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arXiv:1712.00624 · Quantum Information Processing

Telecloning of qudits via partially entangled states

G. Araneda, Nataly Cisternas, Aldo Delgado

Published May 21, 2016• 7 citations
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Abstract

We study the process of quantum telecloning of d -dimensional pure quantum states using partially entangled pure states as quantum channel. This process efficiently mixes optimal universal symmetric cloning with quantum teleportation. It is shown that it is possible to implement universal symmetric telecloning in a probabilistic way using unambiguous state discrimination and quantum state separation schemes. It is also shown that other strategies, such as minimum error discrimination, lead to a decrease in the fidelity of the copies and that certain partially entangled pure states with maximal Schmidt rank lead to an average telecloning fidelity which is always above the optimal fidelity of measuring and preparation of quantum states. We also discuss the case of partially entangled pure states with non-maximal Schmidt rank. The results presented here are valid for arbitrary numbers of copies of a single-input qudit state of any dimension.

DOI
10.1007/s11128-016-1348-2

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We study the process of quantum telecloning of d -dimensional pure quantum states using partially entangled pure states as quantum channel. This process efficiently mixes optimal universal symmetric cloning with quantum teleportation. It is shown that it is possible to implement universal symmetric telecloning in a probabilistic way using unambiguous state discrimination and quantum state separation schemes. It is also shown that other strategies, such as minimum error discrimination, lead to a decrease in the fidelity of the copies and that certain partially entangled pure states with maximal Schmidt rank lead to an average telecloning fidelity which is always above the optimal fidelity of measuring and preparation of quantum states. We also discuss the case of partially entangled pure states with non-maximal Schmidt rank. The results presented here are valid for arbitrary numbers of copies of a single-input qudit state of any dimension.
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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.
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.