Related papers: Quantum Money from Abelian Group Actions
For more than a decade, it was believed that unconditionally secure quantum bit commitment (QBC) is impossible. But basing on a previously proposed quantum key distribution scheme using orthogonal states, here we build a QBC protocol in…
We construct a birational invariant for certain algebraic group actions. We use this invariant to classify linear representations of finite abelian groups up to birational equivalence, thus answering, in a special case, a question of E. B.…
We consider topological quantum memories for a general class of abelian anyon models defined on spin lattices. These are non-universal for quantum computation when restricting to topological operations alone, such as braiding and fusion.…
Smart contracts are cryptographic protocols that are enforced without a judiciary. Smart contracts are used occasionally in Bitcoin and are prevalent in Ethereum. Public quantum money improves upon cash we use today, yet the current…
We continue the analysis of quantum-like description of market phenomena and economics. We show that it is possible to define a risk inclination operator acting in some Hilbert space that has a lot of common with quantum description of the…
Atomicity is a ubiquitous assumption in distributed computing, under which actions are indivisible and appear sequential. In classical computing, this assumption has several theoretical and practical guarantees. In quantum computing,…
A general approach describing quantum decision procedures is developed. The approach can be applied to quantum information processing, quantum computing, creation of artificial quantum intelligence, as well as to analyzing decision…
Using a group theoretical approach we derive an equation of motion for a mixed quantum-classical system. The quantum-classical bracket entering the equation preserves the Lie algebra structure of quantum and classical mechanics: The bracket…
A geometrical approach to quantum computation is presented, where a non-abelian connection is introduced in order to rewrite the evolution operator of an energy degenerate system as a holonomic unitary. For a simple geometrical model we…
Group theory is extremely successful in characterizing the symmetries in quantum systems, which greatly simplifies and unifies our treatments of quantum systems. Here we introduce the concept of the symmetry for a quantum Boltzmann machine…
A theorem is proved which states that no classical key generating protocol could ever be provably secure. Consequently, candidates for provably secure protocols must rely on some quantum effect. Theorem relies on the fact that BB84 Quantum…
We discuss the possibility of creating money that is physically impossible to counterfeit. Of course, "physically impossible" is dependent on the theory that is a faithful description of nature. Currently there are several proposals for…
In this paper, we propose a brand new public key encryption scheme in the Lie group that is a non-abelian group. In particular, we firstly investigate the intractability assumptions in the Lie group, including the non-abelian factoring…
Quantum algorithms are sequences of abstract operations, performed on non-existent computers. They are in obvious need of categorical semantics. We present some steps in this direction, following earlier contributions of Abramsky, Coecke…
In this paper we show that certain special cases of the hidden subgroup problem can be solved in polynomial time by a quantum algorithm. These special cases involve finding hidden normal subgroups of solvable groups and permutation groups,…
Unforgeable quantum money tokens were the first invention of quantum information science, but remain technologically challenging as they require quantum memories and/or long distance quantum communication. More recently, virtual 'S-money'…
Recent developments in quantum computation have made it clear that there is a lot more to computation than the conventional Boolean algebra. Is quantum computation the most general framework for processing information? Having gathered the…
Quantum computations that involve only Clifford operations are classically simulable despite the fact that they generate highly entangled states; this is the content of the Gottesman-Knill theorem. Here we isolate the ingredients of the…
By repeated trials, one can determine the fairness of a classical coin with a confidence which grows with the number of trials. A quantum coin can be in a superposition of heads and tails and its state is most generally a density matrix.…
We obtain explicit formulas for the number of non-isomorphic elliptic curves with a given group structure (considered as an abstract abelian group). Moreover, we give explicit formulas for the number of distinct group structures of all…