50 research outputs found
Concurrence vs. purity: Influence of local channels on Bell states of two qubits
We analyze how a maximally entangled state of two-qubits (e.g., the singlet
) is affected by action of local channels described by completely
positive maps \cE . We analyze the concurrence and the purity of states
\varrho_\cE=\cE\otimes\cI[\psi_s].Using the concurrence-{\it vs}-purity phase
diagram we characterize local channels \cE by their action on the singlet
state . We specify a region of the concurrence-{\it vs.}-purity diagram
that is achievable from the singlet state via the action of unital channels. We
show that even most general (including non-unital) local channels acting just
on a single qubit of the original singlet state cannot generate the maximally
entangled mixed states (MEMS). We study in detail various time evolutions of
the original singlet state induced by local Markovian semigroups. We show that
the decoherence process is represented in the concurrence-{\it vs.}-purity
diagram by a line that forms the lower bound of the achievable region for
unital maps. On the other hand, the depolarization process is represented by a
line that forms the upper bound of the region of maps induced by unital maps.Comment: 9 pages, 6 figure
Dynamics of open quantum systems initially entangled with environment: Beyond the Kraus representation
We present a general analysis of the role of initial correlations between the
open system and an environment on quantum dynamics of the open system.Comment: 5 revtex pages, no figures, accepted for publication in Phys. Rev.
Quantum walks with random phase shifts
We investigate quantum walks in multiple dimensions with different quantum
coins. We augment the model by assuming that at each step the amplitudes of the
coin state are multiplied by random phases. This model enables us to study in
detail the role of decoherence in quantum walks and to investigate the
quantum-to-classical transition. We also provide classical analogues of the
quantum random walks studied. Interestingly enough, it turns out that the
classical counterparts of some quantum random walks are classical random walks
with a memory and biased coin. In addition random phase shifts "simplify" the
dynamics (the cross interference terms of different paths vanish on average)
and enable us to give a compact formula for the dispersion of such walks.Comment: to appear in Phys. Rev. A (10 pages, 5 figures
Approximate programmable quantum processors
A quantum processor is a programmable quantum circuit in which both the data
and the program, which specifies the operation that is carried out on the data,
are quantum states. We study the situation in which we want to use such a
processor to approximate a set of unitary operators to a specified level of
precision. We measure how well an operation is performed by the process
fidelity between the desired operation and the operation produced by the
processor. We show how to find the program for a given processor that produces
the best approximation of a particular unitary operation. We also place bounds
on the dimension of the program space that is necessary to approximate a set of
unitary operators to a specified level of precision.Comment: 8 page
Quantum interference with molecules: The role of internal states
Recent experiments have shown that fullerene and fluorofullerene molecules
can produce interference patterns. These molecules have both rotational and
vibrational degrees of freedom. This leads one to ask whether these internal
motions can play a role in degrading the interference pattern. We study this by
means of a simple model. Our molecule consists of two masses a fixed distance
apart. It scatters from a potential with two or several peaks, thereby
mimicking two or several slit interference. We find that in some parameter
regimes the entanglement between the internal states and the translational
degrees of freedom produced by the potential can decrease the visibility of the
interference pattern. In particular, different internal states correspond to
different outgoing wave vectors, so that if several internal states are
excited, the total interference pattern will be the sum of a number of
patterns, each with a different periodicity. The overall pattern is
consequently smeared out. In the case of two different peaks, the scattering
from the different peaks will excite different internal states so that the path
the molecule takes become entangled with its internal state. This will also
lead to degradation of the interference pattern. How these mechanisms might
lead to the emergence of classical behavior is discussed.Comment: 12 pages, 4 eps figures, quality of figures reduced because of size
restriction
Entanglement, purity and energy: Two qubits vs Two modes
We study the relationship between the entanglement, mixedness and energy of
two-qubit and two-mode Gaussian quantum states. We parametrize the set of
allowed states of these two fundamentally different physical systems using
measures of entanglement, mixedness and energy that allow us to compare and
contrast the two systems using a phase diagram. This phase diagram enables one
to clearly identify not only the physically allowed states, but the set of
states connected under an arbitrary quantum operation. We pay particular
attention to the maximally entangled mixed states (MEMS) of each system.
Following this we investigate how efficiently one may transfer entanglement
from two-mode to two-qubit states.Comment: 13 figures. References and 1 figure adde
When Non-Gaussian States are Gaussian: Generalization of Non-Separability Criterion for Continuous Variables
We present a class of non-Gaussian two-mode continuous variable states for
which the separability criterion for Gaussian states can be employed to detect
whether they are separable or not. These states reduce to the two-mode Gaussian
states as a special case.Comment: Removed 1 figure, added reference
Singlet states and the estimation of eigenstates and eigenvalues of an unknown Controlled-U gate
We consider several problems that involve finding the eigenvalues and
generating the eigenstates of unknown unitary gates. We first examine
Controlled-U gates that act on qubits, and assume that we know the eigenvalues.
It is then shown how to use singlet states to produce qubits in the eigenstates
of the gate. We then remove the assumption that we know the eigenvalues and
show how to both find the eigenvalues and produce qubits in the eigenstates.
Finally, we look at the case where the unitary operator acts on qutrits and has
eigenvalues of 1 and -1, where the eigenvalue 1 is doubly degenerate. The
eigenstates are unknown. We are able to use a singlet state to produce a qutrit
in the eigenstate corresponding to the -1 eigenvalue.Comment: Latex, 10 pages, no figure