15,678 research outputs found
Noncyclic geometric changes of quantum states
Non-Abelian quantum holonomies, i.e., unitary state changes solely induced by
geometric properties of a quantum system, have been much under focus in the
physics community as generalizations of the Abelian Berry phase. Apart from
being a general phenomenon displayed in various subfields of quantum physics,
the use of holonomies has lately been suggested as a robust technique to obtain
quantum gates; the building blocks of quantum computers. Non-Abelian holonomies
are usually associated with cyclic changes of quantum systems, but here we
consider a generalization to noncyclic evolutions. We argue that this open-path
holonomy can be used to construct quantum gates. We also show that a structure
of partially defined holonomies emerges from the open-path holonomy. This
structure has no counterpart in the Abelian setting. We illustrate the general
ideas using an example that may be accessible to tests in various physical
systems.Comment: Extended version, new title, journal reference adde
Random Unitary Evolution Model of Quantum Darwinism with pure decoherence
We study the behavior of Quantum Darwinism (Zurek, [8]) within the iterative,
random unitary operations qubit-model of pure decoherence (Novotny et al, [6]).
We conclude that Quantum Darwinism, which describes the quantum mechanical
evolution of an open system S from the point of view of its environment E, is
not a generic phenomenon, but depends on the specific form of input states and
on the type of S-E-interactions. Furthermore, we show that within the random
unitary model the concept of Quantum Darwinism enables one to explicitly
construct and specify artificial input states of environment E that allow to
store information about an open system S of interest with maximal efficiency.Comment: 18 pages, 7 figure
Entanglement of bosonic modes of nonplanar molecules
Entanglement of bosonic modes of material oscillators is studied in the
context of two bilinearly coupled, nonlinear oscillators. These oscillators are
realizable in the vibrational-cum-bending motions of C-H bonds in
dihalomethanes. The bilinear coupling gives rise to invariant subspaces in the
Hilbert space of the two oscillators. The number of separable states in any
invariant subspace is one more than the dimension of the space. The dynamics of
the oscillators when the initial state belongs to an invariant subspace is
studied. In particular, the dynamics of the system when the initial state is
such that the total energy is concentrated in one of the modes is studied and
compared with the evolution of the system when the initial state is such
wherein the modes share the total energy. The dynamics of quantities such as
entropy, mean of number of quanta in the two modes and variances in the
quadratures of the two modes are studied. Possibility of generating maximally
entangled states is indicated.Comment: 21 pages, 6 figure
Group-invariant soliton equations and bi-Hamiltonian geometric curve flows in Riemannian symmetric spaces
Universal bi-Hamiltonian hierarchies of group-invariant (multicomponent)
soliton equations are derived from non-stretching geometric curve flows
\map(t,x) in Riemannian symmetric spaces , including compact
semisimple Lie groups for , . The derivation
of these soliton hierarchies utilizes a moving parallel frame and connection
1-form along the curve flows, related to the Klein geometry of the Lie group
where is the local frame structure group. The soliton
equations arise in explicit form from the induced flow on the frame components
of the principal normal vector N=\covder{x}\mapder{x} along each curve, and
display invariance under the equivalence subgroup in that preserves the
unit tangent vector T=\mapder{x} in the framing at any point on a curve.
Their bi-Hamiltonian integrability structure is shown to be geometrically
encoded in the Cartan structure equations for torsion and curvature of the
parallel frame and its connection 1-form in the tangent space T_\map M of the
curve flow. The hierarchies include group-invariant versions of sine-Gordon
(SG) and modified Korteweg-de Vries (mKdV) soliton equations that are found to
be universally given by curve flows describing non-stretching wave maps and
mKdV analogs of non-stretching Schrodinger maps on . These results provide
a geometric interpretation and explicit bi-Hamiltonian formulation for many
known multicomponent soliton equations. Moreover, all examples of
group-invariant (multicomponent) soliton equations given by the present
geometric framework can be constructed in an explicit fashion based on Cartan's
classification of symmetric spaces.Comment: Published version, with a clarification to Theorem 4.5 and a
correction to the Hamiltonian flow in Proposition 5.1
Non-Abelian generalization of off-diagonal geometric phases
If a quantum system evolves in a noncyclic fashion the corresponding
geometric phase or holonomy may not be fully defined. Off-diagonal geometric
phases have been developed to deal with such cases. Here, we generalize these
phases to the non-Abelian case, by introducing off-diagonal holonomies that
involve evolution of more than one subspace of the underlying Hilbert space.
Physical realizations of the off-diagonal holonomies in adiabatic evolution and
interferometry are put forward.Comment: Additional material, journal reference adde
Non-adiabatic holonomic quantum computation in linear system-bath coupling
Non-adiabatic holonomic quantum computation in decoherence-free subspaces
protects quantum information from control imprecisions and decoherence. For the
non-collective decoherence that each qubit has its own bath, we show the
implementations of two non-commutable holonomic single-qubit gates and one
holonomic nontrivial two-qubit gate that compose a universal set of
non-adiabatic holonomic quantum gates in decoherence-free-subspaces of the
decoupling group, with an encoding rate of . The proposed scheme
is robust against control imprecisions and the non-collective decoherence, and
its non-adiabatic property ensures less operation time. We demonstrate that our
proposed scheme can be realized by utilizing only two-qubit interactions rather
than many-qubit interactions. Our results reduce the complexity of practical
implementation of holonomic quantum computation in experiments. We also discuss
the physical implementation of our scheme in coupled microcavities.Comment: 2 figures; accepted by Sci. Re
Perfect routing of quantum information in regular cavity QED networks
We introduce a scheme for perfect routing of quantum states and entanglement
in regular cavity QED networks. The couplings between the cavities are
quasi-uniform and each cavity is doped with a two-level atom. Quasi-uniform
couplings leads the system to evolve in invariant subspaces. Combination the
evolutions of the system in its invariant subspaces with quite simple local
operations on atoms in the networks, gives the perfect routing of quantum
states and entanglement through the network. To provide the protocol be robust
due to decoherence arisen from photon loss, the field mode of the cavities are
only virtually excited
- …