2,139 research outputs found
More order with less law: on contract enforcement, trust, and crowding
Most contracts, whether between voters and politicians or between house owners and contractors, are incomplete. “More law,” it typically is assumed, increases the likelihood of contract performance by increasing the probability of enforcement and/or the cost of breach. We examine a contractual relationship in which the first mover has to decide whether she wants to enter a contract without knowing whether the second mover will perform. We analyze how contract enforceability affects individual performance for exogenous preferences. Then we apply a dynamic model of preference adaptation and find that economic incentives have a nonmonotonic effect on behavior. Individuals perform a contract when enforcement is strong or weak but not with medium enforcement probabilities: Trustworthiness is “crowded in” with weak and “crowded out” with medium enforcement. In a laboratory experiment we test our model’s implications and find support for the crowding prediction. Our finding is in line with the recent work on the role of contract enforcement and trust in formerly Communist countries
Partial transpose criteria for symmetric states
We express the positive partial transpose (PPT) separability criterion for
symmetric states of multi-qubit systems in terms of matrix inequalities based
on the recently introduced tensor representation for spin states. We construct
a matrix from the tensor representation of the state and show that it is
similar to the partial transpose of the density matrix written in the
computational basis. Furthermore, the positivity of this matrix is equivalent
to the positivity of a correlation matrix constructed from tensor products of
Pauli operators. This allows for a more transparent experimental interpretation
of the PPT criteria for an arbitrary spin-j state. The unitary matrices
connecting our matrix to the partial transpose of the state generalize the
so-called magic basis that plays a central role in Wootters' explicit formula
for the concurrence of a 2-qubit system and the Bell bases used for the
teleportation of a one or two-qubit state.Comment: 8 page
Quantumness of spin-1 states
We investigate quantumness of spin-1 states, defined as the Hilbert-Schmidt
distance to the convex hull of spin coherent states. We derive its analytic
expression in the case of pure states as a function of the smallest eigenvalue
of the Bloch matrix and give explicitly the closest classical state for an
arbitrary pure state. Numerical evidence is provided that the exact formula for
pure states provides an upper bound on the quantumness of mixed states. Due to
the connection between quantumness and entanglement we obtain new insights into
the geometry of symmetric entangled states
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