Related papers: Covariant constancy of quantum Steenrod operations
We study the $S_n$-equivariant log-concavity of the cohomology of flag varieties, also known as the coinvariant ring of $S_n$. Using the theory of representation stability, we give computer-assisted proofs of the equivariant log-concavity…
Considerable work has recently been directed toward developing resource theories of quantum coherence. In most approaches, a state is said to possess quantum coherence if it is not diagonal in some specified basis. In this letter we…
In the paper, the dynamical additivity of bi-stochastic quantum operations is characterized and the strong dynamical additivity is obtained under some restrictions.
We introduce operations with p-adic integer coefficients, associated to idempotents in the quantum cohomology of a monotone symplectic manifold, and apply them to the structure of the quantum connection.
We determine the two-point invariants of the equivariant quantum cohomology of the Hilbert scheme of points of surface resolutions associated to type A_n singularities. The operators encoding these invariants are expressed in terms of the…
We discuss a general quantum theoretical example of quantum cohomology and show that various mathematical aspects of quantum cohomology have quantum mechanical and also observable significance.
Coherent-state representations are a standard tool to deal with continuous-variable systems, as they allow one to efficiently visualize quantum states in phase space. Here, we work out an alternative basis consisting of monomials on the…
We observe a new equivariant relationship between topological Hochschild homology and cohomology. We also calculate the topological Hochschild homology of the topological Hochschild cohomology of a finite prime field, which can be viewed as…
In quantum information, most information processing processes involve quantum channels. One manifestation of a quantum channel is quantum operation acting on quantum states. The coherence of quantum operations can be considered as a quantum…
We introduce an equivariant version of contextuality with respect to a symmetry group, which comes with natural applications to quantum theory. In the equivariant setting, we construct cohomology classes that can detect contextuality. This…
We provide formulas for invariants defined on a tensor product of defining representations of unitary groups, under the action of the product group. This situation has a physical interpretation, as it is related to the quantum mechanical…
We explore and extend the application of homological algebra to describe quantum entanglement, initiated in arXiv:1901.02011, focusing on the Hodge-theoretic structure of entanglement cohomology in finite-dimensional quantum systems. We…
For a covariant functor W. Fulton and R. MacPherson defined \emph{an operational bivariant theory} associated to this covariant functor. In this paper we will show that given a contravariant functor one can similarly construct a ``dual"…
This note explores the interaction between cohomology operations in a generalized cohomology theory and a string topology loop coproduct dual to the Chas--Sullivan loop product. More precisely, we ask for a description for the failure of a…
In this note we prove that the constant and equivariant cyclic cohomology of algebras coincide. This shows that constant cyclic cohomology is rich and computable.
Quantum entanglement obscures the notion of local operations; there exist quantum states for which all local actions on one subsystem can be equivalently realized by actions on another. We characterize the states for which this fundamental…
In this work a generalization of the consistent histories approach to quantum mechanics is presented. We first critically review the consistent histories approach to nonrelativistic quantum mechanics in a mathematically rigorous way and…
Let X be a smooth projective variety. Using modified psi classes on the stack of genus zero stable maps to X, a new associative quantum product is constructed on the cohomology space of X. When X is a homogeneous variety, this structure…
We unify the resource-theoretic and the cohomological perspective on quantum contextuality. At the center of this unification stands the notion of the contextual fraction. For both symmetry and parity based contextuality proofs, we…
We construct shift operators on equivariant symplectic cohomology which generalise the shift operators on equivariant quantum cohomology in algebraic geometry. That is, given a Hamiltonian action of the torus $T$, we assign to a cocharacter…