2 research outputs found
Quartic quantum theory: an extension of the standard quantum mechanics
We propose an extended quantum theory, in which the number K of parameters
necessary to characterize a quantum state behaves as fourth power of the number
N of distinguishable states. As the simplex of classical N-point probability
distributions can be embedded inside a higher dimensional convex body of mixed
quantum states, one can further increase the dimensionality constructing the
set of extended quantum states. The embedding proposed corresponds to an
assumption that the physical system described in N dimensional Hilbert space is
coupled with an auxiliary subsystem of the same dimensionality. The extended
theory works for simple quantum systems and is shown to be a non-trivial
generalisation of the standard quantum theory for which K=N^2. Imposing certain
restrictions on initial conditions and dynamics allowed in the quartic theory
one obtains quadratic theory as a special case. By imposing even stronger
constraints one arrives at the classical theory, for which K=N.Comment: 30 pages in latex with 6 figures included; ver.2: several
improvements, new references adde
Quantum key distribution based on orthogonal states allows secure quantum bit commitment
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 which the density matrices of the quantum states encoding the commitment do
not satisfy a crucial condition on which the no-go proofs of QBC are based.
Thus the no-go proofs could be evaded. Our protocol is fault-tolerant and very
feasible with currently available technology. It reopens the venue for other
"post-cold-war" multi-party cryptographic protocols, e.g., quantum bit string
commitment and quantum strong coin tossing with an arbitrarily small bias. This
result also has a strong influence on the Clifton-Bub-Halvorson theorem which
suggests that quantum theory could be characterized in terms of
information-theoretic constraints.Comment: Published version plus an appendix showing how to defeat the
counterfactual attack, more references [76,77,90,118-120] cited, and other
minor change