Superdense Coding and Quantum Teleportation

What is it?

Superdense Coding is a quantum communication protocol that allows for a sender to send two classical bits of information to another user by utilizing only one qubit. This algorithm takes advantage of something called a ‘bell circuit’. A bell circuit is a combination of a "Hadamard gate" going into the control bit of the controlled not gate.

A two qubit bell circuit will have an equal probability of getting either 00 or 11 as results. (Assuming the computer is noiseless.)

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.

How it works?

In the superdense coding algorithm we have three different users.

User1: The first user shares the two outputs of a two qubit bell state with the receiver and the sender.

User2: The second user who is the sender, encodes the qubits.

User3: The final user receives those qubits and decodes them.

To understand the working consider the following scenario: It requires two parties who wish to communicate a two-bit message, a pair of entangled qubits, and a quantum channel.

User1 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 separated (even with great distances).

User1 then sends those qubits to User2 and User3 so that they can share them between themselves (1 qubit with User2 and the other with User3). However, before User2 can attempt to transmit 2 classical bits of information's to User3 using User2 Bell state qubit, User2 has to apply a single gate operation based off of the intended message:

User2 qubits are entangled the two qubits must be in one of the four Bell states. So, once User3 receives User2 encoded qubit, User3 will pass it and the untouched Bell state qubit through a reverse Bell circuit (where User2 qubit acts as the control and User3 is the target) in order to decode User2 message. Thus, User3 will obtain two classical bits of information from a single qubit!

A good thing to try and think about is how a bell state truly works. Think about it, the control bit is entangled with the not gate. So when we set the control bit into a super position it also changes the target bit to a superposition as well, because they are entangled.

We can denote the bell state mathematically like so

With those rules in consideration, the final design will look like this;

Security

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 intruder will intercept User2 encoded qubit en rout to User3. The intruder would only have 1/2 of an entangled state and without access to User3’s qubit (which is necessary to decode User2’s qubit), intruder would have no way of getting the information from User2's qubit. Furthermore, any attempt to measure either User2’s or User3’s qubit would collapse the state of said qubit and alert both of them.

Advantages

Other than providing a very secure way of transmitting information, Superdense Coding (and quantum information 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. Furthermore, Superdense Coding also allows for two times faster classical bit transfer compared to classical transmissions.