Teleportation entanglement

Besides quantum computations, entanglement has also been at the core of other active research such as quantum teleportation [32, 33], dense coding [34, 35], quantum communication [36], and quantum cryptography [37]. It is believed that the conceptual puzzles posed by entanglement have now become a physical source of novel ideas that might result in applications. 

Following is a highly idealized account of how one might teleport the quantum state of a boson. Consider a boson which has just two possible states, say, x and y—like a photon with its two polarizations. Suppose that we have boson 1 in an arbitrary state I (l) = a x ) b y ), where a and b are complex coefficients. We let this state become entangled with the two-boson state x2, which is the... 

Finally, I would like to say a few words about entanglement in communication, as the last caveat to the Jozsa-Linden theorem. I will just use the example of quantum teleportation. 

In the absence of shared entanglement between Alice and Bob the mean fidelity of the output state F = (t/.jpout t/, ) is bounded. For example, for teleporting qubits, F < 2/3, whereas for the teleportation of coherent states in an infinite-dimensional Hilbert space it is bounded by F < 1/2 [Braunstein 2000 (b)]. 

Fidelities beating these bounds have been achieved experimentally when the sender and receiver share entanglement. So teleportation is a success and entanglement really matters. 

Entanglement is a vital information resource employed in quantum teleportation, dense coding and quantum computation [Nielsen 2000], The fundamental role played by the entanglement in quantum information science was discussed in part I this part of the book is devoted to the generation and characterization of the entanglement of photons and their usage in quantum communication and computation protocols. 

A proposal for spin state teleportation was given in Ref. [Duan 2000 (d)]. Three atomic samples are needed as shown in Fig. 3 (a). Adjacent samples are oriented oppositely along the rc-axis so that both collective measurements on cells 1 and 2 and on cells 1 and 3 will be regular entangling interactions as... 

Figure 3. (a) Teleporting an unknown quantum state first cells 1 and 2 are entangled. Then... 

One may envision extensions of the present approach to matter teleportation [Opatrny 2001] and quantum computation based on continuous variables [Braunstein 1998 (a) Lloyd 1998 Lloyd 1999], Such extensions may involve the coupling of entangled atomic ensembles in optical lattices by photons carrying quantum information. 

A research group at the University of [nnsbruck used entangled quantum states to perform teleportation of a photon state that is, to prepare at a distance any state of a photon with simultaneous disappearance of this state from the teleportation site (details are given at the end of this chapter). 

The teleportation protocol was proposed by Bennett and coworkers, and applied by Anton Zeilinger s group. The latter used the entangled states (EPR effect) of two photons described above. ... 

Assume that photon A (number 1) from the entangled state belongs to Alice, and photon B (number 2) to Bob. Alice and Bob introduce a common fixed coordinate system. Both photons have identical polarizations in this coordinate system, but neither Alice nor Bob knows which. Alice may measure the polarization of her photon and send this information to Bob, who may prepare his photon in that state. This, however, does not amount to teleportation because the original state could be a linear combination of the 0) (parallel) and 1) (perpendicular) states. 

It turned out that in the Bohr-Einstein controversy, Bohr was right. The Einstein-Podolsky-Rosen paradox resulted (in agreement with Bohr s view) in the concept of entangled states. These states have been used experimentally teleport a photon state without violating the Heisenberg uncertainty principle. Also, the entangled states stand behind the idea of quantum computing with a superposition (qubit) of two states a 0) + b l) instead of 0) and 1) as information states. 

P. van Loock S. L. Braunstein. Multipartite Entanglement for Continuous Variables A Quantum Teleportation Network. Physical Review Letters 1999 Jun 17 84(15) 3482-3485. 

Entangled states constitute a powerful natural resource for QIP. In this section, two of the most interesting applications are illustrated superdense coding and the teleport. 

Teleport is a process through which the state of a qubit is transferred to another, using the non-local properties of entangled states [17]. Differently from superdense coding, no qubit is transferred in teleport, but only a quantum state. 

In the simplest case of teleport, three qubits are involved, two with Alice (let s label them lira)) and one with Bob (labelled fc . As in the superdense coding process, initially Alice and Bob qubits, a) and b), are in a cat state. Alice wishes to transmit to Bob the unknown state of a third qubit, IV ) = a 0> -I- 8 1>. Of course, she cannot measure ir), for she would only get 0 or 1, with the probabilities a and p, respectively. The quantum circuit that describes the teleport process is illustrated in Figure 3.8, where the top line represents the qubit Alice wants to teleport to Bob ( V >), and the second and third lines, represent the entangled qubit pair, the second one with Alice and the third one with Bob. 

Figure 6.2 Entanglement fidelity obtained from the teleportation experiment of Nielsen, Knill and Laflamme. The top curve represents the full teleportation experiment, and the bottom one the control experiment. Adapted with permission from [11].

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