33,090 research outputs found
Invariance of separability probability over reduced states in 4x4 bipartite systems
The geometric separability probability of composite quantum systems is
extensively studied in the last decades. One of most simple but strikingly
difficult problem is to compute the separability probability of qubit-qubit and
rebit-rebit quantum states with respect to the Hilbert-Schmidt measure. A lot
of numerical simulations confirm the P(rebit-rebit)=29/64 and
P(qubit-qubit)=8/33 conjectured probabilities. Milz and Strunz studied the
separability probability with respect to given subsystems. They conjectured
that the separability probability of qubit-qubit (and qubit-qutrit) depends on
sum of single qubit subsystems (D), moreover it depends just on the Bloch radii
(r) of D and it is constant in r. Using the Peres-Horodecki criterion for
separability we give mathematical proof for the P(rebit-rebit)=29/64
probability and we present an integral formula for the complex case which
hopefully will help to prove the P(qubit-qubit)=8/33 probability too. We prove
Milz and Strunz's conjecture for rebit-rebit and qubit-qubit states. The case,
when the state space is endowed with the volume form generated by the operator
monotone function f(x)=sqrt(x) is studied too in detail. We show, that even in
this setting the Milz and Strunz's conjecture holds and we give an integral
formula for separability probability according to this measure.Comment: 24 pages, 1 figur
Quantity-setting games with a dominant firm
We consider a possible game-theoretic foundation of Forchheimer's model of dominant-firm price leadership based on quantity-setting games with
one large firm and many small firms. If the large firm is the exogenously given first mover, we obtain Forchheimer's model. We also investigate whether the large firm can emerge as a first mover of a timing game
The political districting problem: A survey
Computer scientists and social scientists consider the political districting problem from different viewpoints. This paper gives an overview of both strands of the literature on districting in which the connections and the differences between the two approaches are highlighted
Limits of Random Trees
Local convergence of bounded degree graphs was introduced by Benjamini and
Schramm. This result was extended further by Lyons to bounded average degree
graphs. In this paper, we study the convergence of a random tree sequence where
the probability of a given tree is proportional to . We show that this sequence is convergent and describe the limit
object, which is a random infinite rooted tree
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