Superdense Coding (Quantum Protocols)

Quantum information protocols enable tasks that are impossible to achieve with classical methods. One such remarkable protocol is Superdense Coding. 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. Before diving into the details, let’s review some foundational concepts.

Circuit Diagram

In the circuit diagram, we have two sections: Alice’s section and Bob’s section, separated by a dashed line. Here’s what the lines represent:

• Parallel lines (→) indicate the flow of classical information.
• Single lines (→) indicate the flow or evolution of quantum information.

Initial Setup

Initially, Alice has two classical bits and one quantum bit (qubit). This qubit is entangled with Bob’s qubit. The key idea here is that through the communication of one quantum bit from Alice to Bob, Alice can effectively communicate two classical bits of information to Bob. This phenomenon is known as Superdense Coding, as it compresses two classical bits of information into a single quantum bit.

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The Process

1. Entanglement: Alice and Bob share an entangled pair of qubits. Let’s denote Alice’s qubit as QA and Bob’s qubit as QB​. Initially, the entangled state can be represented as:

Encoding: Alice encodes her two classical bits (let’s say 00, 01, 10, or 11) into her qubit QA. She applies a combination of quantum gates .

Initially, Alice has two classical bits and one Quantum bit (Qubit) and that one Qubit is entangled with the Bob’s qubit.

CIRCUIT DIAGRAM

• Transmission: Alice sends her qubit QA ​ to Bob.
• Decoding: Bob now has both qubits QA and QB . He applies a CNOT gate (with QA ​ as control and QB as target) followed by a Hadamard gate to QA ​. Finally, Bob measures both qubits to retrieve the two classical bits.

Here in this following table we can see that how the two classical bit information is transmitted via single Quantum bit ,and by manipulating the entangled qubits with Hadamard and cnot gate. will be getting the exact similar information as quantum information as ii is in the classical information