1,021 research outputs found
Discrimination of the Bell states of qudits by means of linear optics
The question of the discrimination of the Bell states of two qudits (i.e.,
d-dimensional quantum systems) by means of passive linear optical elements and
conditional measurements is discussed. A qudit is supposed to be represented by
d optical modes containing exactly one photon altogether. From recent results
of Calsamiglia it follows that there is no way how to distinguish the Bell
states of two qudits for d>2 - not even with the probability of success lower
than one - without any auxiliary photons in ancillary modes. Following the
results of Carollo and Palma it is proved that it is impossible to distinguish
even only one such a Bell state with certainty (i.e., with the probability of
success equal to one), irrespective of how many auxiliary photons are involved.
However, it is shown that auxiliary photons can help to discriminate the Bell
states of qudits with the high probability of success: A Bell-state analyzer
based on the idea of linear optics quantum computation that can achieve the
probability of success arbitrarily close to one is described. It requires many
auxiliary photons that must be first "combined" into entangled states.Comment: 4 pages, 5 figure
Adiabatic Markovian Dynamics
We propose a theory of adiabaticity in quantum Markovian dynamics based on a
decomposition of the Hilbert space induced by the asymptotic behavior of the
Lindblad semigroup. A central idea of our approach is that the natural
generalization of the concept of eigenspace of the Hamiltonian in the case of
Markovian dynamics is a noiseless subsystem with a minimal noisy cofactor.
Unlike previous attempts to define adiabaticity for open systems, our approach
deals exclusively with physical entities and provides a simple, intuitive
picture at the underlying Hilbert-space level, linking the notion of
adiabaticity to the theory of noiseless subsystems. As an application of our
theory, we propose a framework for decoherence-assisted computation in
noiseless codes under general Markovian noise. We also formulate a
dissipation-driven approach to holonomic computation based on adiabatic
dragging of subsystems that is generally not achievable by non-dissipative
means.Comment: 4+3 page
Comment on "Nongeometric Conditional Phase Shift via Adiabatic Evolution of Dark Eigenstates: A New Approach to Quantum Computation"
In [Phys. Rev. Lett. 95, 080502 (2005)], Zheng proposed a scheme for
implementing a conditional phase shift via adiabatic passages. The author
claims that the gate is "neither of dynamical nor geometric origin" on the
grounds that the Hamiltonian does not follow a cyclic change. He further argues
that "in comparison with the adiabatic geometric gates, the nontrivial cyclic
loop is unnecessary, and thus the errors in obtaining the required solid angle
are avoided, which makes this new kind of phase gates superior to the geometric
gates." In this Comment, we point out that geometric operations, including
adiabatic holonomies, can be induced by noncyclic Hamiltonians, and show that
Zheng's gate is geometric. We also argue that the nontrivial loop responsible
for the phase shift is there, and it requires the same precision as in any
adiabatic geometric gate
Maximum efficiency of a linear-optical Bell-state analyzer
In a photonic realization of qubits the implementation of quantum logic is
rather difficult due the extremely weak interaction on the few photon level. On
the other hand, in these systems interference is available to process the
quantum states. We formalize the use of interference by the definition of a
simple class of operations which include linear optical elements, auxiliary
states and conditional operations.
We investigate an important subclass of these tools, namely linear optical
elements and auxiliary modes in the vacuum state. For this tools, we are able
to extend a previous quantitative result, a no-go theorem for perfect Bell
state analyzer on two qubits in polarization entanglement, by a quantitative
statement. We show, that within this subclass it is not possible to
discriminate unambiguously four equiprobable Bell states with a probability
higher than 50 %.Comment: 6 pages, 2 fig
Extension of germs of holomorphic foliations
We consider the problem of extending germs of plane holomorphic foliations to
foliations of compact surfaces. We show that the germs that become regular
after a single blow up and admit meromorphic first integrals can be extended,
after local changes of coordinates, to foliations of compact surfaces. We also
show that the simplest elements in this class can be defined by polynomial
equations. On the other hand we prove that, in the absence of meromorphic first
integrals there are uncountably many elements without polynomial
representations.Comment: 17 page
A transfer principle: from periods to isoperiodic foliations
In this paper we study the dynamics and topology of the isoperiodic foliation
defined on the Hodge bundle over the moduli space of genus curves
The oriented graph of multi-graftings in the Fuchsian case
We prove the connectedness and calculate the diameter of the oriented graph
of graftings associated to exotic complex projective structures on a compact
surface S with a given holonomy representation of Fuchsian type.
The oriented graph of graftings is the graph whose vertices are the
equivalence classes of marked CP^1-structures on S with a given fixed holonomy,
and there is an oriented edge between two structures if the second is obtained
from the first by grafting.Comment: Improved version. The paper chaged title: from "The oriented graph of
graftings..." to "The oriented graph of multi-graftings...
The role of auxiliary states in state discrimination with linear optical evices
The role of auxiliary photons in the problem of identifying a state secretly
chosen from a given set of L-photon states is analyzed. It is shown that
auxiliary photons do not increase the ability to discriminate such states by
means of a global measurement using only optical linear elements, conditional
transformation and auxiliary photons.Comment: 5 pages. 1 figure. RevTex documen
The Strong Law of Demand
We show that a demand function is derived from maximizing a quasilinear utility function subject to a budget constraint if and only if the demand function is cyclically monotone. On finite data sets consisting of pairs of market prices and consumption vectors, this result is equivalent to a solution of the Afriat inequalities where all the marginal utilities of income are equal. We explore the implications of these results for maximization of a random quasilinear utility function subject to a budget constraint and for representative agent general equilibrium models. The duality theory for cyclically monotone demand is developed using the Legendre-Fenchel transform. In this setting, a consumer's surplus is measured by the conjugate of her utility function.Permanent income hypothesis, Afriat's theorem, Law of demand, Consumer's surplus, Testable restrictions
- …