We are now ready to look at our first protocols for quantum information. In this section, we examine two communication protocols which can be implemented using the tools we have developed in the preceding sections. These protocols are known as superdense coding and quantum teleportation. Both are inherently quantum: there are no classical protocols which behave in the same way. Both involve two parties who wish to perform some communication task between them. In descriptions of such communication protocols (especially in cryptography), it is very common to name the two parties ‘Alice’ and ‘Bob’, for convenience. We will follow this tradition. We will repeatedly refer to communication channels. A quantum communication channel refers to a communication line (e.g. a fiberoptic cable), which can carry qubits between two remote locations. A classical communication channel is one which can carry classical bits (but not qubits).1 The protocols (like many in quantum communication) require that Alice and Bob initially share an entangled pair of qubits in the Bell state The above Bell state is sometimes referred to as an EPR pair. Such a state would have to be created ahead of time, when the qubits are in a lab together and can be made to interact in a way which will give rise to the entanglement between them. After the state is created, Alice and Bob each take one of the two qubits away with them. Alternatively, a third party could create the EPR pair and give one particle to Alice and the other to Bob. If they are careful not to let them interact with the environment, or any other quantum system, Alice and Bob’s joint state will remain entangled. This entanglement becomes a resource which Alice and Bob can use to achieve protocols such as the following. Suppose Alice wishes to send Bob two classical bits of information. Superdense coding is a way of achieving this task over a quantum channel, requiring only that Alice send one qubit to Bob. Alice and Bob must initially share the Bell state Suppose Alice is in possession of the first qubit and Bob the second qubit.
This study presents a generalized
n--bit superdense coding protocol that enables the transmission of n classical bits of information using an entangled
n--qubit quantum system and the transmission of
n−1 qubits. The protocol involves creating a maximally entangled
n--qubit GHZ state, encoding the classical message with Pauli--Z and Pauli--X gates, and then transmitting and decoding the message via quantum communication, quantum operations, and measurements. The key novelty of this work is an explicit, scalable
n--bit encoding routine, realized on the GHZ channel with a low--depth encoding layer using only single--qubit Pauli--X and Pauli--Z operations.
The protocol was tested on real quantum hardware using Qiskit 2.0 and the IBM--Fez quantum computer for message lengths of 4, 6, 8, and 10 bits, as a circuit--level proof of concept on a single processor; the physical transmission of qubits between the parties was not implemented. Results show that success rates decrease as message length, transpiled circuit depth and gate count increase; the latter two are set mainly by transpilation rather than by the encoding itself. A mutual information analysis shows that the transmitted information exceeds the classical bound of
n−1 bits only for short messages. Strategies to improve performance include sending messages in shorter segments and advances in qubit coherence and gate fidelity. This work offers a practical and easily scalable quantum communication protocol with potential applications in quantum networks and communication systems.
We explicitly show a protocol in which an arbitrary two qubit state $\ensuremath{\mid}\ensuremath{\phi}⟩=a\ensuremath{\mid}00⟩+b\ensuremath{\mid}01⟩+c\ensuremath{\mid}10⟩+d\ensuremath{\mid}11⟩$ is faithfully and deterministically teleported from Alice to Bob. We construct the 16 orthogonal generalized Bell states that can be used to teleport the two qubits. The local operations Bob must perform on his qubits in order to recover the teleported state are also constructed. They are restricted only to single-qubit gates. This means that a controlled-NOT gate is not necessary to complete the protocol. A generalization where
N qubits are teleported is also shown. We define a generalized magic basis, which possesses interesting properties. These properties help us to suggest a generalized concurrence from which we construct a measure of entanglement that has a clear physical interpretation: A multipartite state has maximum entanglement if it is a genuine quantum teleportation channel.
This chapter is concerned with the measure of information contained in qubits . This can be done only through quantum measurement , an operation that has no counterpart in the classical domain. I shall first describe in detail the case of single qubit measurements, which shows under which measurement conditions “classical” bits can be retrieved. Next, we consider the measurements of higher-order or n -qubits. Particular attention is given to the Einstein–Podolsky–Rosen (EPR) or Bell states , which, unlike other joint tensor states, are shown being entangled . The various single-qubit measurement outcomes from the EPR–Bell states illustrate an effect of causality in the information concerning the other qubit. We then focus on the technique of Bell measurement , which makes it possible to know which Bell state is being measured, yielding two classical bits as the outcome. The property of EPR–Bell state entanglement is exploited in the principle of quantum superdense coding , which makes it possible to transmit classical bits at twice the classical rate, namely through the generation and measurement of a single qubit. Another key application concerns quantum teleportation . It consists of the transmission of quantum states over arbitrary distances, by means of a common EPR–Bell state resource shared by the two channel ends. While quantum teleportation of a qubit is instantaneous, owing to the effect of quantum-state collapse, it is shown that its completion does require the communication of two classical bits , which is itself limited by the speed of light.
Abstract Superdense coding uses entanglement as a resource to communicate classical information efficiently through quantum channels. A superdense coding method is optimal when its capacity reaches Holevo bound. We show that for optimality, maximal entanglement is a necessity across the bipartition of Alice and Bob, but neither absolute nor genuine multipartite entanglement is required. Unlike the previous schemes, which can transmit either even or odd bits of information, we demonstrate a generalized dense coding protocol using the genuine multipartite entangled GHZ state to send arbitrary information bits. Expressed in the eigenbasis of different Pauli operators, GHZ state is characterized by a unique parity pattern which enables us to formulate a security checking technique to ensure absolute security of the protocol. We show this method is better applicable in a scenario, where the initial information is distributed among spatially separated parties. Finally, optimizing the number of qubit(s) sent to Bob, we construct a distributed dense coding method, which completely depicts absolutely secure quantum communication between many to one party.