arXiv subjects

Jacek Jurkowski

Publications and source records attributed to Jacek Jurkowski.

6 recordsLinked to original sources

arXiv2013

On separable decompositions of quantum states with strong positive partial transposes

We analyze a class of positive partial transpose states (PPT) such that the positivity of its partial transposition is recognized with respect to canonical factorization of the original density operator (Cholesky block decomposition). We call such PPT states strong PPT states (SPPT). This property, contrary to PPT, is basis dependent. It is shown that there exists a proper subset of SPPT states which are separable and provide a separable decomposition for any of these states.

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arXiv2012

Discord Derived from Tsallis Entropy

Due to some ambiguity in defining mutual Tsallis entropy in the classical probability theory, its generalization to quantum theory is discussed and, as a consequence, two types of generalized quantum discord, called $q$-discords, are defined in terms of quantum Tsallis entropy. $q$-discords for two-qubit Werner and isotropic states are calculated and it is shown that one of them is positive, at least for states under investigation, for all $q>0$. Finally, an analytical expression for $q$-discord of certain family of two-qubit X states is presented.

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arXiv2010

Estimating Concurrence via Entanglement Witnesses

We show that each entanglement witness detecting given bipartite entangled state provides an estimation of its concurrence. We illustrate our result with several well known examples of entanglement witnesses and compare the corresponding estimation of concurrence with other estimations provided by the trace norm of partial transposition and realignment.

quant-ph↗

arXiv2007

Memory in a nonlocally damped oscillator

We analyze the new equation of motion for the damped oscillator. It differs from the standard one by a damping term which is nonlocal in time and hence it gives rise to a system with memory. Both classical and quantum analysis is performed. The characteristic feature of this nonlocal system is that it breaks local composition low for the classical Hamiltonian dynamics and the corresponding quantum propagator.

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arXiv2007

Quantum states with strong positive partial transpose

We construct a large class of bipartite M x N quantum states which defines a proper subset of states with positive partial transposes (PPT). Any state from this class is PPT but the positivity of its partial transposition is recognized with respect to canonical factorization of the original density operator. We propose to call elements from this class states with strong positive partial transposes (SPPT). We conjecture that all SPPT states are separable.

quant-ph↗

arXiv2005

Quantum damped oscillator I: dissipation and resonances

Quantization of a damped harmonic oscillator leads to so called Bateman's dual system. The corresponding Bateman's Hamiltonian, being a self-adjoint operator, displays the discrete family of complex eigenvalues. We show that they correspond to the poles of energy eigenvectors and the corresponding resolvent operator when continued to the complex energy plane. Therefore, the corresponding generalized eigenvectors may be interpreted as resonant states which are responsible for the irreversible quantum dynamics of a damped harmonic oscillator.

quant-ph↗