1,132 research outputs found
Some Ulam's reconstruction problems for quantum states
Provided a complete set of putative -body reductions of a multipartite
quantum state, can one determine if a joint state exists? We derive necessary
conditions for this to be true. In contrast to what is known as the quantum
marginal problem, we consider a setting where the labeling of the subsystems is
unknown. The problem can be seen in analogy to Ulam's reconstruction conjecture
in graph theory. The conjecture - still unsolved - claims that every graph on
at least three vertices can uniquely be reconstructed from the set of its
vertex-deleted subgraphs. When considering quantum states, we demonstrate that
the non-existence of joint states can, in some cases, already be inferred from
a set of marginals having the size of just more than half of the parties. We
apply these methods to graph states, where many constraints can be evaluated by
knowing the number of stabilizer elements of certain weights that appear in the
reductions. This perspective links with constraints that were derived in the
context of quantum error-correcting codes and polynomial invariants. Some of
these constraints can be interpreted as monogamy-like relations that limit the
correlations arising from quantum states. Lastly, we provide an answer to
Ulam's reconstruction problem for generic quantum states.Comment: 22 pages, 3 figures, v2: significantly revised final versio
Positive maps and trace polynomials from the symmetric group
With techniques borrowed from quantum information theory, we develop a method
to systematically obtain operator inequalities and identities in several matrix
variables. These take the form of trace polynomials: polynomial-like
expressions that involve matrix monomials
and their traces . Our
method rests on translating the action of the symmetric group on tensor product
spaces into that of matrix multiplication. As a result, we extend the polarized
Cayley-Hamilton identity to an operator inequality on the positive cone,
characterize the set of multilinear equivariant positive maps in terms of
Werner state witnesses, and construct permutation polynomials and tensor
polynomial identities on tensor product spaces. We give connections to concepts
in quantum information theory and invariant theory.Comment: 28 pages, 3 figures, 2 tables. Extensively rewritten: asymmetric
maps, proof for Motzkin matrix polynomial, and connections to QIT added.
Comments welcome
FPGA-based operational concept and payload data processing for the Flying Laptop satellite
Flying Laptop is the first small satellite developed by the Institute of Space Systems at the Universität Stuttgart. It is a test bed for an on-board computer with a reconfigurable, redundant and self-controlling high computational ability based on the field pro- grammable gate arrays (FPGAs). This Technical Note presents the operational concept and the on-board payload data processing of the satellite. The designed operational concept of Flying Laptop enables the achievement of mission goals such as technical demonstration, scientific Earth observation, and the payload data processing methods. All these capabilities expand its scientific usage and enable new possibilities for real-time applications. Its hierarchical architecture of the operational modes of subsys- tems and modules are developed in a state-machine diagram and tested by means of MathWorks Simulink-/Stateflow Toolbox. Furthermore, the concept of the on-board payload data processing and its implementation and possible applications are described
Entanglement detection with trace polynomials
We provide a systematic method for nonlinear entanglement detection based on
trace polynomial inequalities. In particular, this allows to employ
multi-partite witnesses for the detection of bipartite states, and vice versa.
We identify witnesses for which linear detection of an entangled state fails,
but for which nonlinear detection succeeds. With the trace polynomial
formulation a great variety of witnesses arise from immamant inequalities,
which can be implemented in the laboratory through randomized measurements
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