Showing papers on "Quantum capacity published in 1993"
03 Nov 1993
TL;DR: It is shown that any function computable in polynomial time by a quantum Turing machine has aPolynomial-size quantum circuit, and this result enables us to construct a universal quantum computer which can simulate a broader class of quantum machines than that considered by E. Bernstein and U. Vazirani (1993), thus answering an open question raised by them.
Abstract: We propose a complexity model of quantum circuits analogous to the standard (acyclic) Boolean circuit model. It is shown that any function computable in polynomial time by a quantum Turing machine has a polynomial-size quantum circuit. This result also enables us to construct a universal quantum computer which can simulate, with a polynomial factor slowdown, a broader class of quantum machines than that considered by E. Bernstein and U. Vazirani (1993), thus answering an open question raised by them. We also develop a theory of quantum communication complexity, and use it as a tool to prove that the majority function does not have a linear-size quantum formula. >
768 citations
TL;DR: The possible amount of information transfer between any source and any user via a quantum system is bounded through the quantum entropy function, which shows that infinite information transfer implies infinite entropy.
Abstract: The possible amount of information transfer between any source and any user via a quantum system is bounded through the quantum entropy function. In contrast to the classical case, this shows that infinite information transfer implies infinite entropy. The entropy bound is also applied to obtain the ultimate quantum information transmission capacity of the free electromagnetic field under a power and a bandwidth constraint.
179 citations
TL;DR: In this article, two localization theorems are proved: the dispersion entropy theorem shows that under special conditions, which are commonly satisfied to a good approximation, the mean quantum dispersion, which measures the mean dispersion or delocalization of the quantum states, decreases at a rate equal to a weighted sum of effective interaction rates, so that the localization always increases in the mean.
Abstract: The quantum state diffusion model introduced in an earlier paper represents the evolution of an individual open quantum system by an Ito diffusion equation for its quantum state. The diffusion and drift terms in this equation are derived from interaction with the environment. In this paper two localization theorems are proved. The dispersion entropy theorem shows that under special conditions, which are commonly satisfied to a good approximation, the mean quantum dispersion entropy, which measures the mean dispersion or delocalization of the quantum states, decreases at a rate equal to a weighted sum of effective interaction rates, so that the localization always increases in the mean, except when the effective interaction with the environment is zero. The general localization theorem provides a formula for more general conditions.
153 citations
TL;DR: A quantitative information theory is developed for both classical and quantum spin systems and gives an explanation to the surprising result that the capacity per bit can be greater than one.
Abstract: A quantitative information theory is developed for both classical and quantum spin systems. The theory is examined by heavy numerical simulations, which show that the information embedded in each weight of the system increases with the size of the system. The difference between the notions of capacity and information is examined carefully and gives an explanation to the surprising result that the capacity per bit can be greater than one.
TL;DR: In this article, the authors show that compact quantum systems have underlying compact kinematical Lie algebras, in contrast to familiar non-compact quantum systems built on the Weyl-Heisenberg algebra.
Abstract: Compact quantum systems have underlying compact kinematical Lie algebras, in contrast to familiar noncompact quantum systems built on the Weyl-Heisenberg algebra. Pauli asked in the latter case: to what extent does knowledge of the probability distributions in coordinate and momentum space determine the state vector? The analogous question for compact quantum systems is raised, and some preliminary results are obtained.
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TL;DR: In this paper, the authors considered the virtual charge distribution generated by quantum corrections in the leading log, short range approximation and adopted for it a statistical interpretation, and showed that this virtual charge density has fractal structure, and it describes a system where the equilibrium state is at its classical limit.
Abstract: Quantum fluctuations, through quantum corrections, have the potential to lead to irreversibility in quantum field theory. We consider the virtual ``charge" distribution generated by quantum corrections in the leading log, short range approximation, and adopt for it a statistical interpretation. This virtual charge density has fractal structure, and it is seen that, independently of whether the theory is or is not asymptotically free, it describes a system where the equilibrium state is at its classical limit ($\hbar \rightarrow 0$). We also present a simple analysis of how diffusion of the charge density proceeds as a function of the distance at which the system is probed.