Related papers: Operator transpose within normal ordering and its …
By virtue of the integration method within P-ordered product of operators and the property of entangled state representation, we reveal new physical interpretation of the generalized two-mode squeezing operator (GTSO), and find it be…
Recent results on the construction and applications of the transmutation (transformation) operators are discussed. Three new representations for solutions of the one-dimensional Schr\"odinger equation are considered. Due to the fact that…
We obtain criteria for the boundedness and compactness of weighted composition operators between different Fock spaces in $\mathbb{C}^n$. We also give estimates for essential norm of these operators.
Exponential operator decompositions are an important tool in many fields of physics, for example, in quantum control, quantum computation, or condensed matter physics. In this work, we present a method for obtaining such decompositions,…
Using simultaneously two operator identities, we consider the inversion of the convolution operators on a rectangular. The structure of the inverse operators and of some corresponding forms, which are important in signal processing, is…
Realignment operation has a significant role in detecting bound as well as free entanglement. Just like partial transposition, it is also based on permutations of the matrix elements. However, the physical implementation of realignment…
In this letter we discuss a new entanglement measure. It is based on the Hilbert-Schmidt norm of operators. We give an explicit formula for calculating the entanglement of a large set of states on C^2 \times C^2. Furthermore we find some…
We study weighted composition operators acting between Fock spaces. The following results are obtained: (1) Criteria for the boundedness and compactness; (2) Characterizations of compact differences and essential norm; (3) Complete…
We investigate spaces of operators which are invariant under translations or modulations by lattices in phase space. The natural connection to the Heisenberg module is considered, giving results on the characterisation of such operators as…
We introduce the quantum fractional Hadamard transform with continuous variables. It is found that the corresponding quantum fractional Hadamard operator can be decomposed into a single-mode fractional operator and two single-mode squeezing…
We use the method of atomic decomposition and a new family of Banach spaces to study the action of transfer operators associated to piecewise-defined maps. It turns out that these transfer operators are quasi-compact even when the…
In this thesis, we establish a necessary and sufficient condition for a weighted composition operator to commute with a self-adjoint weighted composition operator on the Fock space, then obtain a sufficient condition for these commuting…
The present article is devoted to the investigation of some properties of the generalized shift operator of numbers represented in terms of numeral systems with a variable alphabet.
Entanglement is known to serve as an order parameter for true topological order in two-dimensional systems. We show how entanglement of disconnected partitions defines topological invariants for one-dimensional topological superconductors.…
The purpose of this paper is to systematically study compactness and essential norm properties of operators on a very general class of weighted Fock spaces over $\C$. In particular, we obtain rather strong necessary and sufficient…
Recently, it has been shown that locally randomized measurements can be employed to get partial transpose moments of a density matrix [Elben A., {\it et al.} Phys. Rev. Lett. {\bf 125}, 200501 (2020)]. Consequently, two general entanglement…
Transformers are arguably the main workhorse in recent Natural Language Processing research. By definition a Transformer is invariant with respect to reordering of the input. However, language is inherently sequential and word order is…
Classical surfaces in phase space correspond to quantum states in Hilbert space. Subsystems specify factor spaces of the Hilbert space. An entangled state corresponds semiclassically to a surface that cannot be decomposed into a product of…
The partial transposition(PT) operation is an effecient tool in detecting the inseparability of a mixed state. We give an explicit formula for the PT operation for the continuous variable states in Fock space. We then give the necessary and…
In quantum field theory, physicists routinely use "normal ordering" of operators, which just amounts to shuffling all creation operators to the left. Potentially confusing, then, is the occurrence in the literature of normal-ordered…