BB8 protocol for encoding key bits. It consists of 45-degree diagonal and 135-degree anti-diagonal polarization states. The script explains that when the diagonal basis is chosen, a Hadamard gate is applied to create a superposition, and Bob's measurement basis must match Alice's choice for accurate bit interpretation.

💡Measurement

Measurement in quantum mechanics refers to the act of observing a quantum system, which causes the system to collapse into one of its possible states. In the context of the video, Bob's measurement of the photons' polarization states is a critical step in determining the shared key. The script also discusses how Eve's measurement of the photons can introduce errors, which can be detected, thus ensuring the security of the key exchange.

Highlights

Introduction of the BB8 protocol, the first quantum key distribution protocol.

Use of the polarization state of single photons to encode key bits.

Two bases for bit representation: rectilinear and diagonal.

Four possible quantum states for encoding bits: 0, 1, +, -.

Accessing a quantum computer through Q-Scape simulations on the IBM platform.

Use of the Pauli-X gate for state conversion and the Hadamard gate for superposition.

Simulation circuit without Eve, using five bits and key exchange security.

Histogram showing Alice and Bob having the same qubits with a probability of 1.

Simulation with Eve, demonstrating the detection of eavesdropping.

Requirement of an authenticated public classical channel between Alice and Bob.

Role of Alice as the sender and Bob as the receiver in the quantum key distribution.

Process of Alice choosing a random bit string and photon polarization.

Bob's random choice of measurement basis for each photon.

Special properties of the rectilinear and diagonal bases in information loss.

Bob's method of obtaining meaningful data from half the photons detected.

Process of Alice and Bob comparing bases and discarding mismatches.

Verification of measurement results and formation of the key.

Introduction of Eve as an eavesdropper intercepting Alice's photons.

Eve's impact on the system by measuring and retransmitting photons.

Detection of eavesdropping through inconsistencies in measurement results.

Eve's inability to break the security of the BB8 protocol.

Conclusion on the security of the BB8 quantum key distribution protocol.

Transcripts

hello everyone today I'm going to

introduce you to my topic that is

implementation of quantum key

distribution

bb-8 for bb-8 for is the first quantum

key distribution protocol and it uses

the polarization state of single photons

to encode the key bits therefore a bit

can be represented by polarizing the

photon in either of the two bases first

rectilinear basal which consists of 0

degree horizontal and 90 degree vertical

polarization second diagonal basis which

consists of 45 degree diagonal and 135

degree anti-diagonal polarization the

four possible quantum states are 0 1

from the rectilinear basis plus minus

from the diagonal basis how to access

the quantum computer I did this by using

Q scape simulations on IBM platform

there are two main gates used for the

simulation first is the poly Xcode which

allows to convert the state of the qubit

and the other is the high Hadamard gate

which allows to create a superposition

of 0 and 1 this is my circuit for the

simulation without Eve with five of bits

where I apply the x-naught gate to

create the bit value 1 and Hadamard gate

to create superpositions whenever

diagonal basis is chosen measurement and

comparing the basis tells if the key

exchange is secure the histogram

represents that Alice and Bob have the

same qubits with probability equal to 1

similarly this is my circuit for the

simulation of the circuit with 5 bits

kiss-kiss circuit with Eve measurement

and comparing the basis tells if the key

exchange has been tampered the histogram

represents that the qubits received by

Bob are not the same sent by Alice with

the probability of 1

my result is that if comparison of bases

agree and alison bob find no

inconsistency eavesdropper can be

detected thus bd8 phone is secure now

the question is who and what do we need

for this implementation so let's meet

the team firstly there is alice the

sender then there is bob the receiver an

authenticated public classical channel

between them is required which means

that all the information exchanged using

this channel is secured a private

quantum Channel which may not be secure

and following other steps step one Alice

chooses a random bit string step 2 to

create a photon Alice randomly chooses a

polarization from the four possibilities

and so her photons look like this then

using the quantum Channel Alice sends

the string of photons to Bob Bob decides

randomly for each photon whether to

measure the photon in rectilinear

polarization or its diagonally

realization what is so special about

these bases all information is lost when

one attempts to measure the rectilinear

polarization of a diagonal photon or

vice versa if Alice sends 0 or 1 and Bob

happens to choose the rectilinear basis

then his measurement will pick out the

correct state and his bit assignment

will exactly match the one Alice sent

but if he chooses the rectilinear basis

for a photon plus or minus then a

measurement on plus and minus will yield

0 or 1 with equal probability

due to the rectilinear basis similarly

if the diagonal basis is used for 0 or 1

the result will be random

Bob obtains meaningful data from only

half the photons he detects those for

which he guessed the correct

polarization basis

for each bit Bob records the results of

the measurements but keeps them secret

Bob announces to the classical channel

only his choice of measurement bases

alice compares the bases announced by

Bob with bases chosen by her and answers

of the encoding bases and a measurement

bases agree for each bit they discard

the positions that do not have the same

bases chosen by both of them then they

discuss the positions of more than 25%

of the bases from the correct bases to

check the measurement results and the

measurement result is verified for those

bases the other results from the correct

bases become the key and this is how the

key is obtained now we have an

additional person in the system Eve the

eavesdropper who wants to intercept the

information shared by Alice and Bob we

assume an attack that Eve intercepts

Alice photons measures them in randomly

chosen bases and forward the photons to

Bob now we will see how it will affect

the system step 1

Alice chooses a random bit string step 2

for each photon Alice randomly chooses

the polarization from the four

possibilities and this is how Alice

photons will look like but before Alice

could send these photons to Bob Eve

intercepts the photons Eve decides

randomly for each photon whether to

measure the photons rectilinear or

diagonally pollenization but the act of

measuring a quantum system disturbs the

system and because of the wrong

prediction of some bases Eve could not

produce the exact same photons as Alice

to send to Bob and therefore Eve sends

his version of Alice photons to Bob Bob

decides randomly for each photo

whether to measure the photons

rectilinear or diagonally ization for

each bit Bob records the results of the

measurements but keeps them secret and

through the classical channel only his

choicest measurement bases as he would

do if he was not present is announced

eve has full access to the announced

information on the classical channel but

she can only listen and cannot tamper

with the signals alice compares the

basis announced by Bob with the basis

chosen by her Alice answers if the

encoding basis and the measurement basis

agree for each bit they discard the bit

positions that do not have the same

basis chosen by both of them then they

discuss the positions of more than 25%

of the basis from the correct basis to

check the measurement results due to the

eats interception the measurement

results are not correct and this is how

eavesdropping is detected so can Eve

brings the security and the answer is if

it decides to measure and retransmit all

the photons which intercepts she may

learn the correct polarization for half

of the photons but at the same time this

action of force induces a disagreement

to about 1/4 of the photons which Bob

may measure during using direct basis

thus if cannot break the security thank

you