Quantum teleportation is the disembodied transport of an unknown quantum state |ψ〉 from one place to another. All protocols for accomplishing such transport require nonlocal correlations, or entanglement, between systems shared by sender and receiver. The sender is normally called Alice and the receiver is called Bob . Most attention has focused on teleporting the states of finite-dimensional systems, such as the two-dimensional polarization of a photon or the discrete level structure of an atom. First proposed in 1993 by Charles Bennett and his colleagues [17, 24, 138] quantum teleporation thus allows physicists to take a photon or any other quantum scale particle such as an atom and transfer its properties (such as the polarization) to another photon even if the two photons are on opposite sides of the galaxy. This scheme transports the particle’s properties to the remote location and not the particle itself. The state of the original particle must be destroyed to create an exact reconstruction at the other end. This is a consequence of the no cloning theorem. A role in the teleportation scheme is played by an entangled ancillary pair of particles which will be initially shared by Alice and Bob.
Quantum teleportation is the disembodied transport of an unknown quantum state |ψ〉 from one place to another. All protocols for accomplishing such transport require nonlocal correlations, or entanglement, between systems shared by sender and receiver. The sender is normally called Alice and the receiver is called Bob . Most attention has focused on teleporting the states of finite-dimensional systems, such as the two-dimensional polarization of a photon or the discrete level structure of an atom. First proposed in 1993 by Charles Bennett and his colleagues [17, 24, 138] quantum teleporation thus allows physicists to take a photon or any other quantum scale particle such as an atom and transfer its properties (such as the polarization) to another photon even if the two photons are on opposite sides of the galaxy. This scheme transports the particle’s properties to the remote location and not the particle itself. The state of the original particle must be destroyed to create an exact reconstruction at the other end. This is a consequence of the no cloning theorem. A role in the teleportation scheme is played by an entangled ancillary pair of particles which will be initially shared by Alice and Bob.
The science fiction depiction of teleportation refers to the transfer of matter between two spatially separated spaces without the transfer of information. This largely differs from the concept of quantum teleportation, one of the most exciting concepts in modern quantum theory, though often misunderstood.1 The key difference between the sci-fi portrayal and quantum teleportation is that information is transferred between two spatially separated parties, rather than a direct transfer of matter. Applications may include quantum key distribution and quantum cryptography. At the heart of such teleportation is the phenomenon of quantum entanglement, in which the quantum state corresponding to non-local particles cannot be described independently. Sender (Alice) and receiver (Bob) share a pair of particles that are entangled. Alice performs a set of measurements (known as the Bell states analysis) on the state of her particle and that of a third particle (Charlie)—the particle whose state should be teleported to Bob. Based on the outcome of her measurements, Alice sends a signal to Bob. Bob applies a set of unitary transformations, without knowing the state, to the state of his particle. After these transformations, the state of Bob’s particle is identical to Charlie’s. Note that, during this process, Alice and Bob have no information about the state of Charlie’s particle. This process is probabilistic when implemented with entangled photons and linear optics,2 and means that sometimes Alice’s measurement outcome—that of two particles’ Bell states analysis—is not determined. Thus, Bob does not receive any classical signal, and the teleportation fails. Nevertheless, when Bob receives the signal from Alice, the state is the correct one, and teleportation has succeeded with a 100% fidelity. We can use a single particle possessing two different quantum properties to present a non-separable state, where Figure 1. (a) The setup for remote-hybrid-teleportation of photons from the spin to the orbital-angular-momentum degree of freedom (OAM DOF). A UV laser pumps a barium borate (BBO) crystal to generate photon pairs that are entangled in their OAM DOF. A polarizing Sagnac interferometer containing a dove prism (PSI-DP), shown in the inset, in combination with the half-wave plate (H), spatial light modulator (SLM), bandpass interference filter (IF) and single mode optical fiber (SMF) perform the single photon spin-OAM non-separable Bell state measurement.4 The photons couple via a fiber coupler (FC) into the SMF for detection by an avalanche photodiode (APD). The APD triggers the intensified charge-coupled camera (ICCD) to record the spatial distribution of photon B. During the preparation and measurement of photon A, photon B propagates in the delay line (D), compensating for electronic delay. (b) First and second columns show the polarization (SAM) state of C and the OAM state of the teleported photon to B. jLi, jH i, and jV i: left, horizontal, and vertical polarization, respectively. M: Mirror. PBS: Polarizing beam splitter. TEM: Transverse electromagnetic mode—this refers to the fundamental transverse mode (beam with a Gaussian profile). Q: Quarter-wave plate.
Teleportation here is a process by which a quantum state is transferred from one place to another, a bit analogous to the teleportation taking place in Star Trek. Alice (A) has particle 1 in a state φ (1) that she wants to transfer to Bob (B). A source sends one of a singlet pair of particles, particle 2, to A and the other, particle 3, to B. A does a Bell-state measurement on the 1–2 pair. A sends the result to B via normal communication methods, which tells B what transformation should be done on the particle B received, so that the state ends in the original φ (3). Experiments have confirmed the method. The chapter discusses the nature of the two-particle Bell states and how experimenter can measure such states. Teleportation, since it involves information transfer, may have applications in quantum computing.
We suggest a method for teleporting an unknown quantum state. In this method the sender Alice first uses a Controlled-Not operation on the particle in the unknown quantum state and an ancillary particle which she wants to send to the receiver Bob. Then she sends ancillary particle to Bob. When Alice is informed by Bob that the ancillary particle is received, she performs a local measurement on the particle and sends Bob the outcome of the local measurement via a classical channel. Depending on the outcome Bob can restore the unknown quantum state, which Alice destroyed, on the ancillary particle successfully. As an application of this method we propose a quantum secure direct communication protocol.
The beauty of the quantum circuit lies in the fact that it can perform certain tasks which are impossible in the classical world. For example, consider teleportation and superdense coding. Teleportation is a quantum task in which an unknown quantum state is transmitted from a sender (Alice) to a spatially separated receiver (Bob) via an entangled quantum channel and with the help of some classical communications. Dense coding is another communication scheme in which if Alice and Bob share a prior entanglement then one of them can send n bits of classical information to the other by communicating m-qubits (m < n). Before we go into the technical details of these two schemes let us try to lucidly visualize the uniqueness of teleportation. Suppose Alice and Bob are spatially separated and Alice wants to send an unknown quantum state |ψ〉 = α|0〉 + β|1〉 to Bob. For some reason she is not allowed to send the state directly through a quantum channel. She cannot measure it and send the information to Bob because the moment she will try to measure the state, it will collapse either to |0〉 or to |1〉. But the state can be sent by using a simple quantum circuit (pre-shared entanglement) and some classical communications. In the process the unknown quantum state gets destroyed at Alice’s end and reappears at Bob’s end. The state never exists in the communication channel. This process is called quantum teleportation. The uniqueness of quantum teleportation will be clearer if we note that the Fax is not an example of teleportation because the original copy remains with the sender. Again a letter posted in a letter box is not an example of teleportation because the letter exists (travels) in its original form in the communication channel. In brief, there is no classical analogue of quantum teleportation. The same is true for dense coding. In this chapter we will describe these two unique quantum communication schemes and discuss their significance and applications.
FINDING: Quantum teleportation is a protocol for transferring an unknown quantum state via shared entanglement and classical communication — not physical matter transport. The core math is the Bell basis projection and the Pauli correction operators. MATH: - State to teleport: ∣ψ⟩=α∣0⟩+β∣1⟩, with ∣α∣2+∣β∣2=1. - Shared entangled pair: Bell state ∣Φ+⟩=21(∣00⟩+∣11⟩). - Total 3-qubit state: ∣ψ⟩⊗∣Φ+⟩. - Alice performs Bell measurement — projecting onto one of 4 Bell states: ∣Φ±⟩=21(∣00⟩±∣11⟩), ∣Ψ±⟩=21(∣01⟩±∣10⟩). - Outcome determines Pauli correction on Bob's qubit: I,X,Z,XZ (identity, bit-flip, phase-flip, both). - No-cloning theorem: the original state is destroyed — information is transferred, not copied. - Classical communicati Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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.