arXiv subjects

Klára Baksová

Publications and source records attributed to Klára Baksová.

6 recordsLinked to original sources

arXiv2026

Certification of high-dimensional entanglement in continuous-variable systems

The dimensionality of entanglement in high-dimensional quantum systems is quantified by the Schmidt number, whose large value signals potential advantages for quantum communication and quantum computation. A commonly used approach to practical Schmidt-number detection in finite-dimensional systems is based on the estimation of fidelities to pure states with large entanglement dimensionality or lower bounds to these fidelities. However, for mode-entangled continuous-variable systems, the corresponding measurements are typically difficult to realize. Here, we introduce and assess fidelity bounds for Schmidt-number detection based on practically more accessible measurements of the first and second statistical moments of arbitrary continuous-variable quantum states. We provide analytical formulas that allow evaluating these bounds and test them for families of Gaussian and non-Gaussian states, including two-mode squeezed thermal states and photon-added displaced two-mode squeezed vacuum states. We compare our bounds to other methods for the certification of high-dimensional entanglement based on the same measurements.

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arXiv2026

Compressibility of genuine multipartite entanglement under the Hadamard map

One of the most counterintuitive effects in the examination of quantum states is the phenomenon of superactivation, which describes the fact that a quantum state, which is useless for a specific task, may become useful when one considers multiple copies of it. This effect can be observed in the case of genuine multipartite entanglement, where local projections from multiple copies to the single-copy Hilbert space could significantly simplify the practical accessibility of its superactivation. We investigate how such projections behave in the limit of many copies, using the Hadamard map as an example, and studying different state families. We show that, in this scheme, for a fixed map, an optimal number of copies exists, beyond which the obtained entanglement decreases, highlighting the differences between entanglement distillation and local projection schemes.

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arXiv2026

On the existence of fully inseparable biseparable Gaussian states

Genuine multipartite entanglement and full inseparability are two inequivalent quantum resources. Even though all genuinely multipartite entangled states are also fully inseparable, not all fully inseparable states are genuinely multipartite entangled. There exist fully inseparable states that can be prepared as convex mixtures of states separable with respect to different bipartite splits. Here, we are interested in examples of Gaussian states that possess this type of entanglement, so-called fully inseparable biseparable states. We show for several archetypical families of multimode Gaussian states that fully inseparable biseparable candidate states are actually genuinely multipartite entangled. Using projections to finite-dimensional subspaces and fully decomposable witnesses, we observe a shrinking of the regions of potentially fully inseparable biseparable Gaussian states with growing dimension of the projection subspaces. We therefore conjecture that all fully inseparable Gaussian states are genuinely multipartite entangled.

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arXiv2025

Superactivation and Incompressibility of Genuine Multipartite Entanglement

Quantum correlations in the form of entanglement, quantum steering or Bell nonlocality are resources for various information-processing tasks, but their detailed quantification and characterization remain complicated. One counter-intuitive effect is the phenomenon of superactivation, meaning that two copies of a quantum state may exhibit forms of correlations which are absent on the single-copy level. We develop a systematic approach towards a full understanding of this phenomenon using the paradigm of genuine multipartite entanglement. We introduce systematic methods for studying superactivation of entanglement based on symmetries and generalized notions of multipartite distillability. With this, we present novel criteria for superactivation as well as a quantitative theory of it. Finally, we prove the existence of incompressible entanglement, meaning that there are quantum states for which superactivated multipartite entanglement cannot be reduced to the single-copy level.

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arXiv2025

Multi-copy activation of genuine multipartite entanglement in continuous-variable systems

Multi-copy activation of genuine multipartite entanglement (GME) is a phenomenon whereby multiple copies of biseparable but fully inseparable states can exhibit GME. This was shown to be generically possible in finite dimensions. Here, we extend this analysis to infinite dimensions. We provide examples of GME-activatable non-Gaussian states. For Gaussian states, we apply a necessary biseparability criterion for the covariance matrix and show that it cannot detect GME activation. We further identify fully inseparable Gaussian states that satisfy the criterion but show that multiple and, in some cases, even single copies are GME. Thus, we show that the covariance-matrix biseparability criterion is not sufficient even for Gaussian states.

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arXiv2017

Gaussian intrinsic entanglement for states with partial minimum uncertainty

We develop a theory of a quantifier of bipartite Gaussian entanglement called Gaussian intrinsic entanglement (GIE) which was proposed recently in [L. Mišta {\it et al.}, Phys. Rev. Lett. {\bf 117}, 240505 (2016)]. The GIE provides a compromise between computable and physically meaningful entanglement quantifiers and so far it was calculated for two-mode Gaussian states including all symmetric partial minimum-uncertainty states, weakly mixed asymmetric squeezed thermal states with partial minimum uncertainty, and weakly mixed symmetric squeezed thermal states. We improve the method of derivation of GIE and we show, that all previously derived formulas for GIE of weakly mixed states in fact hold for states with higher mixedness. In addition, we derive analytical formulas for GIE for several new classes of two-mode Gaussian states with partial minimum uncertainty. Finally, it is shown, that like for all previously known states, also for all new states the GIE is equal to Gaussian Rényi-2 entanglement of formation. This finding strengthens a conjecture about equivalence of GIE and Gaussian Rényi-2 entanglement of formation for all bipartite Gaussian states.

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