87 research outputs found
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
Regularly Decomposable Tensors and Classical Spin States
A spin- state can be represented by a symmetric tensor of order and
dimension . Here, can be a positive integer, which corresponds to a
boson; can also be a positive half-integer, which corresponds to a fermion.
In this paper, we introduce regularly decomposable tensors and show that a
spin- state is classical if and only if its representing tensor is a
regularly decomposable tensor. In the even-order case, a regularly decomposable
tensor is a completely decomposable tensor but not vice versa; a completely
decomposable tensors is a sum-of-squares (SOS) tensor but not vice versa; an
SOS tensor is a positive semi-definite (PSD) tensor but not vice versa. In the
odd-order case, the first row tensor of a regularly decomposable tensor is
regularly decomposable and its other row tensors are induced by the regular
decomposition of its first row tensor. We also show that complete
decomposability and regular decomposability are invariant under orthogonal
transformations, and that the completely decomposable tensor cone and the
regularly decomposable tensor cone are closed convex cones. Furthermore, in the
even-order case, the completely decomposable tensor cone and the PSD tensor
cone are dual to each other. The Hadamard product of two completely
decomposable tensors is still a completely decomposable tensor. Since one may
apply the positive semi-definite programming algorithm to detect whether a
symmetric tensor is an SOS tensor or not, this gives a checkable necessary
condition for classicality of a spin- state. Further research issues on
regularly decomposable tensors are also raised.Comment: published versio
Beneficial Betrayal Aversion
Many studies demonstrate the social benefits of cooperation. Likewise, recent studies convincingly demonstrate that betrayal aversion hinders trust and discourages cooperation. In this respect, betrayal aversion is unlike socially “beneficial” preferences including altruism, fairness and inequity aversion, all of which encourage cooperation and exchange. To our knowledge, other than the suggestion that it acts as a barrier to rash trust decisions, the benefits of betrayal aversion remain largely unexplored. Here we use laboratory experiments with human participants to show that groups including betrayal-averse agents achieve higher levels of reciprocity and more profitable social exchange than groups lacking betrayal aversion. These results are the first rigorous evidence on the benefits of betrayal aversion, and may help future research investigating cultural differences in betrayal aversion as well as future research on the evolutionary roots of betrayal aversion. Further, our results extend the understanding of how intentions affect social interactions and exchange and provide an effective platform for further research on betrayal aversion and its effects on human behavior
Social preferences, accountability, and wage bargaining
We assess the extent of preferences for employment in a collective wage bargaining situation with heterogeneous workers. We vary the size of the union and introduce a treatment mechanism transforming the voting game into an individual allocation task. Our results show that highly productive workers do not take employment of low productive workers into account when making wage proposals, regardless of whether insiders determine the wage or all workers. The level of pro-social preferences is small in the voting game, while it increases as the game is transformed into an individual allocation task. We interpret this as an accountability effect
The Elasticity of Trust: How to Promote Trust in the Arab Middle East and the United States
X band model of Venus atmosphere permittivity
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/94912/1/rds5697.pd
Group Polarization in the Team Dictator Game reconsidered
While most papers on team decision-making find teams to behave more selfish, less trusting and less altruistic than individuals, Cason and Mui (1997) report that teams are more altruistic than individuals in a dictator game. Using a within-subjects design we re-examine group polarization by letting subjects make individual as well as team decisions in an experimental dictator game. In our experiment teams are more selfish than individuals, and the most selfish team member has the strongest influence on team decisions. Various sources of the different findings in Cason and Mui (1997) and in our paper are discussed
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