arXiv subjects

Karol Bartkiewicz

Publications and source records attributed to Karol Bartkiewicz.

At least 19 recordsLinked to original sources

arXiv2026

Temporal nonlocality of a qudit resides in the input state, not the channel, and certifies temporal teleportation up to a fundamental limit

Correlations between two moments in time can be too strong for any classical explanation -- and, remarkably, this can happen for a single quantum system measured twice, with no second particle involved. We show that when one qudit is sent through a noisy channel, the strength of this "nonlocality in time" -- the temporal nonlocality robustness $\mathrm{TNR}$ -- is carried entirely by the starting state: it vanishes precisely when the input is maximally mixed (completely random), $\mathrm{TNR}(ρ_A,\mathcal{E})=0\Leftrightarrowρ_A=\mathbb{1}/d$, for the standard noise families. The resource is not any coherence in the channel but the back-action of the input's mixedness, and it survives even complete decoherence. This is at once a power and a trap. As a power, $\mathrm{TNR}$ device-independently lower-bounds the fidelity of temporal teleportation -- sending an unknown state forward in time -- reaching $7/9$ at $d=3$, without trusting the measuring devices. As a trap, because the certified quantity is decoupled from the channel's actual coherence transmission, it can certify more than the channel delivers: an injective (reversible) unitary attains the maximal temporal-Bell signal yet teleports below the classical baseline. We resolve this over-certification completely -- a universal cap $\mathrm{TNR}\le(d-1)/d$ with an exact channel-resolved value, honest certification for the depolarizing channel and for any sufficiently mixed probe, and a proof that no choice of probes makes it channel-universal. Underpinning the results is a unified semidefinite-programming hierarchy of the temporal entanglement, steering and nonlocality robustnesses ($\mathrm{TER}$, $\mathrm{TSR}$, $\mathrm{TNR}$), with a strict lower hierarchy and an upper one conditional on no-signaling in time ($\mathrm{NSIT}$). All structure is verified numerically for $d=2$ through $5$.

quant-ph↗

arXiv2026

Context-Verified, Error-Budget-Aware Decomposition Selection for Toffoli Networks

Two-qubit-gate error dominates the failure budget of near-term quantum circuits, so the decomposition chosen for each Toffoli (CCX) gate should minimize hardware two-qubit infidelity, not gate count. The cheapest decompositions - relative-phase and approximate Toffolis - are only correct in context: their residual phase or bounded error must be cancelled or absorbed downstream. We present the first compiler pass that selects a per-Toffoli decomposition to minimize a two-qubit-infidelity error budget. It admits each context-dependent decomposition only when an exact, instance-specific equivalence check certifies its validity in that circuit context, coupling an error-budget objective with per-instance verification and closing the gap between context-aware-but-unverified and verified-but-context-free optimizers. The central result is a safety one: pattern-matched relative-phase substitution is silently incorrect. Our verifier flags 66 library rewrites of a deployed open optimizer as non-equivalent without a context check, and count-greedy substitution silently corrupts 6 of 12 benchmark circuits; the verification gate certifies 0 errors while still applying every valid decomposition. The two-qubit-gate reduction is real but workload-dependent: up to 39.5% fewer two-qubit gates and 36.7% lower infidelity over exact-only on a compute/uncompute-heavy suite (approx. 39%/35% versus Qiskit opt-3 and tket), and 15.6% aggregate on a larger 12-24-qubit suite, with decision-diagram checking certifying every substitution past the exhaustive-verification limit. At current superconducting and trapped-ion error rates, the certified substitutions lower estimated circuit infidelity by 36-43%, and on a quantum state-resetting circuit, the pass removes 48.8% of the native two-qubit gates, every substitution verified.

quant-ph↗

arXiv2026

Spin chirality across quantum state copies detects hidden entanglement

Entanglement can hide in two fundamentally different ways. First, multi-copy correlations can carry information that no single-copy measurement on an unknown state is able to access. Second, bound entangled states possess a positive partial transpose, which makes them invisible to the Peres-Horodecki criterion and all moment inequalities that depend on it. Here we show that the moment difference between the partial transpose and purity decomposes exactly as a chirality-chirality correlator, where the relevant operator is the scalar spin chirality -- the same quantity that governs chiral spin liquids and the topological Hall effect. This decomposition identifies the specific physical structure that multi-copy entanglement detection probes. Using the same controlled-SWAP circuits, we develop a multi-channel spectral classifier for bound entanglement. The classifier combines realignment spectral features with chirality corrections and achieves 99.9% recall at zero false positives across all three known 3x3 bound entangled families, compared with ~40% for the CCNR criterion alone. We also introduce a marginal-noise construction that produces CCNR-invisible bound entangled states, which the classifier detects but which remain invisible to all single-parameter criteria. We validate our approach experimentally on three IBM Quantum processors and demonstrate negativity reconstruction with mean errors of 0.002-0.027, chirality detection for pure and mixed entangled states, and bound entanglement detection across two structurally distinct families (Horodecki and chessboard) on a single gate-based superconducting processor.

quant-ph↗

arXiv2025

Resource-efficient quantum correlation measurements via multicopy neural network methods

Measuring complex properties in quantum systems, such as measures of quantum entanglement and Bell nonlocality, is inherently challenging. Traditional methods, like quantum state tomography (QST), necessitate a full reconstruction of the density matrix for a given system and demand resources that scale exponentially with system size. We propose an alternative strategy that reduces the required information by combining multicopy measurements with artificial neural networks (ANNs), resulting in a 67\% reduction in measurement requirements compared to QST. We have successfully measured two-qubit quantum correlations of Bell states subjected to a depolarizing channel (resulting in Werner states) and an amplitude damping channel (leading to Horodecki states) using the multicopy approach on real quantum hardware. Our experiments, conducted with transmon qubits on IBMQ processors, quantified the violation of Bell's inequality and the negativity of two-qubit entangled states. We compared these results with those obtained from the standard QST approach and applied a maximum likelihood method to mitigate noise. We trained ANNs to estimate entanglement and nonlocality measures using optimized sets of projections identified through Shapley's (SHAP) analysis for the Werner and Horodecki states. The ANN output, based on this reduced set of projections, aligns well with expected values and enhances noise robustness. This approach simplifies and improves the error-robustness of multicopy measurements, eliminating the need for complex nonlinear equation analysis. It represents a significant advancement in AI-assisted quantum measurements, making practical implementation on current quantum hardware more feasible.

quant-ph↗

arXiv2025

Quantumness and its hierarchies in PT-symmetric down-conversion models

We investigate the hierarchy of quantum correlations in a quadratic bosonic parity-time-symmetric system (PTSS) featuring distinct dissipation and amplification channels. The hierarchy includes global nonclassicality, entanglement, asymmetric quantum steering, and Bell nonlocality. We elucidate the interplay between the system physical nonlinearity -- which serves as a source of quantumness -- and the specific dynamics of bosonic PTSSs, which are qualitatively influenced by their damping and amplification characteristics. Using a set of quantifiers -- including local and global nonclassicality depths, negativity, steering parameters, and the Bell parameter -- we demonstrate that the standard PTSS typically exhibits weaker quantumness than its counterparts affected solely by damping or solely by amplification. Both the maximum values attained by these quantifiers and the speed and duration of their generation are generally lower in the standard PTSS. A comparative analysis of three two-mode PTSSs -- standard, passive, and active -- with identical eigenvectors and real parts of eigenfrequencies, but differing in their damping and amplification strengths, reveals the crucial role of quantum fluctuations associated with gain and loss. Among them, the passive PTSS yields the most strongly nonclassical states. Nevertheless, under suitable conditions, the standard PTSS can also generate highly nonclassical states. The supremacy of the passive PTSS is further supported by its fundamental advantages in practical realizations.

quant-ph↗

arXiv2024

Experimental Liouvillian exceptional points in a quantum system without Hamiltonian singularities

Hamiltonian exceptional points (HEPs) are spectral degeneracies of non-Hermitian Hamiltonians describing classical and semiclassical open systems with losses and/or gain. However, this definition overlooks the occurrence of quantum jumps in the evolution of open quantum systems. These quantum effects are properly accounted for by considering quantum Liouvillians and their exceptional points (LEPs). Specifically, an LEP corresponds to the coalescence of two or more eigenvalues and the corresponding eigenmatrices of a given Liouvillian at critical values of external parameters [Minganti \emph{et al.}, Phys. Rev. A {\bf 100}, 062131 (2019)]. Here, we explicitly describe how standard quantum process tomography, which reveals the dynamics of a quantum system, can be readily applied to detect and characterize quantum LEPs of quantum non-Hermitian systems. We conducted experiments on an IBM quantum processor to implement a prototype model with one-, two-, and three qubits simulating the decay of a single qubit through competing channels, resulting in LEPs but not HEPs. Subsequently, we performed tomographic reconstruction of the corresponding experimental Liouvillian and its LEPs using both single- and two-qubit operations. This example underscores the efficacy of process tomography in tuning and observing LEPs even in the absence of HEPs.

quant-ph↗

arXiv2024

Experimental relative entanglement potentials of single-photon states

Entanglement potentials (EPs) enable the characterization and quantification of the nonclassicality of single-mode optical fields by measuring the entanglement generated through beam splitting. We experimentally generated single-photon states and tomographically reconstructed the corresponding two-qubit states to determine EPs defined via popular two-qubit measures of entanglement. These include the potentials for the relative entropy of entanglement (REEP), concurrence, and negativity. Among our experimental states, we found those that are very close (at least for some ranges of parameters) to the theoretical upper and lower bounds on relative EPs (or relative nonclassicality), i.e., when one EP is maximized or minimized for a given value if another EP. We experimentally confirmed the counterintuitive theoretical result of Ref. [Phys. Rev. A 92, 062314 (2015)] that the relative nonclassicality (specifically, the negativity potential for given values of the REEP) of single-photon states can be increased by dissipation.

quant-ph↗

arXiv2024

Experimental hierarchy of the nonclassicality of single-qubit states via potentials for entanglement, steering, and Bell nonlocality

Entanglement potentials are a promising way to quantify the nonclassicality of single-mode states. They are defined by the amount of entanglement (expressed by, e.g., the Wootters concurrence) obtained after mixing the examined single-mode state with a purely classical state; such as the vacuum or a coherent state. We generalize the idea of entanglement potentials to other quantum correlations: the EPR steering and Bell nonlocality, thus enabling us to study mutual hierarchies of these nonclassicality potentials. Instead of the usual vacuum and one-photon superposition states, we experimentally test this concept using specially tailored polarization-encoded single-photon states. One polarization encodes a given nonclassical single-mode state, while the other serves as the vacuum place-holder. This technique proves to be experimentally more convenient in comparison to the vacuum and a one-photon superposition as it does not require the vacuum detection.

quant-ph↗

arXiv2023

Quantifying nonclassicality of vacuum-one-photon superpositions via potentials for Bell nonlocality, quantum steering, and entanglement

Entanglement potentials are popular measures of the nonclassicality of single-mode optical fields. These potentials are defined by the amount of entanglement (measured by, e.g., the negativity or concurrence) of the two-mode field generated by mixing a given single-mode field with the vacuum on a balanced beam splitter. We generalize this concept to define the potentials for Bell nonlocality and quantum steering in specific measurement scenarios, in order to quantify single-mode nonclassicality in a more refined way. Thus, we can study the hierarchy of three types of potentials in close analogy to the well-known hierarchy of the corresponding two-mode quantum correlations. For clarity of our presentation, we focus on the analysis of the nonclassicality potentials for arbitrary vacuum-one-photon superpositions (VOPSs), corresponding to a photon-number qubit. We discuss experimentally feasible implementations for the generation of single-mode VOPS states, their mixing with the vacuum on a balanced beam splitter, and their two-mode Wigner-function reconstruction using homodyne tomography to determine the potentials. We analyze the effects of imperfections, including phase damping and unbalanced beam splitting on the quality of the reconstructed two-mode states and nonclassicality potentials. Although we focus on the analysis of VOPS states, single-mode potentials can also be applied to study the nonclassicality of qudits or continuous-variable systems.

quant-ph↗

arXiv2023

Sensitivity versus selectivity in entanglement detection via collective witnesses

In this paper, we present a supervised learning technique that utilizes artificial neural networks to design new collective entanglement witnesses for two-qubit and qubit-qutrit systems. Machine-designed collective entanglement witnesses allow for continuous tuning of their sensitivity and selectivity. These witnesses are, thus, a conceptually novel instrument allowing to study the sensitivity vs. selectivity trade-off in entanglement detection. The chosen approach is also favored due to its high generality, lower number of required measurements compared to quantum tomography, and potential for superior performance with regards to other types of entanglement witnesses. Our findings could pave the way for the development of more efficient and accurate entanglement detection methods in complex quantum systems, especially considering realistic experimental imperfections.

quant-ph↗

arXiv2023

Experimental hierarchy of two-qubit quantum correlations without state tomography

A Werner state, which is the singlet Bell state affected by white noise, is a prototype example of states, which can reveal a hierarchy of quantum entanglement, steering, and Bell nonlocality by controlling the amount of noise. However, experimental demonstrations of this hierarchy in a sufficient and necessary way (i.e., by applying measures or universal witnesses of these quantum correlations) have been mainly based on full quantum state tomography, corresponding to measuring at least 15 real parameters of two-qubit states. Here we report an experimental demonstration of this hierarchy by measuring only six elements of a correlation matrix depending on linear combinations of two-qubit Stokes parameters. We show that our experimental setup can also reveal the hierarchy of these quantum correlations of generalized Werner states, which are any two-qubit pure states affected by white noise.

quant-ph↗

arXiv2023

The effect of thermal photons on exceptional points in coupled resonators

We analyse two quantum systems with hidden parity-time (PT) symmetry: one is an optical device, whereas another is a superconducting microwave-frequency device. To investigate their symmetry, we introduce an equilibrium frame, in which loss and gain terms for a given Hamiltonian are balanced. We show that the non-Hermitian Hamiltonians of both systems can be tuned to reach an exceptional point (EP), i.e., the point in parameter space at which a transition from broken to unbroken hidden PT symmetry takes place. We calculate a degeneracy of a Liouvillian superoperator, which is called the Liouvillian exceptional point (LEP), and show that, in the optical domain, LEP is equivalent to EP obtained from the non-Hermitian Hamiltonian (HEP). We also report breaking the equivalence between LEP and HEP by a non-zero number of thermal photons for the microwave-frequency system.

quant-ph↗

arXiv2022

Synergic quantum generative machine learning

We introduce a new approach towards generative quantum machine learning significantly reducing the number of hyperparameters and report on a proof-of-principle experiment demonstrating our approach. Our proposal depends on collaboration between the generators and discriminator, thus, we call it quantum synergic generative learning. We present numerical evidence that the synergic approach, in some cases, compares favorably to recently proposed quantum generative adversarial learning. In addition to the results obtained with quantum simulators, we also present experimental results obtained with an actual programmable quantum computer. We investigate how a quantum computer implementing generative learning algorithm could learn the concept of a Bell state. After completing the learning process, the network is able both to recognize and to generate an entangled state. Our approach can be treated as one possible preliminary step to understanding how the concept of quantum entanglement can be learned and demonstrated by a quantum computer.

quant-ph↗

arXiv2022

Entanglement quantification from collective measurements processed by machine learning

In this paper, we investigate how to reduce the number of measurement configurations needed for sufficiently precise entanglement quantification. Instead of analytical formulae, we employ artificial neural networks to predict the amount of entanglement in a quantum state based on results of collective measurements (simultaneous measurements on multiple instances of the investigated state). This approach allows us to explore the precision of entanglement quantification as a function of measurement configurations. For the purpose of our research, we consider general two-qubit states and their negativity as entanglement quantifier. We outline the benefits of this approach in future quantum communication networks.

quant-ph↗

arXiv2021

Experimental hierarchy and optimal robustness of quantum correlations of two-qubit states with controllable white noise

We demonstrate a hierarchy of various classes of quantum correlations on experimentally prepared two-qubit Werner-like states with controllable white noise. Werner states, which are white-noise-affected Bell states, are prototypal examples for studying such a hierarchy as a function of the amount of white noise. We experimentally generated Werner states and their generalizations, i.e., partially entangled pure states affected by white noise. These states enabled us to study the hierarchy of the following classes of correlations: separability, entanglement, steering in three- and two-measurement scenarios, and Bell nonlocality. We show that the generalized Werner states (GWSs) reveal fundamentally different aspects of the hierarchy compared to the Werner states. In particular, we find five different parameter regimes of the GWSs, including those steerable in a two-measurement scenario but not violating Bell inequalities. This regime cannot be observed for the usual Werner states. Furthermore, we find threshold curves separating different regimes of the quantum correlations and find the optimal states which allow for the largest amount of white noise, which does not destroy their specific quantum correlations (e.g., unsteerable entanglement). Thus, we could identify the optimal Bell-nondiagonal GWSs, which are, for this specific meaning, more robust against white noise compared to the Bell-diagonal GWSs (i.e., Werner states).

quant-ph↗

arXiv2021

Equilibrium frame reveals hidden PT symmetry of passive systems

We discuss how introducing an equilibrium frame, in which a given Hamiltonian has balanced loss and gain terms, can reveal PT symmetry hidden in non-Hermitian Hamiltonians of dissipative systems. Passive PT-symmetric Hamiltonians, in which only loss is present and gain is absent, can also display exceptional points, just like PT-symmetric systems, and therefore are extensively investigated. We demonstrate that non-Hermitian Hamiltonians, which can be divided into a PT-symmetric term and a term commuting with the Hamiltonian, possess hidden PT symmetries. These symmetries become apparent in the equilibrium frame. We also show that the number of eigenstates having the same value in an exceptional point is usually smaller in the initial frame than in the equilibrium frame. This property is associated with the second part of the Hamiltonian.

quant-ph↗

arXiv2021

Hierarchy and robustness of multilevel two-time temporal quantum correlations

Quantum steering refers to correlations that can be classified as intermediate between entanglement and Bell nonlocality. Every state exhibiting Bell nonlocality exhibits also quantum steering and every state exhibiting quantum steering is also entangled. In low dimensional cases similar hierarchical relations have been observed between the temporal counterparts of these correlations. Here, we study the hierarchy of such temporal correlations for a general multilevel quantum system. We demonstrate that the same hierarchy holds for two definitions of state over time. In order to compare different types of temporal correlations, we show that temporal counterparts of Bell nonlocality and entanglement can be quantified with a temporal nonlocality robustness and temporal entanglement robustness. Our numerical result reveal that in contrast to temporal steering, for temporal nonlocality to manifest itself we require the initial state not to be in a completely mixed state.

quant-ph↗

arXiv2020

How confused can an entanglement witness be to be still persuasive

Detection of entangled states is essential in both fundamental and applied quantum physics. However, this task proves to be challenging especially for general quantum states. One can execute full state tomography but this method is time demanding especially in complex systems. Other approaches use entanglement witnesses, these methods tend to be less demanding but lack reliability. Here, we demonstrate that ANN -- artificial neural networks provide a balance between both approaches. In this paper, we make a comparison of ANN performance against witness-based methods for random general 2-qubit quantum states without any prior information on the states. Furthermore, we apply our approach to real experimental data set.

quant-ph↗