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Quantum Information Processing
Erschienen in: Quantum Information Processing 7/2015

01.07.2015

Applications of quantum cryptographic switch: various tasks related to controlled quantum communication can be performed using Bell states and permutation of particles

verfasst von: Kishore Thapliyal, Anirban Pathak

Erschienen in: Quantum Information Processing | Ausgabe 7/2015

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Abstract

Recently, several aspects of controlled quantum communication (e.g., bidirectional controlled state teleportation, controlled quantum secure direct communication, controlled quantum dialogue, etc.) have been studied using \(n\)-qubit \((n\ge 3)\) entanglement. Specially, a large number of schemes for bidirectional controlled state teleportation are proposed using \(m\)-qubit entanglement \((m\in \{5,6,7\})\). Here, we propose a set of protocols to illustrate that it is possible to realize all these tasks related to controlled quantum communication using only Bell states and permutation of particles. As the generation and maintenance of a Bell state is much easier than a multi-partite entanglement, the proposed strategy has a clear advantage over the existing proposals. Further, it is shown that all the schemes proposed here may be viewed as applications of the concept of quantum cryptographic switch which was recently introduced by some of us. The performances of the proposed protocols as subjected to the amplitude damping and phase damping noise on the channels are also discussed.
Vorheriger Artikel An improved control mode for the ping-pong protocol operation in imperfect quantum channels
Nächster Artikel A quantum optical firewall based on simple quantum devices

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Fußnoten
1
By the same logic, we mean that unless Charlie measures his qubits and discloses the results, Alice and Bob do not know which Bell states they share.
 
2
We can assume that Charlie has a quantum random number generator, and he has generated a large sequence of 0 and 1 through it. He uses the outcomes of the random number generator to decide which Bell state is to be prepared. For example, we may consider that if the first two bit values obtained from the random number generator are 00, 01, 10 and 11 then he prepares \(|\psi ^{+}\rangle ,|\psi ^{-}\rangle ,|\phi ^{+}\rangle ,\) and \(|\phi ^{-}\rangle ,\) respectively.
 
3
BB84 subroutine [36] means eavesdropping is checked by following a procedure similar to that adopted in the original BB84 protocol. Specifically, BB84 subroutine implies that Alice (Bob) randomly selects half of the qubits received by her (him) to form a verification string. She (He) measures the verification qubits randomly in \(\left\{ |0\rangle ,|1\rangle \right\} \) or \(\left\{ |+\rangle ,|-\rangle \right\} \) basis and announces the measurement outcome, the position of that qubit in the string and the basis used for the particular measurement. Bob (Alice) also measures the corresponding qubit using the same basis (if needed) and compares his (her) result with the announced result of Alice (Bob) to detect eavesdropping.
 
4
Usually fidelity \(F(\sigma ,\rho )\) of two quantum states \(\rho \) and \(\sigma \) is defined as \(F(\sigma ,\rho )=Tr\sqrt{\sigma ^{\frac{1}{2}}\rho \sigma ^{\frac{1}{2}}}.\) However, in the present work, we have used (6) as the definition of fidelity.
 
5
AD and GAD channels are the special cases of SGAD channel.
 
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Metadaten
Titel
Applications of quantum cryptographic switch: various tasks related to controlled quantum communication can be performed using Bell states and permutation of particles
verfasst von
Kishore Thapliyal
Anirban Pathak
Publikationsdatum
01.07.2015
Verlag
Springer US
Erschienen in
Quantum Information Processing / Ausgabe 7/2015
Print ISSN: 1570-0755
Elektronische ISSN: 1573-1332
DOI
https://doi.org/10.1007/s11128-015-0987-z

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