scholarly journals Graphical Methods in Device-Independent Quantum Cryptography

Quantum ◽  
2019 ◽  
Vol 3 ◽  
pp. 146
Author(s):  
Spencer Breiner ◽  
Carl A. Miller ◽  
Neil J. Ross
Keyword(s):  
Quantum Mechanics ◽  
Quantum Cryptography ◽  
Graphical Methods ◽  
Proof Assistant ◽  
Security Proofs ◽  
Expansion Protocol ◽  
Categorical Quantum Mechanics ◽  
Proof Verification ◽  
Automated Proof

We introduce a framework for graphical security proofs in device-independent quantum cryptography using the methods of categorical quantum mechanics. We are optimistic that this approach will make some of the highly complex proofs in quantum cryptography more accessible, facilitate the discovery of new proofs, and enable automated proof verification. As an example of our framework, we reprove a previous result from device-independent quantum cryptography: any linear randomness expansion protocol can be converted into an unbounded randomness expansion protocol. We give a graphical proof of this result, and implement part of it in the Globular proof assistant.

Can quantum cryptography imply quantum mechanics? -- reply to Smolin

2005 ◽  
Vol 5 (2) ◽  
pp. 170-175
Author(s):  
H. Halvorson ◽  
J. Bub
Keyword(s):  
Quantum Mechanics ◽  
Quantum Cryptography ◽  
Physical Theory ◽  
Information Theoretic ◽  
Independence Condition

Clifton, Bub, and Halvorson (CBH) have argued that quantum mechanics can be derived from three cryptographic, or broadly information-theoretic, axioms. But Smolin disagrees, and he has given a toy theory that he claims is a counterexample. Here we show that Smolin's toy theory violates an independence condition for spacelike separated systems that was assumed in the CBH argument. We then argue that any acceptable physical theory should satisfy this independence condition.

Quantum Cryptography Key Distribution

2021 ◽  
pp. 325-344
Author(s):  
Bhanu Chander
Keyword(s):  
Quantum Mechanics ◽  
Information Transmission ◽  
Quantum Cryptography ◽  
Quantum Physics ◽  
Large Scale ◽  
Key Distribution ◽  
Computing Power ◽  
Contemporary State ◽  
Quantum Resistant Cryptography ◽  
Quantum Protocol

Quantum cryptography is actions to protect transactions through executing the circumstance of quantum physics. Up-to-the-minute cryptography builds security over the primitive ability of fragmenting enormous numbers into relevant primes; however, it features inconvenience with ever-increasing machine computing power along with current mathematical evolution. Among all the disputes, key distribution is the most important trouble in classical cryptography. Quantum cryptography endows with clandestine communication by means of offering a definitive protection statement with the rule of the atmosphere. Exploit quantum mechanics to cryptography can be enlarging unrestricted, unfailing information transmission. This chapter describes the contemporary state of classical cryptography along with the fundamentals of quantum cryptography, quantum protocol key distribution, implementation criteria, quantum protocol suite, quantum resistant cryptography, and large-scale quantum key challenges.

Quantum cryptography: How to beat the code breakers using quantum mechanics

1995 ◽  
Vol 36 (3) ◽  
pp. 165-195 ◽  
Author(s):  
Simon J. D. Phoenix ◽  
Paul D. Townsend
Keyword(s):  
Quantum Mechanics ◽  
Quantum Cryptography

scholarly journals Dagger linear logic for categorical quantum mechanics

2021 ◽  
Vol Volume 17, Issue 4 ◽  
Author(s):  
Robin Cockett ◽  
Cole Comfort ◽  
Priyaa Srinivasan
Keyword(s):  
Quantum Mechanics ◽  
Hilbert Spaces ◽  
Quantum Physics ◽  
Linear Logic ◽  
Infinite Dimensional ◽  
Graphical Calculus ◽  
Finite Dimensional ◽  
Categorical Quantum Mechanics ◽  
Definition Of ◽  
Categorical Semantics

Categorical quantum mechanics exploits the dagger compact closed structure of finite dimensional Hilbert spaces, and uses the graphical calculus of string diagrams to facilitate reasoning about finite dimensional processes. A significant portion of quantum physics, however, involves reasoning about infinite dimensional processes, and it is well-known that the category of all Hilbert spaces is not compact closed. Thus, a limitation of using dagger compact closed categories is that one cannot directly accommodate reasoning about infinite dimensional processes. A natural categorical generalization of compact closed categories, in which infinite dimensional spaces can be modelled, is *-autonomous categories and, more generally, linearly distributive categories. This article starts the development of this direction of generalizing categorical quantum mechanics. An important first step is to establish the behaviour of the dagger in these more general settings. Thus, these notes simultaneously develop the categorical semantics of multiplicative dagger linear logic. The notes end with the definition of a mixed unitary category. It is this structure which is subsequently used to extend the key features of categorical quantum mechanics.

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