4,519 research outputs found
The Complexity of Relating Quantum Channels to Master Equations
Completely positive, trace preserving (CPT) maps and Lindblad master
equations are both widely used to describe the dynamics of open quantum
systems. The connection between these two descriptions is a classic topic in
mathematical physics. One direction was solved by the now famous result due to
Lindblad, Kossakowski Gorini and Sudarshan, who gave a complete
characterisation of the master equations that generate completely positive
semi-groups. However, the other direction has remained open: given a CPT map,
is there a Lindblad master equation that generates it (and if so, can we find
it's form)? This is sometimes known as the Markovianity problem. Physically, it
is asking how one can deduce underlying physical processes from experimental
observations.
We give a complexity theoretic answer to this problem: it is NP-hard. We also
give an explicit algorithm that reduces the problem to integer semi-definite
programming, a well-known NP problem. Together, these results imply that
resolving the question of which CPT maps can be generated by master equations
is tantamount to solving P=NP: any efficiently computable criterion for
Markovianity would imply P=NP; whereas a proof that P=NP would imply that our
algorithm already gives an efficiently computable criterion. Thus, unless P
does equal NP, there cannot exist any simple criterion for determining when a
CPT map has a master equation description.
However, we also show that if the system dimension is fixed (relevant for
current quantum process tomography experiments), then our algorithm scales
efficiently in the required precision, allowing an underlying Lindblad master
equation to be determined efficiently from even a single snapshot in this case.
Our work also leads to similar complexity-theoretic answers to a related
long-standing open problem in probability theory.Comment: V1: 43 pages, single column, 8 figures. V2: titled changed; added
proof-overview and accompanying figure; 50 pages, single column, 9 figure
The semigroup structure of Gaussian channels
We investigate the semigroup structure of bosonic Gaussian quantum channels.
Particular focus lies on the sets of channels which are divisible, idempotent
or Markovian (in the sense of either belonging to one-parameter semigroups or
being infinitesimal divisible). We show that the non-compactness of the set of
Gaussian channels allows for remarkable differences when comparing the
semigroup structure with that of finite dimensional quantum channels. For
instance, every irreversible Gaussian channel is shown to be divisible in spite
of the existence of Gaussian channels which are not infinitesimal divisible. A
simpler and known consequence of non-compactness is the lack of generators for
certain reversible channels. Along the way we provide new representations for
classes of Gaussian channels: as matrix semigroup, complex valued positive
matrices or in terms of a simple form describing almost all one-parameter
semigroups.Comment: 20 page
Optimal squeezing and entanglement from noisy Gaussian operations
We investigate the creation of squeezing via operations subject to noise and
losses and ask for the optimal use of such devices when supplemented by
noiseless passive operations. Both single and repeated uses of the device are
optimized analytically and it is proven that in the latter case the squeezing
converges exponentially fast to its asymptotic optimum, which we determine
explicitly. For the case of multiple iterations we show that the optimum can be
achieved with fixed intermediate passive operations. Finally, we relate the
results to the generation of entanglement and derive the maximal two-mode
entanglement achievable within the considered scenario.Comment: 4 pages; accepted version (minor changes), Journal-ref adde
Entanglement in fermionic systems
The anticommuting properties of fermionic operators, together with the
presence of parity conservation, affect the concept of entanglement in a
composite fermionic system. Hence different points of view can give rise to
different reasonable definitions of separable and entangled states. Here we
analyze these possibilities and the relationship between the different classes
of separable states. We illustrate the differences by providing a complete
characterization of all the sets defined for systems of two fermionic modes.
The results are applied to Gibbs states of infinite chains of fermions whose
interaction corresponds to a XY-Hamiltonian with transverse magnetic field.Comment: 13 pages, 3 figures, 4 table
Violation of the entropic area law for Fermions
We investigate the scaling of the entanglement entropy in an infinite
translational invariant Fermionic system of any spatial dimension. The states
under consideration are ground states and excitations of tight-binding
Hamiltonians with arbitrary interactions. We show that the entropy of a finite
region typically scales with the area of the surface times a logarithmic
correction. Thus, in contrast to analogous Bosonic systems, the entropic area
law is violated for Fermions. The relation between the entanglement entropy and
the structure of the Fermi surface is discussed, and it is proven, that the
presented scaling law holds whenever the Fermi surface is finite. This is in
particular true for all ground states of Hamiltonians with finite range
interactions.Comment: 5 pages, 1 figur
Quantum Capacities of Bosonic Channels
We investigate the capacity of bosonic quantum channels for the transmission
of quantum information. Achievable rates are determined from measurable moments
of the channel by showing that every channel can asymptotically simulate a
Gaussian channel which is characterized by second moments of the initial
channel. We calculate the quantum capacity for a class of Gaussian channels,
including channels describing optical fibers with photon losses, by proving
that Gaussian encodings are optimal. Along the way we provide a complete
characterization of degradable Gaussian channels and those arising from
teleportation protocols.Comment: 5 pages, 2 figure
Sorafenib prevents human retinal pigment epithelium cells from light-induced overexpression of VEGF, PDGF and PlGF
Background
Cumulative light exposure is significantly associated with progression of age-related macular degeneration (AMD). Inhibition of vascular endothelial growth factor is the main target of current antiangiogenic treatment strategies in AMD. However, other growth factors, such as platelet-derived growth factor (PDGF) and placenta growth factor (PlGF), have a substantial impact on development of AMD. Previous reports indicate that sorafenib, an oral multikinase inhibitor, might have beneficial effects on exudative AMD. This study investigates the effects of sorafenib on light-induced overexpression of growth factors in human retinal pigment epithelial (RPE) cells. Methods
Primary human RPE cells were exposed to white light and incubated with sorafenib. Viability, expression, and secretion of VEGF-A, PDGF-BB, and PlGF and their mRNA were determined by reverse transcription-polymerase chain reactions, immunohistochemistry and enzyme-linked immunosorbent assays.
Results
Light exposure decreased cell viability and increased expression and secretion of VEGF-A, PDGF-BB and PlGF. These light-induced effects were significantly reduced when cells were treated with sorafenib at a dose of 1 mu g/ml.
Conclusion
The results show that sorafenib has promising properties as a potential antiangiogenic treatment for AMD
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