4 citations · 22 across the 17 of their papers we have counts for
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The Infinite-Dimensional Quantum Entropy: the Unified Entropy Case
Roman Gielerak, Joanna Wiśniewska, Marek Sawerwain
By a use of the Fredholm determinant theory, the unified quantum entropy notion has been extended to a case of infinite-dimensional systems. Some of the known (in the finite-dimens…
Renormalized von Neumann entropy with application to entanglement in genuine infinite dimensional systems
Roman Gielerak
A renormalized version of the von Neumann quantum entropy (which is finite and continuous in general, infinite dimensional case) and which obeys several of the natural physical dem…
Maximally entangled states of quantum systems: some numerical studies
Roman Gielerak, Marek Sawerwain
Gram matrix approach to an entanglement analysis of pure states describing -- quantum systems is being introduced. In particular, maximally entangled states are descri…
A Gramian Approach to Entanglement in Bipartite Finite Dimensional Systems: The case of pure states
Roman Gielerak, Marek Sawerwain
It has been observed that the reduced density matrices of bipartite qudit pure states possess a Gram matrix structure. This observation has opened a possibility of analysing the en…
\b{eta}-KMS Green functions generating functionals - the convexity based approach
Roman Gielerak
The notion of the stochastically positive \b{eta}-KMS (Euclidean time ) Green functionals on ( the abelian sectors of ) the CCR-algebras in Weyl form has been introduced .The main…
Schmidt decomposition of mixed-pure states for (d,infinity ) systems and some applications
Roman Gielerak
Summary. A simple derivation of finite Schmidt decomposition of pure states describing finite dimensional systems interacting with the infinite dimensional ones is presented. In pa…
Twopartite, combinatorial approach to partial k-separability problem for general multipartite states
Roman Gielerak Marek Sawerwain
We describe a general methods to localize any sort of k-separability and therefore also the corresponding partial entanglement in genuinely multipartite mixed quantum states. Our m…
Sorting of quantum states with respect to amount of entanglement included
Roman Gielerak, Marek Sawerwain
The canonical Schmidt decomposition of quantum states is discussed and its implementation to the Quantum Computation Simulator is outlined. In particular, the semiorder relation in…
Generalised quantum weakest preconditions
Roman Gielerak, Marek Sawerwain
Generalisation of the quantum weakest precondition result of D'Hondt and Panangaden is presented. In particular the most general notion of quantum predicate as positive operator va…
From Stochastic Differential Equations to Quantum Field Theory
R. Gielerak, P. Lugiewicz
Covariant stochastic partial (pseudo-)differential equations are studied in any dimension. In particular a large class of covariant interacting local quantum fields obeying the Mor…
Stochastically positive structures on Weyl algebras. The case of quasi-free states
R. Gielerak, L. Jakobczyk, R. Olkiewicz
We consider quasi-free stochastically positive ground and thermal states on Weyl algebras in Euclidean time formulation. In particular, we obtain a new derivation of a general form…