Probabilistic teleportation and entanglement matching

Abstract

Teleportation may be taken as sending and extracting quantum information through quantum channels. In this report, it is shown that to get the maximal probability of exact teleportation through partially entangled quantum channels, the sender (Alice) need only to operate a measurement which satisfy an "entanglement matching" to this channel. An optimal strategy is also provided for the receiver (Bob) to extract the quantum information by adopting general evolutions. PACS Number(s) 03.67 * , 03.65.BzQuantum teleportation, the process that transmits an unknown qubit from a sender (Alice) to a receiver (Bob) via a quantum channel with the help of some classical information, is originally concerned by Bennett, Brassard, Crepeau, Jozsa, Peres, and Wootters (BBCJPW) [1]. In their scheme, such a quantum channel is represented by a maximally entangled pair (any of the Bell states) and the original state could be deterministically transmitted to Bob.The process of teleportation may be regarded as sending and extracting quantum information via the quantum channel. We will apply this picture to investigate a partially entangled quantum channel. Because a mixed state can be purified to a Bell state with no probability [2 − 4], a quantum channel of mixed state could never provide an teleportation with fidelity 1. Therefore only pure entangled pairs should be considered if we prefer an exact teleportation (even with some probability). For the reason of Schmidt disposition [5], a partially entangled pair may be expressed as(hereafter, we assume particle 2 is at Alice's site and particle 3 at Bob's site) Absolute value of the Schmidt coefficient |b| is an invariant under local operations, and it corresponds to the entanglement entropy E of the state [6]. Such a state can be concentrated to a Bell state [6,7] with the probability of 2b 2 and the concentrated pair may be used as a new quantum channel to carry out a teleportation. In this report, Alice performs a Von-Neumann measurement on her side while Bob performs a corresponding general evolution to reestablish the initial state with a certain probability. We will give a measure of the entanglement degree to Alice's measurement and show that the optimal probability of an exact teleportation is determined by the less one of the entanglement degrees of Alice's measurement and the quantum channel. Thus the matching of these entanglement degrees should be considered and the entanglement degree of the measurement is endowed a meaning of Alice's ability to send quantum information.First, we consider the case Alice operates a Bell measurement and give Bob's proper general evolution to reestablish the initial state with an optimal probability. Considering the previously shared pair shown in Eq. (1) and the unknown state (which is to be send) of particle 1 | φ 1 = α |0 1 + β |1 1 , the total state could be written as |Ψ 1,2,3 = |φ 1 |Φ 2,3 = αa |000 1,2,3 + αb |011 1,2,3 + βa |100 1,2,3 + βb |111 1,2,3 . If Alice operates a Bell measurement, Bob will get the corresponding unnomalized s...

Probabilistic Teleportation via Quantum Channel with Partial Information

“…Secondly, the sender Alice or the receiver Bob has partial information about the quantum channel. For the first condition, some proposals of probabilistic teleportation have been presented, and the concrete realization procedures of the relative schemes can be obtained in [6,8]. However, the previous proposals are not valid under the second condition.…”

“…It should be underlined that one can not make use of the former schemes [6,8] to realize probabilistic teleportation under the case that the sender Alice and the receiver Bob only have partial information about the quantum channel, respectively. In this section, two proposals would be presented for these cases.…”

“…Quantum teleportation is the basic theory and a crucial task of quantum computation and quantum information [2], and a growing number of theoretical and experimental works [3][4][5][6][7][8][9][10] have appeared in the teleportation in the past years. The quantum entangled state can be viewed as a resource in quantum information science, because it can be used in many information processing schemes.…”

“…For instance, Lo [5] introduced a concept "remote preparation" and presents a method of teleportation in lower cost. Li et al [6] proposed a scheme of probabilistic teleportation to transmit an unknown single-qubit when the receiver extracts the quantum information by adopting a general evolution. Teleportation also can be obtained via super-radiance without Hadamard and CNOT transformations by Chen et al [35].…”

Teleportation of a two-particle entangled state via W class states

“…Since the seminal work of Bennett et al [1], there have been extensive works in the field of quantum teleportation in theory and experiment [4][5][6][7][8][9][10][11][12]. Entangled states, which are called quantum channels, make it possible to send an unknown state a long distance.…”