How Superdense Coding Works

To begin discussing superdense coding, it is important to understand its classical counterpart. Let’s say that Alice wants to communicate a number from one to four to Bob. Each person, Alice and Bob, would each need 2 bits to represent this where sending/receiving 00 would equate to a 1, a 01 would equate to receiving a 2, and so on. However, with superdense coding, Alice and Bob wouldn’t need to use a total of 4 bits.

Superdense coding uses quantum entanglement to communicate information by sending half as many qubits as classical bits. This is done using the four different bell states that are maximally entangled.

Superdense coding is a particular protocol for quantum communication. With that, there are several phases to it.

Phase 0: Sharing

Phase 0 is the first phase, also known as the sharing phase, that happens before the actual protocol. The first step of this phase is to create the first bell state.

The second step of this phase is to create a decision scheme using the four bell states. To keep it simple, below will be the decision scheme for this example.

This decision scheme must be agreed upon and known by both parties: Alice and Bob. The final step of this phase is for each party to take one qubit that has been prepared and is entangled. Since Alice is the sender, she will keep qubit 0, the qubit that controls the CX gate and Bob will take qubit 1, the target qubit from the CX gate. This does not mean they are measuring the qubits though.

Phase 1: Sending

The second phase is Phase 1, also known as the sending phase. The first step of this phase is to decide which gates to apply on the qubit to create the message based on the decision scheme for each bell state. Based on our earlier example, let’s say Alice wants to send Bob a 2, this equates to 01 as notated before. In the decision scheme, this lines up with the second bell state.

Alice will then apply a Z gate to her qubit to change the circuit to the second bell state. The second step of this phase is to send the qubit to the receiver. Practically, this may be done via an optic fiber cable.

Phase 2: Receiving & Measuring

The final phase, Phase 2, is for receiving and measuring the qubits. The first step is for the receiver to measure the qubits. However, Bob can’t just directly measure the qubits because the outcome will be probabilistic. He won’t know which state Alice was trying to communicate, since the two possible states of measuring the second bell state are 00 and 11. To solve this, Bob will apply the same gates that were initially used to create the bell state, but in reverse. This will cancel out the entanglement and superposition. The gates he applies are the CX gate then the H gate. Depending on the decision scheme, the receiver may also need to apply one or two X gates to get the correct output.

After measuring this circuit, the last step is for the receiver, Bob, to read the message based on the bell state, which will turn out to be what Alice sent, a 2.

As seen in this example, superdense coding uses half the number of qubits to send the same amount of information classically with bits. This is one of the main advantages of using this protocol. However, one of the main challenges right now is due to the noise of quantum computers. Due to this heavy noise, superdense coding can’t be used in an efficient manner.