arXiv subjects

Jakub Czartowski

Publications and source records attributed to Jakub Czartowski.

At least 19 recordsLinked to original sources

arXiv2026

Energetic Costs of Subspace Quantum Error Correction

Quantum error correction acts as an entropy pump, transferring noise-induced uncertainty from a protected quantum system into syndrome information stored in an auxiliary memory. Repeated operation requires this memory to be cleared which unavoidably contributes to the energetic cost of error correction. Here, we characterise this contribution for subspace quantum error-correcting codes and identify how it depends on the joint structure of the code, the noise, and the representation of the retained syndrome information. Starting from the Knill-Laflamme conditions, we construct an effective syndrome state whose von Neumann entropy sets a lower bound on the ideal work required to maintain a reusable syndrome register. Projective syndrome readout generally generates additional entropy, and we quantify the resulting gap through measurement inefficiency. We then specialise to stabiliser codes under independent local Pauli noise and analyse two classical levels of syndrome representation. At the level of abstract error labels, degeneracies among single-qubit errors reduce the leading-order entropy of processed recovery labels. At the parity-check level, lower-weight checks reduce the marginal entropy generated by individual measurement outcomes in the low-noise regime. We identify the additional burden associated with retaining and separately erasing these outcomes as a bit-level inefficiency, and illustrate both costs for the five-qubit, Steane, generalised Shor, and rotated surface codes. Our results establish a hierarchy of syndrome-memory energetic costs and identify the code, noise, and measurement structures that control the ideal thermodynamic burden of subspace quantum error correction.

quant-ph↗

arXiv2026

Limits of Stochastic Semigroups and Block-Triangular Majorisation

We investigate limits of semigroups of stochastic matrices defined by their invariant distribution. Given probability vectors $γ(β)$ depending on a parameter $β$, we introduce a notion of convergence as $β\to\infty$ for the corresponding semigroups of $γ(β)$-preserving stochastic matrices and investigate the structure of the resulting limit. In general, the limiting semigroup differs from the semigroup preserving the limiting distribution, showing that these two operations do not commute. We develop a general framework for such limiting semigroups and study in detail the case in which the invariant distributions are Gibbs vectors at the inverse temperature $β$. We show that the limiting semigroup consists of block-upper-triangular stochastic matrices subject to additional substochasticity constraints. We characterise and enumerate their extremal elements and determine the preorder on probability vectors induced by the action of the semigroup. The resulting notion of Block-Triangular majorisation interpolates between ordinary majorisation and upper triangular (aka unordered) majorisation. We show that it is completely characterised by a finite family of monotones and analyse the corresponding behaviour of Rényi $α$-entropies as $β\to\infty$.

math-ph↗

arXiv2026

A Study in Thermal: Advantage framework for resource engines

Thermal engines have been one of the principal topics of thermodynamics ever since its beginning. Today, in the era of the second quantum revolution, although the thermal processes in constant temperatures are relatively well understood in the language of resource theories, a framework to describe thermal engines is still in its infancy. In this work we formalize the resource theory of engines, initially put forward in~\cite{KAMIL}, and define such quantities as engine efficiency. Then, we turn to a detailed study of thermal engines based on free operations arising from the resource theory of athermality under different restrictions: thermal operation, semilocal thermal operations and local thermal operation with classical communication. In order to provide analytic lower bounds for thermal engine operation we construct tree-states -- free states, which can be obtained from Gibbs state in simple protocol consisting solely of two-level operations. Furthermore, we derive a full description of the engine based on semilocal thermal operations by describing free states, faithful monotones and catalytic advantages.

quant-ph↗

arXiv2026

Approximate pushforward designs and image bounds on approximations

We extend the framework of quantum pushforward designs to the approximate setting, in which moment operators agree only up to finite precision. We first formulate a general transfer theorem for maps that act linearly at the level of moments. This separates direct applications, controlled by standard Schatten-norm estimates, from refinements that use additional tensorial structure. Dephasing is shown to be contractive and therefore sends an approximate projective design to a simplex design without increasing its error. Ordinary partial-trace estimates give immediate bounds for mixed-state and channel designs. We then prove a sharp Schatten-norm bound for the partial trace restricted to the totally symmetric subspace. This replaces the full-environment norm coefficient by one governed by a symmetric-subspace dimension and yields asymptotically tighter estimates for both mixed-state and channel designs. Numerical simulations for induced mixed-state designs are consistent with the resulting hierarchy of bounds.

quant-ph↗

arXiv2026

The Trinity of Markovian Quantum Thermodynamics: Unifying the Axiomatic, Microscopic, and Operational Paradigms

Thermodynamics imposes fundamental constraints on the evolution of quantum systems. These constraints and their dynamical consequences have been formulated within distinct paradigms, including axiomatic approaches based on quantum master equations, microscopic descriptions of open-system dynamics, and operational formulations rooted in resource theories. While each perspective has yielded important insights into thermodynamically consistent quantum dynamics, their precise relationship has remained unresolved. Here we establish the exact equivalence of these three paradigms in the Markovian regime. We prove that thermal Lindbladians satisfying Markovianity, time-translation symmetry, and quantum detailed balance are precisely those admitting a microscopic realisation as an energy-conserving thermal collision model and, equivalently, those generating Markovian thermal operations. This unifies the existing approaches to Markovian quantum thermodynamics and identifies its dynamical underpinnings. We further provide an explicit microscopic protocol for simulating thermal Markovian processes with controlled finite-time simulation errors. We illustrate its applicability by providing faithful thermal collision-model implementations of a qubit thermalising in a bosonic environment and of a three-level autonomous thermal machine. In the latter case, the protocol gives rise to a finite-stroke thermal engine that not only reproduces the continuous-time dynamics but also its steady-state thermodynamic performance. As a whole, these results establish a unified foundation for Markovian quantum thermodynamics, showing that its axiomatic, microscopic, and operational formulations are exactly equivalent and providing a universal protocol for implementing thermal processes and machines.

quant-ph↗

arXiv2026

Trading athermality for nonstabiliserness

Quantum advantage arises from quantum states that cannot be efficiently simulated on a classical computer. Such states are characterised by a property known as nonstabiliserness. In this work, we investigate whether nonstabiliserness can be generated by placing an initially stabiliser state in contact with a heat bath. Under minimal thermodynamic assumptions, we derive a necessary and sufficient condition for when this is possible. This yields an analytic characterisation of all nonstabiliser qubit states reachable through such thermal processes, together with explicit bounds on their nonstabiliserness. This, in turn, allows us to identify optimal regimes for generating this resource, including the Hamiltonians that maximise nonstabiliserness and the critical temperatures at which it emerges. Beyond the qubit case, we establish a general trade-off between the nonstabiliserness attainable under thermal operations and the initial nonequilibrium free energy of the system.

quant-ph↗

arXiv2026

Quantum Resource Theories beyond Convexity

A class of quantum resource theories, based on non-convex star-shape sets, presented in this work captures the key quantum properties that cannot be studied by standard convex theories. We provide operational interpretations for a resource of this class and demonstrate its advantage to improve performance of correlated quantum discrimination tasks and testing of quantum combs. Proposed techniques provide useful tools to describe quantum discord, total correlations in composite quantum systems and to estimate the degree of non-Markovianity of an analyzed quantum dynamics. Other applications include the problem of unistochasticity of a given bistochastic matrix, with relevance for quantization of classical dynamics and studies of violation of CP-symmetry in high energy physics. In all these cases, the non-linear witnesses introduced here outperform the standard linear witnesses. Importance of our findings for quantum information theory is also emphasized.

quant-ph↗

arXiv2026

Quantum convolutional channels and multiparameter families of 2-unitary matrices

Many alternative approaches to construct quantum channels with large entangling capacity were proposed in the past decade, resulting in multiple isolated gates. In this work, we put forward a novel one, inspired by convolution, which provides greater freedom of nonlocal parameters. Although quantum counterparts of convolution have been shown not to exist for pure states, several attempts with various degrees of rigorousness have been proposed for mixed states. In this work, we follow the approach based on coherifications of multi-stochastic operations and demonstrate a surprising connection to gates with high entangling power. In particular, we identify conditions necessary for the convolutional channels constructed using our method to possess maximal entangling power. Furthermore, we establish new, continuous classes of bipartite 2-unitary matrices of dimension $d^2$ for $d = 7$ and $d = 9$, with $2$ and $4$ free nonlocal parameters beyond simple phasing of matrix elements, corresponding to perfect tensors of rank $4$ or 4-partite absolutely maximally entangled states.

quant-ph↗

arXiv2026

Product Weyl-Heisenberg covariant MUBs and Maximizers of Magick

In this work we investigate discrete structures in product Hilbert spaces. For monopartite systems of size $d$ one relies on the Weyl-Heisenberg group $WH(d)$, while in the case of composite Hilbert spaces we identify designs covariant with respect to the product group, $[WH(p)]^{\otimes n}$. In analogy with magic -a quantity attaining its maximum for states fiducial with respect to $WH(d)$ -we introduce a similar notion of magick, defined with respect to the product group. The maximum of this quantity over all equimodular vectors yields fiducial states that generate $d$ $\textit{a priori}$ isoentangled mutually unbiased bases (MUBs), which, when supplemented by the identity, form their complete set. Such fiducial states are explicitly constructed in all prime-power dimensions $p^n$ with $p\ge 3$. The result for $p\ge 5$ extends the construction of Klappenecker and Rötteler, whereas for $p=3$ it is mathematically distinct and is based on Galois rings. The global maximum of magick for $d=2^3$ yields fiducial states corresponding to the symmetric informationally complete (SIC) generalized measurement of Hoggar. Our approach feeds into a unifying perspective in which highly symmetric quantum designs emerge from fiducial states with extremal properties via structured group-orbit constructions.

quant-ph↗

arXiv2026

Local Thermal Operations and Classical Communication

In quantum thermodynamics, understanding the interplay between locality, thermal constraints, and communication remains an open challenge. In this manuscript, we introduce Local Thermal Operations and Classical Communication (LTOCC), a novel operational framework that unifies the distant laboratories paradigm with thermodynamic restrictions, defining the fundamental limits on transformations between spatially separated systems. We establish a hierarchy of LTOCC protocols, demonstrating inclusion relations between different levels and revealing their deep connection to semilocal thermal operations. To formalize this framework, we develop thermal tensors and bithermal tensors, extending stochastic and tristochastic tensors to thermodynamic settings and providing new mathematical tools for constrained quantum processes. Finally, we present limitations imposed by LTOCC on single- and multi-copy CHSH scenario, demonstrating no violation in former and a gap between thermal and athermal local operations in the latter with respect to their capability to detect entanglement.

quant-ph↗

arXiv2026

Manipulating heterogeneous quantum resources over a network

Quantum information processing relies on a variety of resources, including entanglement, coherence, non-Gaussianity, and magic. In realistic settings, protocols run on networks of parties with heterogeneous local resource constraints, so different resources coexist and interact. Yet, resource theories have mostly treated each resource in isolation, and a general theory for manipulation in such distributed settings has been lacking. We develop a unified framework for composite quantum resource theories that describes distributed networks of locally constrained parties. We formulate natural axioms a composite theory should satisfy to respect the local structure, and from these axioms derive fundamental bounds on resource manipulation that hold universally, independent of the particular network characteristics. We apply our results to central operational tasks, including resource conversion and assisted distillation, and introduce new methods to construct new resource monotones from this setup. Our framework further reveals previously unexplored phenomena in the remote certification of quantum resources. Together, these results establish foundational laws for distributed quantum resource manipulation across diverse physical platforms.

quant-ph↗

arXiv2025

Relative volume of comparable pairs under semigroup majorization

Any semigroup $\mathcal{S}$ of stochastic matrices induces a semigroup majorization relation $\prec^{\mathcal{S}}$ on the set $Δ_{n-1}$ of probability $n$-vectors. Pick $X,Y$ at random in $Δ_{n-1}$: what is the probability that $X$ and $Y$ are comparable under $\prec^{\mathcal{S}}$? We review recent asymptotic ($n\to\infty$) results and conjectures in the case of majorization relation (when $\mathcal{S}$ is the set of doubly stochastic matrices), discuss natural generalisations, and prove a new asymptotic result in the case of majorization, and new exact finite-$n$ formulae in the case of UT-majorization relation, i.e. when $\mathcal{S}$ is the set of upper-triangular stochastic matrices.

math-ph↗

arXiv2025

Efficient state estimation on quantum processors

We present two scalable and entanglement-free methods for estimating the collective state of an n-qubit quantum computer. The first method consists of a fixed set of five quantum circuits-regardless of the number of qubits-that avoid the use of entanglement as a measurement resource, relying instead on classical communication between selected pairs of qubits. The second method requires only 2n+1 circuits, each of which applies a single local gate to one of the n qubits during the measurement stage. Unlike traditional estimation methods, our approaches do not require any costly post-processing procedure to estimate a quantum state, enabling scalability to relatively large system sizes. We experimentally compare both methods on freely available IBM quantum processors, and observe how the state estimation varies with increasing number of qubits and shots. We further validated our results by estimating the 4-qubit entangled state of two remote ion-trap quantum processors, demonstrating that the optimized 2n+1 tomographic scheme achieves estimates consistent with standard methods while using exponentially fewer measurements.

quant-ph↗

arXiv2025

Cyclic measurements and simplified quantum state tomography

Tomographic reconstruction of quantum states plays a fundamental role in benchmarking quantum systems and accessing information encoded in quantum-mechanical systems. Among the informationally complete sets of quantum measurements, the tight ones provide a linear reconstruction formula and minimize the propagation of statistical errors. However, implementing tight measurements in the lab is challenging due to the high number of required measurement projections, involving a series of experimental setup preparations. In this work, we introduce the notion of cyclic tight measurements, which allow us to perform full quantum state tomography while considering only repeated application of a single unitary-based quantum device during the measurement stage. This type of measurement significantly simplifies the complexity of the experimental setup required to retrieve the quantum state of a physical system. Additionally, we design a feasible setup preparation procedure that produces well-approximated cyclic tight measurements in every finite dimension.

quant-ph↗

arXiv2025

Comment and correction for "On Explicit Construction of Simplex $t$-designs" by M. S. Baladram

In [Bal18] a new method of constructing simplex designs based on cyclic group on $n$ elements has been proposed. One of the claims put forward therein is existence of 3-point simplex 3-design in dimension $d = 3$. In this manuscript we present explicit counterarguments and suggest a manner to rectify the existing proofs. By doing this, we show that the results presented in [Bal18] can be utilised to construct simplex 3-designs scaling as $d^2$, which suggest a general scaling of $d^{t-1}$. Finally, we put forward a notion that encompasses the objects conforming with bounds given in [Bal18], which we refer to as symmetry-restricted simplex $t$-designs.

math.CO↗

arXiv2025

Quantum Pushforward Designs

Designs, structures connected to averaging with respect to a given measure using finite sets of points, have proven themselves as invaluable tools across the field of quantum information, finding their uses in state and process tomography, key distribution and others. In this work, we introduce a new concept of pushforward designs, which allows us to obtain new structures from already existing ones by mapping them between the spaces, with specific examples including simplex designs and mixed state designs from complex projective designs. Based on the general concept, we put forward a structure called channel $[t,k]$-design, allowing for averaging over space of quantum channels for systems in contact with an environment of dimension $k$. Based on this notion, we introduce the concept of effective environment dimensionality $k^*$, which we estimate for the IBM Kyoto quantum computer to be below $2.2$ for times up to $350μ\text{s}$.

quant-ph↗

arXiv2024

Catalytic transformations for thermal operations

What are the fundamental limits and advantages of using a catalyst to aid thermodynamic transformations between quantum systems? In this work, we answer this question by focusing on transformations between energy-incoherent states under the most general energy-conserving interactions among the system, the catalyst, and a thermal environment. The sole constraint is that the catalyst must return unperturbed and uncorrelated with the other subsystems. More precisely, we first upper bound the set of states to which a given initial state can thermodynamically evolve (the catalysable future) or from which it can evolve (the catalysable past) with the help of a strict catalyst. Secondly, we derive lower bounds on the dimensionality required for the existence of catalysts under thermal process, along with bounds on the catalyst's state preparation. Finally, we quantify the catalytic advantage in terms of the volume of the catalysable future and demonstrate its utility in an exemplary task of generating entanglement and cooling a quantum system using thermal resources.

quant-ph↗

arXiv2024

Minimal-noise estimation of noncommuting rotations of a spin

We propose an analogue of $\text{SU}(1,1)$ interferometry to measure rotation of a spin by using two-spin squeezed states. Attainability of the Heisenberg limit for the estimation of the rotation angle is demonstrated for maximal squeezing. For a specific direction and strength an advantage in sensitivity for all equatorial rotation axes (and hence non-commuting rotations) over the classical bound is shown in terms of quadratic scaling of the single-parameter quantum Fisher information for the corresponding rotation angles. Our results provide a method for measuring magnetic fields in any direction in the $x$-$y$-plane with the same optimized initial state.

quant-ph↗