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Self-adjoint commuting differential operators and commutative subalgebras of the Weyl algebra
Self-adjoint commuting differential operators commutative subalgebras the Weyl algebra Mathematical Physics
2011/9/13
Abstract: In this paper we give enough conditions when the operator of the fourth order included in a commutative ring of ordinary differential operators of rank 2 is formally self-adjoint. In the cas...
On rings of commuting partial differential operators
partial differential operators Algebraic Geometry
2011/7/27
Abstract: We give a natural generalization of the classification of commutative rings of ordinary differential operators, given in works of Krichever, Mumford, Mulase, and determine commutative rings ...
Parameter Dependent Commuting Matrices, Plücker relations and Related Quantum Glass Models
Parameter Dependent Commuting Matrices Plücker relations Related Quantum Glass Models
2010/11/11
Type-I matrices were introduced recently as finite dimensional prototypes of quantum integrable systems. These matrices are linearly dependent on an "interaction" type parameter, and possess interesti...
Device-Independent Quantum Key Distribution with Commuting Measurements
Device-Independent Quantum Key Distribution ommuting Measurements
2010/10/19
We consider quantum key distribution in the device-independent scenario, i.e., where the
legitimate parties do not know (or trust) the exact specification of their apparatus. We show
how secure key ...
Generalized Tsirelson Inequalities, Commuting-Operator Provers and Multi-Prover Interactive Proof Systems
Commuting-Operator Provers Multi-Prover Interactive Proof Systems
2012/11/30
A central question in quantum information theory and computational complexity is how powerful nonlocal strategies are in cooperative games with imperfect information, such as multi-prover interactive ...