arXiv subjects

Martin Zeman

Publications and source records attributed to Martin Zeman.

5 recordsLinked to original sources

arXiv2026

Adaptive Negativity Estimation via Collective Measurements

This paper explores an efficient method for entanglement quantification in two-qubit and qubit-qutrit quantum systems based upon the framework of collective measurements in conjunction with machine learning. We introduce an adaptive measurement procedure in which measurement settings are dynamically adjusted based on prior measurement outcomes aiming to optimize the inference precision given a limited number of these measurement settings. The procedure makes use of the Long Short-Term Memory networks to recurrently process collective measurements on two copies of the investigated states. Obtained results demonstrate the tangible benefits of the adaptive measurements in comparison to previously described non-adaptive strategies.

quant-ph↗

arXiv2021

Ideals and Strong Axioms of Determinacy

We show that the following two theories are equiconsistent: (T) ZFC, CH and "There is a dense ideal on the first uncountable cardinal such that if j is the generic embedding associated with it then its restriction on ordinals is independent of the generic object is". (S) ZF, ADR and "Theta is a regular cardinal." The main result of this paper is that T implies that the minimal model of S exists. Woodin, in unpublished work, showed that the consistency of S implies the consistency of T. We will also give a proof of this result, which, together with our main theorem, establishes the equiconsistency of T and S. Our main result partially resolves a well-known conjecture of Woodin, and completely solves one of the main Core Model Induction problems dating back to 90s.

math.LO↗

arXiv2020

Games with Filters

This paper has two parts. The first is concerned with a variant of a family of games introduced by Holy and Schlicht, that we call \emph{Welch games}. Player II having a winning strategy in the Welch game of length $\omega$ on $\kappa$ is equivalent to weak compactness. Winning the game of length $2^\kappa$ is equivalent to $\kappa$ being measurable. We show that for games of intermediate length $\gamma$, II winning implies the existence of precipitous ideals with $\gamma$-closed, $\gamma$-dense trees. The second part shows the first is not vacuous. For each $\gamma$ between $\omega$ and $\kappa^+$, it gives a model where II wins the games of length $\gamma$, but not $\gamma^+$. The technique also gives models where for all $\omega_1< \gamma\le\kappa$ there are $\kappa$-complete, normal, $\kappa^+$-distributive ideals having dense sets that are $\gamma$-closed, but not $\gamma^+$-closed.

math.LO↗

arXiv2012

Square principles in Pmax extensions

By forcing with $\mathbb{P}_{\rm max}$ over strong models of determinacy, we obtain models where different square principles at $\omega_2$ and $\omega_3$ fail. In particular, we obtain a model of $2^{\aleph_0}=2^{\aleph_1}=\aleph_2 + \lnot\square(\omega_2) + \lnot\square(\omega_3)$.

math.LO↗

arXiv2012

Downward transference of mice and universality of local core models

If M is a proper class inner model of ZFC and omega_2^M=omega_2, then every sound mouse projecting to omega and not past 0-pistol belongs to M. In fact, under the assumption that 0-pistol does not belong to M, K^M \| omega_2 is universal for all countable mice in V. Similarly, if M is a proper class inner model of ZFC, delta>omega_1 is regular, (delta^+)^M = delta^+, and in V there is no proper class inner model with a Woodin cardinal, then K^M \| delta is universal for all mice in V of cardinality less than delta.

math.LO↗