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Quantum Money is a quantum cryptographic scheme that was first introduced by Wiesner [Wie83] in 1983. Informally, the quantum money object is a unique (e.g. has a public classical serial number) and unforgeable (e.g. unclonable) physical object that is created by a third party called Mint (that could be trusted or not trusted). Then, it is circulated among potentially untrusted parties, Holder, who might attempt to forge it for double spending. However a Merchant, upon receiving it, should be able to verify the money has not been forged and originated from Mint. There are various verification schemes based on different types of communication and types of key encryption used by Mint (see Protocols).
Quantum Money is a quantum cryptographic scheme that was first introduced by Wiesner [Wie83] in 1983. Informally, a quantum money is a unique (e.g. has a serial number) and unforgeable (e.g. unclonable) physical object that is created by a third party called Mint (that could be trusted or not trusted). Then, it is circulated among potentially untrusted parties, Holder, who might attempt to forge it for double spending. However a Merchant, upon receiving it, should be able to verify the money has not been forged and originated from Mint. There are various verification schemes based on different types of communication they use and type of key encryption used by Mint see Protocols.


== Protocols ==
== Protocols ==
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=== Private Key with Quantum Verification ===
=== Private Key with Quantum Verification ===


Mint generates the quantum money and hands it to Holder. Bank shares a secret classical key with Mint for all distributed money. For verification, Merchant sends the quantum money to Bank through a quantum channel. Bank performs local quantum measurements, dictated by the secret classical key, and accepts or rejects the money conditioned on the measurement outcomes.
It involves a trusted party called Bank, who shares secrete key with Mint for all distributed money. For verification, Merchant sends quantum money to Bank through a quantum channel. Bank performs local quantum operations depending on the secret key they hold to reject or accept the money.  
 
*[[Wiesner quantum Money]]: [[:Category: Quantum Memory Network Stage|Quantum Memory Network Stage]]


*[[Wiesner Quantum Money]]: [[:Category: Quantum Memory Network Stage|Quantum Memory Network Stage]]
*[[Quantum Cheque]]


=== Private Key with Classical Verification ===
=== Private Key with Classical Verification ===


Mint generates the quantum money and hands it to Holder. Bank shares a secret classical key with Mint for all distributed money. For verification, Merchant performs local quantum operations on the money and sends classical data to Bank who accepts or rejects based on the secret key they hold.  
 
It involves a trusted party called Bank, who shares secrete key with Mint for all distributed money. For verification, Merchant performs local quantum operations on the money and sends classical data to Bank who accepts or rejects based on the secret key they holds.  


*[[Quantum Coin]]: [[:Category: Quantum Memory Network Stage|Quantum Memory Network Stage]]
*[[Quantum Coin]]: [[:Category: Quantum Memory Network Stage|Quantum Memory Network Stage]]
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=== Public Key with Quantum Verification ===
=== Public Key with Quantum Verification ===


Mint generates the quantum money and hands it to Holder. All Holder and Merchant parties can verify the authenticity of the money themselves with the help of a public key.


== Properties ==
=== Public Key with Classical Verification ===




*A QMoney scheme is '''correct''' if an original quantum money issued by Mint is accepted by Bank with unit probability.
*[[Prepare and Measure Quantum Digital Signature]]: [[:Category: Prepare and Measure Network Stage|Prepare and Measure Network Stage]]
*A QMoney scheme is information-theoretically (resp. computationally) '''secure''' if no adversarial holder with unlimited (resp. computational) power can pass verification with different Merchants or Banks at the same time with high probability.
*[[Measurement Device Independent Quantum Digital Signature (MDI-QDS)]]: [[:Category:Entanglement Distribution Network stage|Entanglement Distribution Network Stage]]
* A QMoney is '''reusable''' if an honest Holder can pass verification with different Merchants or Banks at different times.
*[[Quantum Digital Signature with Quantum Memory]]: [[:Category: Quantum Memory Network Stage|Quantum Memory Network Stage]]


==Use-cases==
== Properties ==
* [[Cross-platform finance]]
* [[Toward regulation for security and privacy]]
 
==Knowledge Graph==
{{graph}}


== Further Information ==
reusable
correctness
Transferability
Unforgeability
verifiability
Security
Authenticity


<div style='text-align: right;'>''*contributed by Mahshid Delavar and Mathieu Bozzio''</div>
<div style='text-align: right;'>''*contributed by Mashid Delavar''</div>
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