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arXiv:quant-ph/0510143 · Physical Review A

Broadcasting of entanglement at a distance using linear optics and telecloning of entanglement

Iulia Ghiu, Anders Karlsson

Published Sep 26, 2005• 20 citations
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Abstract

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 $R$. In particular for $R=\frac{1}{3}$ 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.

DOI
10.1103/physreva.72.032331

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International Symposium on Communication Systems, Networks and Digital Signal Processing (CSNDSP)•Jul 1, 2010•1 citation
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.
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 $\stackrel{\ensuremath{\rightarrow}}{1}2$ 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.
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.
Quantum telecloning, a pivotal multiuser quantum communication protocol in the realm of quantum information science, facilitates the copy of a quantum state across M distinct locations through teleportation technique. In the continuous-variable regime, the implementation of quantum telecloning necessitates the distribution of multipartite entanglement among the sender and M receiver parties. Following this, the sender carries out optic-electro conversion and transmits information via classical channel to M spatially separated receivers simultaneously. To successfully reconstruct the input state, electro-optic conversion needs to be employed by each receiver. However, due to these conversions, the bandwidth of the optical mode in this process is largely constrained. In this Letter, we present an all-optical version of the 1→2 continuous-variable quantum telecloning scheme, wherein both optic-electro and electro-optic conversions are replaced by optical components. Our scheme allows the two receivers to achieve input state reconstruction solely by utilizing beam splitters, significantly simplifying its complexity. We experimentally demonstrate all-optical 1→2 quantum telecloning of coherent state and achieve the fidelities of 58.6%±1.0% and 58.6%±1.1% for two clones, exceeding the corresponding classical limits (51.9%±0.5% and 51.9%±0.6%). Our results establish a platform for constructing a flexible all-optical multiuser quantum network and promote the field of all-optical quantum information processing.
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 demonstrate an experiment on entanglement swapping using an optimal Bell-state measurement capable of identifying two of the four Bell-states for polarization entangled photons, which is the optimum with linear optical elements. The two final photons belong to separately created paris. They are entangled after their original partner photons have been subjected to the Bell state measurement, whose outcome determines the type of entanglement of the final photon pair. The resulting violation of Bell's inequality in both cases confirms the success of the teleportation protocol.
Quantum entanglement distribution is an essential part of quantum communication and computation protocols. Here, linear optic elements are employed for distribution of quantum entanglement over long distance. Polarization beam splitters and wave plates are used for realization of an error-free protocol for broadcasting quantum entanglement in optical quantum communication. This protocol can determine maximum distance of quantum communication to transmit quantum information without decoherence. Error detection and error correction are performed in the proposed scheme. In other words, if bit-flip occurs along the quantum channel, the end stations (Alice and Bob) can detect this state changing and obtain the correct state (entangled photon) on the another port. Existing general error detection protocols are based on the quantum controlled-NOT (CNOT) or similar quantum logic operations, which are very difficult to implement experimentally. Here we present a feasible scheme for the implementation of entanglement distribution based on linear optics element that does not need quantum CNOT gate.