103 research outputs found
Majorization in Quantum Adiabatic Algorithms
The majorization theory has been applied to analyze the mathematical
structure of quantum algorithms. An empirical conclusion by numerical
simulations obtained in the previous literature indicates that step-by-step
majorization seems to appear universally in quantum adiabatic algorithms. In
this paper, a rigorous analysis of the majorization arrow in a special class of
quantum adiabatic algorithms is carried out. In particular, we prove that for
any adiabatic algorithm of this class, step-by-step majorization of the ground
state holds exactly. For the actual state, we show that step-by-step
majorization holds approximately, and furthermore that the longer the running
time of the algorithm, the better the approximation.Comment: 7 pages;1 figur
Optimal conclusive discrimination of two states can be achieved locally
This paper constructs a LOCC protocol that achieves the global optimality in
conclusive discrimination of any two states with arbitrary a priori
probability. This can be interpreted that there is no ``non-locality'' in the
conclusive discrimination of two multipartite states.Comment: 9 pages, RevTeX, no figure. Comments, criticisms and suggestions are
welcom
Efficiency of Deterministic Entanglement Transformation
We prove that sufficiently many copies of a bipartite entangled pure state
can always be transformed into some copies of another one with certainty by
local quantum operations and classical communication. The efficiency of such a
transformation is characterized by deterministic entanglement exchange rate,
and it is proved to be always positive and bounded from top by the infimum of
the ratios of Renyi's entropies of source state and target state. A careful
analysis shows that the deterministic entanglement exchange rate cannot be
increased even in the presence of catalysts. As an application, we show that
there can be two incomparable states with deterministic entanglement exchange
rate strictly exceeding 1.Comment: 7 pages, RevTex4. Journal versio
An Algebra of Quantum Processes
We introduce an algebra qCCS of pure quantum processes in which no classical
data is involved, communications by moving quantum states physically are
allowed, and computations is modeled by super-operators. An operational
semantics of qCCS is presented in terms of (non-probabilistic) labeled
transition systems. Strong bisimulation between processes modeled in qCCS is
defined, and its fundamental algebraic properties are established, including
uniqueness of the solutions of recursive equations. To model sequential
computation in qCCS, a reduction relation between processes is defined. By
combining reduction relation and strong bisimulation we introduce the notion of
strong reduction-bisimulation, which is a device for observing interaction of
computation and communication in quantum systems. Finally, a notion of strong
approximate bisimulation (equivalently, strong bisimulation distance) and its
reduction counterpart are introduced. It is proved that both approximate
bisimilarity and approximate reduction-bisimilarity are preserved by various
constructors of quantum processes. This provides us with a formal tool for
observing robustness of quantum processes against inaccuracy in the
implementation of its elementary gates
The LU-LC conjecture is false
The LU-LC conjecture is an important open problem concerning the structure of
entanglement of states described in the stabilizer formalism. It states that
two local unitary equivalent stabilizer states are also local Clifford
equivalent. If this conjecture were true, the local equivalence of stabilizer
states would be extremely easy to characterize. Unfortunately, however, based
on the recent progress made by Gross and Van den Nest, we find that the
conjecture is false.Comment: Added a new part explaining how the counterexamples are foun
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