Related papers: State Property Systems and Closure Spaces: Extract…
We consider the product of infinitely many copies of a spin-$1\over 2$ system. We construct projection operators on the corresponding nonseparable Hilbert space which measure whether the outcome of an infinite sequence of $\sigma^x$…
By definition a separable state has the form \sum A_i \otimes B_i, where 0 \leq A_i, B_i for each i. In this paper we consider the class of states which admit such a decomposition with B_1, ..., B_p having independent images. We give a…
Abstract separation systems provide a simple general framework in which both tree-shape and high cohesion of many combinatorial structures can be expressed, and their duality proved. Applications range from tangle-type duality and tree…
In a setting of noncommutative space with minimal length we confirm the general assertion that the more nonclassical an input state for a beam splitter is, the more entangled its output state becomes. By analysing various nonclassical…
We study the back-reaction of quantum systems onto classical ones. Taking the starting point that semi-classical physics should be described at all times by a point in classical phase space and a quantum state in Hilbert space, we consider…
I consider deterministic distinguishability of a set of orthogonal, bipartite states when only a single copy is available and the parties are restricted to local operations and classical communication, but with the additional requirement…
We discuss the classical statistics of isolated subsystems. Only a small part of the information contained in the classical probability distribution for the subsystem and its environment is available for the description of the isolated…
The Schmidt decomposition is an important tool in the study of quantum systems especially for the quantification of the entanglement of pure states. However, the Schmidt decomposition is only unique for bipartite pure states, and some…
The class of problems complete for NP via first-order reductions is known to be characterized by existential second-order sentences of a fixed form. All such sentences are built around the so-called generalized IS-form of the sentence that…
We investigate certain classes of integrable classical or quantum spin systems. The first class is characterized by the recursively defined property $P$ saying that the spin system consists of a single spin or can be decomposed into two…
This paper introduces semiopen and semiclosed soft sets in soft topological spaces. The notions of interior and closure are generalized using these sets. A detail study is carried out on properties of semiopen, semiclosed soft sets, semi…
In this paper we define and study a new class of states (the empty states). These states are the superposition of two identical states (self-superposition state). We defined three different representations of theses states, namely, the…
We address perfect discrimination of two separable states. When available states are restricted to separable states, we can theoretically consider a larger class of measurements than the class of measurements allowed in quantum theory. The…
Gaussian states with nonclassical properties such as squeezing and entanglement serve as crucial resources for quantum information processing. Accurately quantifying these properties within multi-mode Gaussian states has posed some…
In classical coding, a single quantum state is encoded into classical information. Decoding this classical information in order to regain the original quantum state is known to be impossible. However, one can attempt to construct a state…
Understanding the power and limitations of classical and quantum information and how they differ is a fundamental endeavor. In property testing of distributions, a tester is given samples over a typically large domain $\{0,1\}^n$. An…
For an associative algebra $A$ with a simple module $M$ with trivial endomorphisms and trivial annihilator we verify the countable separation property (CSP), i.e. we prove that there exists a list of nonzero elements $a_1, a_2,\ldots$ of…
We present a scheme to explicitly construct and classify general topological states jointly protected by an onsite symmetry group and a spatial symmetry group. We show that all these symmetry protected topological states can be…
This paper considers the problem of distinguishing between classical and quantum domains in macroscopic phenomena using tests based on probability and it presents a condition on the ratios of the outcomes being the same (Ps) to being…
A causal input-output system may be described by a function space for inputs, a function space for outputs, and a causal operator mapping the input space into the output space. A particular representation of the state of such a system at…