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arXiv:quant-ph/0303060 · Physical Review A

Asymmetric quantum telecloning ofd-level systems and broadcasting of entanglement to different locations using the “many-to-many” communication protocol

Iulia Ghiu

Published Jan 29, 2003• 75 citations
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Abstract

We propose a generalization of quantum teleportation: the so-called many-to-many quantum communication of the information of a d-level system from N spatially separated senders to $M>N$ receivers situated at different locations. We extend the concept of asymmetric telecloning from qubits to d-dimensional systems. We investigate the broadcasting of entanglement by using local $\stackrel{\ensuremath{\rightarrow}}{1}2$ optimal universal asymmetric Pauli machines and show that the maximal fidelities of the two final entangled states are obtained when symmetric machines are applied. Cloning of entanglement is studied using a nonlocal optimal universal asymmetric cloning machine and we show that the symmetric machine optimally copies the entanglement. The ``many-to-many'' teleportation scheme is applied in order to distribute entanglement shared between two observers to two pairs of spatially separated observers.

DOI
10.1103/physreva.67.012323

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We propose a generalization of quantum teleportation: the so-called many-to-many quantum communication of the information of a d-level system from N spatially separated senders to M>NM>NM>N receivers situated at different locations. We extend the concept of asymmetric telecloning from qubits to d-dimensional systems. We investigate the broadcasting of entanglement by using local 1\ensuremath→2\stackrel{\ensuremath{\rightarrow}}{1}21\ensuremath→​2 optimal universal asymmetric Pauli machines and show that the maximal fidelities of the two final entangled states are obtained when symmetric machines are applied. Cloning of entanglement is studied using a nonlocal optimal universal asymmetric cloning machine and we show that the symmetric machine optimally copies the entanglement. The ``many-to-many'' teleportation scheme is applied in order to distribute entanglement shared between two observers to two pairs of spatially separated observers.
In the original one-to-one teleportation protocol of Bennett et al. [1], an observer, Alice, transmits the information of a d -level system to another observer, Bob, with perfect fidelity, by using a maximally entangled state. We introduce a generalization called the many-to-many teleportation, where the information is sent from N observers to M receivers situated at different locations. One of the most interesting applications of quantum cloning is the symmetric broadcasting of entanglement proposed by Buzek et al. [2]. We propose the splitting of entanglement based on a local optimal universal asymmetric cloning machine and, then, by applying the Peres-Horodecki criterion, we analyze the inseparability of the final states.
We present a generalization of quantum teleportation that distributes quantum information from a sender's d-level particle to No{N}_{o}No​ particles held by remote receivers via an initially shared multiparticle entangled state. This entangled state functions as a multiparty quantum information distribution channel between the sender and the receivers. The structure of the distribution channel determines how quantum information is processed. Our generalized teleportation scheme allows multiple receivers at arbitrary locations, and can be used for applications such as optimal quantum information broadcasting, asymmetric telecloning, and quantum error correction.
Symmetric N→MN \to MN→M telecloning and remote quantum state inference
Teleporting unknown quantum states between distant nodes of a network is a significant feature of quantum communication. Few studies, however, have been conducted on N→MN \to MN→M telecloning, in which NNN copies of an unknown quantum state are optimally teleported to M≥NM \geq NM≥N receivers. Previous work requires global POVMs on all copies and auxiliaries; here, we show that symmetric N→MN \to MN→M telecloning can be probabilistically performed using only sequential (or parallel) Bell state measurements (BSMs), allowing the copies to be spatially separated. When successful, the fidelity of each receiver's reduced state saturates the bound imposed by the no-cloning theorem, with the probability of success being independent of MMM. In the case of an `unsuccessful' BSM, we show that the teleportation fidelity is likely to remain high, with the measurement outcome also providing information about the closest Pauli eigenbasis to the unknown state being telecloned. In this sense, each receiver can remotely infer the unknown quantum state with a level of confidence that scales with the number of copies, even if the fidelity of their own reduced state is sub-optimal. We additionally analyze the required resources to ensure the classical-communication fidelity bound is surpassed, both in terms of two-qubit inseparability and varying classes of multipartite entanglement. Surprisingly, we uncover that, at a given iteration of the protocol, pairwise entanglement is not always necessary to increase the teleportation fidelity and is never required to beat the classical bound for N≥2N \geq 2N≥2.
We propose a scheme for broadcasting entanglement at a distance based on linear optics. We show that an initial polarization entangled state can be simultaneously split and transmitted to a pair of observers situated at different locations with the help of two conditional Bell-state analyzers based on two beam splitters characterized by the same reflectivity RRR. In particular for R=13R=\frac{1}{3}R=31​ the final states coincide with the output states obtained by the broadcasting protocol proposed by Buzek et al. [Phys. Rev. A 55, 3327 (1997)]. Further we present a different protocol called telecloning of entanglement, which combines the many-to-many teleportation and nonlocal optimal asymmetric cloning of an arbitrary entangled state. This scheme allows the optimal transmission of the two nonlocal optimal clones of an entangled state to two pairs of spatially separated receivers.
A scheme combining three processes of quantum teleportation, optimal universal quantum flipping and optimal universal quantum cloning for universal teleflipping and telecloning of arbitrary qubit is proposed. When a particular four-particle entangled state shared by the sender and three spatially separated receivers is used as quantum information channel, after the sender's Bell measurement, class ical communication and each receiver's local unitary operation, one receiver can get one orthogonal complementing state of the original unknown state with the o ptimal fidelity of 2/3, the other two receivers can respectively get one copy of the original unknown state with the optimal fidelity of 5/6. This scheme implem ents the universal quantum teleflipping and telecloning simultaneously with corr esponding optimal fidelity by using the reduced entanglement. The key to realizi ng this scheme is the construction of the particular four-particle entangled sta te shared by the sender and three receivers used as quantum information channel. The entanglement structure of the special four-particle entangled state is anal yzed.
We propose two different implementations of an asymmetric two-output probabilistic quantum processor, which can implement a restricted set of one-qubit operations. One of them is constructed by combining asymmetric telecloning with a quantum gate array. We analyze the efficiency of this processor by evaluating the fidelities between the desired operation and the one generated by the processor and show that the two output states are the same as the ones produced by the optimal universal asymmetric Pauli cloning machine. The schemes require only local operations and classical communication, they have the advantage of transmitting the two output states directly to two spatially separated receivers but they have a success probability of 1/2. We show further that we can perform the same one-qubit operation with unity probability at the cost of using nonlocal operations. We finally generalize the two schemes for D-level systems and find that the local ones are successful with a probability of 1/D and the nonlocal generalized scheme is always successful.