Editing Quantum Cloning
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==Protocols== | ==Protocols== | ||
*'''Approximate cloning protocols for discrete quantum systems''' Cloning protocols for discrete quantum systems (DV) have been included in this section. The simple case of copying a qubit is an example of these cloning machines. The more general case of these quantum cloning machines is N <math>\rightarrow</math> M cloner which will produce M identical copies of N initial states. The discrete quantum cloning machines can be divided into two main categories: universal and non-universal. | *'''Approximate cloning protocols for discrete quantum systems''' Cloning protocols for [[discrete quantum systems (DV)]] have been included in this section. The simple case of copying a qubit is an example of these cloning machines. The more general case of these quantum cloning machines is N <math>\rightarrow</math> M cloner which will produce M identical copies of N initial states. The discrete quantum cloning machines can be divided into two main categories: universal and non-universal. | ||
**'''Universal quantum cloning protocols:''' Universal cloning machines produce copies of any arbitrary states. These protocols produce copies which are approximately close to the original state at every round. Also, a universal cloning machine can be | **'''Universal quantum cloning protocols:''' Universal cloning machines produce copies of any arbitrary states. These protocols produce copies which are approximately close to the original state at every round. Also, a universal cloning machine can be | ||
***[[Optimal | ***Symmetric or [[Optimal Cloning|Optimal Cloning protocols]] | ||
***[[Asymmetric | ***[[Asymmetric Cloning|Asymmetric Cloning protocols]] | ||
**'''Non-universal quantum cloning protocols''' It is possible to have a cloning machine which is not universal and these machines have their own functionalities and advantages. In this category, we have | **'''Non-universal quantum cloning protocols''' It is possible to have a cloning machine which is not universal and these machines have their own functionalities and advantages. In this category, we have | ||
***[[State Dependent | ***[[State Dependent cloning|State-dependent cloning]] | ||
***[[Phase | ***[[Phase Covariant Cloning|Phase-covariant cloning]]. | ||
*'''Approximate cloning protocols for | *'''Approximate cloning protocols for continous variables''' The cloning of several quantum states such as photonic states which are in the regime of [[continuous variables (CV)]] have been presented in this section. The N <math>\rightarrow</math> M approximate Gaussian cloning protocol is the most important cloning protocol in CV with a wide variety of application in photonic or quantum oscillator systems. | ||
*'''Probabilistic Cloning''' Another way of having an imperfect cloner is to have a probabilistic cloning machine will produce the copies with some probability of success. In these protocols coping task can succeed with probability, but if it is successful, we can always obtain perfect | *'''Probabilistic Cloning''' Another way of having an imperfect cloner is to have a probabilistic cloning machine will produce the copies with some probability of success. In these protocols coping task can succeed with probability, but if it is successful, we can always obtain perfect copie. The probabilistic cloning machines will no longer consists of unitary operations only. But these machines are represented by quantum maps instead. This quantum cloning machine is useful, in particular, in studying the B92 quantum key distribution protocol. | ||
**[[Probabilistic Cloning|Probabilistic Cloning]] | **[[Probabilistic Cloning|Probabilistic Cloning protocols]] | ||
==Use Case== | |||
Signing e-Marksheet, Financial Transactions, Software Distribution, Cryptocurrencies, e-voting | |||
==Properties== | ==Properties== | ||
All QDS protocols are divided into two phases, distribution and messaging. Distribution phase enables sender to generate private keys (kept secret with sender) and public keys (information distributed to recipients) while messaging phase enables exchange of messages using the above keys. For simlicity, most protocols use the case of three parties, one sender (Seller) and two recipients (Buyer and Verifier) exchanging one-bit classical messages signed by Quantum Digital Signatures (QDS). | |||
*A QDS scheme is correct if a message signed by a genuine sender is accepted by a recipient with unit probability. | |||
*A QDS scheme is secure if no one but the sender can sign a message such that it is accepted by a recipient with non-negligible probability. | |||
*'''Transferability''' means that at any point a recipient (buyer) can prove it to another recipient (verifier) that the concerned message has been signed by the claimed sender (Seller). | |||
*'''Unforgeability''' ensures that a dishonest recipient (buyer) can neither alter a DS nor sign a message with a fake DS (DS that has not come from a genuine sender) and forward it to other recipients (verifier) successfully. | |||
*'''Non-Repudiation''' implies that at any point a dishonest sender (seller) cannot deny having signed the message sent to a genuine recipient (Buyer). | |||
==Discussion== | |||
#[https://www.semanticscholar.org/paper/Unconditionally-Secure-Quantum-Signatures-Amiri-Andersson/2c9a298c9e902c5162496cc13f5d560427873412 AA (2015)] Discusses various classical and quantum digital signature schemes | |||
#Wallden P. (2018) (In preparation): Discusses the development of Quantum Digital Signatures from the first protocol by Gottesman and Chuang, elaborating advancements in further protocols to turn it into a practical QDS scheme. | |||