Understanding Superdense Coding
An in-depth explanation and tutorial of Superdense Coding, a very important quantum communication protocol.
What is it?
Superdense coding is a quantum communication protocol that allows a sender to send two classical bits of information to another user by only utilizing one qubit.
Superdense coding was first proposed by Charles Bennett and Stephen Wiesner in 1992 and experimentally actualized four years later, in 1996.
Now, it is important to note that while Superdense Coding and Quantum Teleportation are closely related, there is a key difference between them. Quantum teleportation is a process by which a user can transmit one qubit using two classical bits whereas Superdense Coding is a process by which a user can transmit two classical bits using one qubit. Basically, Superdense Coding can be thought of as the flipped version of Quantum Teleportation.
Superdense coding involves three parties, let’s just call them Charlie, Alice and Bob. It requires two parties who wish to communicate a two-bit message, a pair of entangled qubits, and a quantum channel.
Charlie prepares a pair of Bell state, or maximally entangled, qubits, which just means that the two qubits exhibit perfect correlations even though they are spatially seperated (even with great distances).
Charlie then sends those qubits to Alice and Bob so that they can share them between themselves (1 qubit with Alice and the other with Bob). However, before Alice can attempt to transmit 2 classical bits of infortmation to Bob using her Bell state qubit, she has to apply a single gate operation based off of the intended message:
Now, Bob is a very smart guy. He knows that since Alice’s qubits are entangled the two qubits must be in one of the four Bell states. So, once Bob recieves Alice’s encoded qubit, he will pass it and his untouched Bell state qubit through a reverse Bell circuit (where Alice’s qubit acts as the control and Bob’s is the target) in order to decode Alice’s message. Thus, Bob will obtain two classical bits of information from a single qubit!
Superdense Coding, along with Quantum Teleportation, is the underlying principle of secure quantum coding since it eliminates the possibility of eavesdroppers intercepting messages.
Let’s say an eavesdropper named Eve intercepted Alice’s encoded qubit en rout to Bob. Eve would only have 1/2 of an entangled state and without access to Bob’s qubit (which is necessary to decode Alice’s qubit), Eve would have no way of getting the information from Alices qubit. Furthermore, any attempt to measure either Alice’s or Bob’s qubit would collapse the state of said qubit and alert both of them.
Coding it in Qiskit
Now that we have a foundational undertsanding about Superdense Coding, we can utilize Qiskit, an open-source software development kit for working with quantum computers, to test it out. You can access their official tutorial here.
1. Import the neccessary packages
2. Create the entangled qubit pair by applying an H-gate followed by a CNOT in a 2 qubit circuit
3. Encode message with appropriate gates
4. Decode message by applying a CNOT followed by a H-gate
Here’s a visual representation of the quantum circuit:
Other than providing a very secure way of transmitting infortmation, Superdense Coding (and quantum infortmation in general) allows you to provide some resource in advance, way before deciding what the content is that you want to send and before you actually decide to communicate said content. It allows you to do the least amount of work neccesary in the instant you decide to sent some information over to Bob.
Furthermore, Superdense Coding also allows for two times faster classical bit transfer compared to classical transmissions.
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