arXiv subjects

Grzegorz Rajchel-Mieldzioć

Publications and source records attributed to Grzegorz Rajchel-Mieldzioć.

At least 19 recordsLinked to original sources

arXiv2026

Absolutely maximally entangled pure states of multipartite quantum systems

Absolutely maximally entangled (AME) pure states of a system composed of $N$ parties are distinguished by the property that for any splitting at least one partial trace is maximally mixed. Due to maximal possible correlations between any two selected subsystems these states have numerous applications in various fields of quantum information processing including multi-user teleportation, quantum error correction and secret sharing. We present an updated survey of various techniques to generate such strongly entangled states, including those going beyond the standard construction of graph and stabilizer states. Our contribution includes, in particular, analysis of the degree of entanglement of reduced states obtained by partial trace of AME projectors, states obtained by a symmetric superposition of GHZ states, an orthogonal frequency square representation of the "golden" AME state and an updated summary of the number of local unitary equivalence classes.

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

CovAngelo: A hybrid quantum-classical computing platform for accurate and scalable drug discovery

We present a computational platform for modeling chemical reactions in complex molecular environments, focused on ligand-protein binding in drug discovery. The platform implements our new quantum-in-quantum-in-classical (QM/QM/MM) multiscale embedding model that integrates molecular dynamics with a quantum-information-enhanced density matrix embedding theory and quantum chemistry solvers, including explicit solvent. Quantum-information metrics are utilized to generate entanglement-consistent orbitals, enabling a high-accuracy description of strongly correlated regions. The framework supports multiple computational backends, including multi-CPU, NVIDIA multi-GPU architectures, and quantum hardware (IQM, IonQ, IBM) integrated under CUDA-Q, and is designed for compatibility with future fault-tolerant quantum systems. The new platform's capabilities are demonstrated by modeling covalent docking of zanubrutinib to Bruton's tyrosine kinase via a Michael addition mechanism, computing the full reaction energy profiles and energy barriers at a reduced computational cost relative to existing methods. As a 2nd-generation anticancer agent, zanubrutinib serves as a proof of concept for covalent inhibitor discovery. Accurate first-principles reaction barrier estimations provided by our method can contribute to reducing false positive and negative rates in drug discovery pipelines. Scalability is validated through benchmarks on GPU clusters, cloud-based CPU infrastructures. We demonstrate integration with quantum devices (up to 20 qubits), alongside resource estimates for fault-tolerant quantum computing, indicating potential speedups of up to 20x. Beyond single reactions, the platform supports the construction of reaction networks in chemical metric space, facilitating ligand screening and systematic exploration of reactive pathways.

physics.chem-ph↗

arXiv2026

A Bipartite Quantum Key Distribution Protocol Based on Indefinite Causal Order

We propose a bipartite quantum key distribution (QKD) protocol based on causal nonseparability: the presence of a resource -- a process matrix -- that does not correspond to any definite causal order between two parties. In our protocol, Alice and Bob perform local operations arranged in a ``causal-order guessing game,'' whereby each round yields an 85.35\% probability of matching bits when the communication is undisturbed. This raw matching probability (or equivalently, a $\sim14.65\%$ error rate) is amenable to standard forward error-correction strategies. We further discuss the practical construction of the QKD protocol using indefinite causal order, where several different scenarios are deeply analyzed.

quant-ph↗

arXiv2026

Quantum algorithm for solving generalized eigenvalue problems with application to the Schrödinger equation

Accurate computation of multiple eigenvalues of quantum Hamiltonians is essential in quantum chemistry, materials science, and molecular spectroscopy. Estimating excited-state energies is challenging for classical algorithms due to exponential scaling with system size, posing an even harder problem than ground-state calculations. We present a quantum algorithm for estimating eigenvalues and singular values of parameterized matrix families, including solving generalized eigenvalue problems that frequently arise in quantum simulations. Our method uses quantum amplitude amplification and phase estimation to identify matrix eigenvalues by locating minima in the singular value spectrum. We demonstrate our algorithm by proposing a quantum-computing formulation of the pseudospectral collocation method for the Schrödinger equation. We estimate fault-tolerant quantum resource requirements for the quantum collocation method, showing favorable scaling in the size of the problem $N$ (up to $\widetilde{\mathcal{O}}(\sqrt{N})$) compared to classical implementations with $\widetilde{\mathcal{O}}(N)$, for certain well-behaved potentials. Additionally, unlike the standard collocation method, which results in a generalized eigenvalue problem requiring matrix inversion, our algorithm circumvents the associated numerical instability by scanning a parameterized matrix family and detecting eigenvalues through singular value minimization. This approach is particularly effective when multiple eigenvalues are needed or when the generalized eigenvalue problem involves a high condition number. In the fault-tolerant era, our method may thus be useful for simulating high-dimensional molecular systems with dense spectra involving highly excited states, such as those encountered in molecular photodynamics or quasi-continuum regimes in many-body and solid-state systems.

quant-ph↗

arXiv2025

Sufficient criteria for absolute separability in arbitrary dimensions via linear map inverses

Quantum states that remain separable (i.e., not entangled) under any global unitary transformation are known as absolutely separable and form a convex set. Despite extensive efforts, the complete characterization of this set remains largely unknown. In this work, we employ linear maps and their inverses to derive new sufficient analytical conditions for absolute separability in arbitrary dimensions, providing extremal points of this set and improving its characterization. Additionally, we employ convex geometry optimization to refine the characterization of the set when multiple non-comparable criteria for absolute separability are available. We also address the closely related problem of characterizing the absolute PPT (positive partial transposition) set, which consists of quantum states that remain positive under partial transposition across all unitary transformations. Finally, we extend our results to multipartite states.

quant-ph↗

arXiv2025

Spoofing of Quantum Channels Enables Low-Rank Projective Simulation

The ability to characterise and discern quantum channels is a crucial aspect of noisy quantum technologies. In this work, we explore the problem of distinguishing quantum channels when limited to sub-exponential resources, framed as von Neumann (projective) measurements. We completely characterise equivalence classes of quantum channels with different Kraus ranks that have the same marginal distributions under compatible projective measurements. In doing so, we explicitly identify gauge freedoms which can be varied without changing those compatible marginal outcome distributions, opening new avenues for quantum channel simulation, variational quantum channels, as well as novel adversarial strategies in noisy quantum device certification. Specifically, we show how a Sinkhorn-like algorithm enables us to find the minimum admissible Kraus rank that generates the correct outcome marginals. For a generic $d$-dimensional quantum system, this lowers the Kraus rank from $d^2$ to the theoretical minimum of $d$. For up to $d = 20$, we numerically demonstrate our findings, for which the code is available and open source. Finally, we provide an analytic algorithm for the special case of spoofing Pauli channels.

quant-ph↗

arXiv2025

Quantum Circuits for High-Dimensional Absolutely Maximally Entangled States

Absolutely maximally entangled (AME) states of multipartite quantum systems exhibit maximal entanglement across all possible bipartitions. These states lead to teleportation protocols that surpass standard teleportation schemes, determine quantum error correction codes and can be used to test performance of current term quantum processors. Several AME states can be constructed from graph states using minimal quantum resources. However, there exist other constructions that depart from the stabilizer formalism. In this work, we present explicit quantum circuits to generate exemplary non-stabilizer AME states of four subsystems with four, six, and eight levels each and analyze their capabilities to perform quantum information tasks.

quant-ph↗

arXiv2024

Introduction to quantum entanglement in many-body systems

The quantum mechanics formalism introduced new revolutionary concepts challenging our everyday perceptions. Arguably, quantum entanglement, which explains correlations that cannot be reproduced classically, is the most notable of them. Besides its fundamental aspect, entanglement is also a resource, fueling emergent technologies such as quantum simulators and computers. The purpose of this chapter is to give a pedagogical introduction to the topic with a special emphasis on the multipartite scenario, i.e., entanglement distributed among many degrees of freedom. Due to the combinatorial complexity of this setting, particles can interact and become entangled in a plethora of ways, which we characterize here. We start by providing the necessary mathematical tools and elementary concepts from entanglement theory. A part of this chapter will be devoted to classifying and ordering entangled states. Then, we focus on various entanglement structures useful in condensed-matter theory such as tensor-network states or symmetric states useful for quantum-enhanced sensing. Finally, we discuss state-of-the-art methods to detect and certify such correlations in experiments, with some relevant illustrative examples.

quant-ph↗

arXiv2024

Entanglement classification and \emph{non-k}-separability certification via Greenberger-Horne-Zeilinger-class fidelity

Many-body quantum systems can be characterised using the notions of \emph{k}-separability and entanglement depth. A quantum state is \emph{k}-separable if it can be expressed as a mixture of \emph{k} entangled subsystems, and its entanglement depth is given by the size of the largest entangled subsystem. In this paper we propose a multipartite entanglement measure that satisfies the following criteria: (i) it can be used with both pure and mixed states; (ii) it is encoded in a single element of the density matrix, so it does not require knowledge of the full spectrum of the density matrix; (iii) it can be applied to large systems; and (iv) it can be experimentally verified. The proposed method allows the certification of \emph{non-k}-separability of a given quantum state. We show that the proposed method successfully classifies three-qubit systems into known stochastic local operations and classical communication (SLOCC) classes, namely bipartite, \mbox{W-,} and GHZ-type entanglement. Furthermore, we characterise the \emph{non-k}-separability in known nine SLOCC classes of four-qubit states, absolutely maximally entangled states for five and six qubits and for arbitrary size qubit Dicke states.

quant-ph↗

arXiv2024

Enhancing quantum state tomography via resource-efficient attention-based neural networks

Resource-efficient quantum state tomography is one of the key ingredients of future quantum technologies. In this work, we propose a new tomography protocol combining standard quantum state reconstruction methods with an attention-based neural network architecture. We show how the proposed protocol is able to improve the averaged fidelity reconstruction over linear inversion and maximum-likelihood estimation in the finite-statistics regime, reducing at least by an order of magnitude the amount of necessary training data. We demonstrate the potential use of our protocol in physically relevant scenarios, in particular, to certify metrological resources in the form of many-body entanglement generated during the spin squeezing protocols. This could be implemented with the current quantum simulator platforms, such as trapped ions, and ultra-cold atoms in optical lattices.

quant-ph↗

arXiv2024

Multi-Unitary Complex Hadamard Matrices

We analyze the set of real and complex Hadamard matrices with additional symmetry constrains. In particular, we link the problem of existence of maximally entangled multipartite states of $2k$ subsystems with $d$ levels each to the set of complex Hadamard matrices of order $N=d^k$. To this end, we investigate possible subsets of such matrices which are, dual, strongly dual ($H=H^{\rm R}$ or $H=H^{\rmΓ}$), two-unitary ($H^R$ and $H^Γ$ are unitary), or $k$-unitary. Here $X^{\rm R}$ denotes reshuffling of a matrix $X$ describing a bipartite system, and $X^{\rm Γ}$ its partial transpose. Such matrices find several applications in quantum many-body theory, tensor networks and classification of multipartite quantum entanglement and imply a broad class of analytically solvable quantum models in $1+1$ dimensions.

quant-ph↗

arXiv2024

Metrological robustness of high photon number optical cat states

In the domain of quantum metrology, cat states have demonstrated their utility despite their inherent fragility with respect to losses. Here, we introduce noise robust optical cat states which exhibit a metrological robustness for phase estimation in the regime of high photon numbers. These cat states are obtained from the intense laser driven process of high harmonic generation (HHG), and show a resilience against photon losses. Focusing on a realistic scenario including experimental imperfections we opt for the case in which we can maximize the lower bound of the quantum Fisher information (QFI) instead of analyzing the best case scenario. We show that the decrease of the QFI in the lossy case is suppressed for the HHG-cat state compared to the even and odd counterparts. In the regime of small losses of just a single photon, the HHG-cat state remains almost pure while the even/odd cat state counterparts rapidly decohere to the maximally mixed state. More importantly, this translates to a significantly enhanced robustness for the HHG-cat against photon loss, demonstrating that high photon number optical cat states can indeed be used for metrological applications even in the presence of losses.

quant-ph↗

arXiv2024

Operation fidelity explored by numerical range of Kraus operators

Present-day quantum devices require precise implementation of desired quantum channels. To characterize the quality of implementation one uses the average operation fidelity $F$, defined as the fidelity between an initial pure state and its image with respect to the analyzed operation, averaged over an ensemble of pure states. We analyze statistical properties of the operation fidelity for low-dimensional channels and study its extreme values and probability distribution, both of which can be used for statistical channel discrimination. These results are obtained with help of the joint numerical range of the set of Kraus operators representing a channel. Analytic expressions for the density $P\left(F\right)$ are derived in some particular cases including unitary and mixed unitary channels as well as quantum maps represented by commuting Kraus operators. Measured distributions of operation fidelity can be used to distinguish between two quantum operations.

quant-ph↗

arXiv2023

Certifying the quantum Fisher information from a given set of mean values: a semidefinite programming approach

We introduce a semidefinite programming algorithm to find the minimal quantum Fisher information compatible with an arbitrary dataset of mean values. This certification task allows one to quantify the resource content of a quantum system for metrology applications without complete knowledge of the quantum state. We implement the algorithm to study quantum spin ensembles. We first focus on Dicke states, where our findings challenge and complement previous results in the literature. We then investigate states generated during the one-axis twisting dynamics, where in particular we find that the metrological power of the so-called multi-headed cat states can be certified using simple collective spin observables, such as fourth-order moments for small systems, and parity measurements for arbitrary system sizes.

quant-ph↗

arXiv2023

Rényi-Holevo inequality from $α$-$z$-Rényi relative entropies

We investigate bounds in the transmission of classical information through quantum systems. Our focus lies in the generalized Holevo theorem, which provides a single-letter Holevo-like inequality from arbitrary quantum distance measures. Through the introduction of the $α$-$z$-Rényi relative entropies, which comprise known relevant quantities such as the Rényi relative entropy and the sandwiched Rényi relative entropy, we establish the Holevo-Rényi inequality. This result leads to a quantum bound for the $α$-mutual information, suggesting new insights into communication channel performance and the fundamental limits for reliability functions in memoryless multi-letter communication channels.

quant-ph↗

arXiv2022

9 $\times$ 4 = 6 $\times$ 6: Understanding the quantum solution to the Euler's problem of 36 officers

The famous combinatorial problem of Euler concerns an arrangement of $36$ officers from six different regiments in a $6 \times 6$ square array. Each regiment consists of six officers each belonging to one of six ranks. The problem, originating from Saint Petersburg, requires that each row and each column of the array contains only one officer of a given rank and given regiment. Euler observed that such a configuration does not exist. In recent work, we constructed a solution to a quantum version of this problem assuming that the officers correspond to quantum states and can be entangled. In this paper, we explain the solution which is based on a partition of 36 officers into nine groups, each with four elements. The corresponding quantum states are locally equivalent to maximally entangled two-qubit states, hence each officer is entangled with at most three out of his $35$ colleagues. The entire quantum combinatorial design involves $9$ Bell bases in nine complementary $4$-dimensional subspaces.

quant-ph↗

arXiv2022

Quantum mappings and designs

In order to use quantum devices for computations, it is necessary to understand the intricacies of the theoretical description. To this end, we provide several novel constructions useful for the comprehension of quantum mechanics from the perspective of mappings and designs. The unistochasticity problem, which relates the classical and the quantum domain, is solved in specific cases, e.g. for all matrices of dimension 4. Furthermore, we provide an explicit formula for entangling power in the multipartite case. Most importantly, the thesis presents and elaborates on the path that lead to the recent construction of absolutely maximally entangled state of four subsystems six levels each. Finally, we study cardinality as a measure of "quantumness" of quantum Latin squares and quantum Sudoku (SudoQ). Arrays of the highest cardinality yield families of quantum measurements of special properties. A connection between SudoQ designs and mutually unbiased bases is demonstrated.

quant-ph↗