arXiv subjects

Paul Skrzypczyk

Publications and source records attributed to Paul Skrzypczyk.

At least 19 recordsLinked to original sources

arXiv2026

Such stuff as magic is made on: compact operator algebra, stabilizer polytope and the structure of reduced density matrices in a Kitaev spin liquid

Quantum many-body systems exhibit rich and complex behaviour. Magic has recently emerged as a powerful new diagnostic for probing such systems, complementing other key features such as many-body entanglement. Here, starting from an investigation of the onset of magic within subsystems of a larger many-body quantum system, we show that intricate structures emerge which shed important light on the underlying many-body physics. Focusing on the Kitaev honeycomb model, we first identify the temperature below which local subsystems acquire magic. Remarkably, we find that the optimal magic witnesses active at the onset of magic reveal compact operator spaces that continue to capture the local thermal states throughout their subsequent evolution. For the six-site hexagonal marginal, this connection can be made stronger: the same operator space emerges independently from the symmetries of the local marginal and forms the symmetry-resolved plaquette algebra. When these symmetries are realized exactly, the local state lies entirely within this algebra and the reduced robustness of magic is equal to the full robustness of magic. The same reduced description can also be applied to other local quantum resources, which we illustrate using genuine multipartite entanglement. Furthermore, the operator spaces possess a rich algebraic structure in the form of finite-dimensional Euclidean Jordan algebras, with a natural interpretation in terms of bond and bond-cycle operators. Our general methodology therefore show how the onset of local magic can reveal a compact, physically meaningful operator structure underlying the finite-temperature Kitaev spin liquid, and opens up a new avenue towards reduced descriptions of quantum resources in many-body systems.

cond-mat.str-el↗

arXiv2026

Reducing measurement error with adaptivity

We show that adaptivity, also called feed-forward, is a powerful resource in reducing the error of measurement circuits that combine multiple uses of a noisy measuring device. In previous work, it has been shown that error in measurements can be mitigated by using the measuring device multiple times. So far, the most effective protocols have been parallel measurement schemes, where all measurements are simultaneous. We extend this idea to adaptive measurement schemes, where the results of previous measurements can influence our choice of processing further down the circuit. We show that adaptive measurement circuits can in general reduce overall measurement errors further than any non-adaptive measurement circuit could with the same number of measurements. In particular, we show that for a large class of noisy two-outcome qubit measurements, such an adaptive advantage can exist when as few as three measurements are used. We also show that the adaptive advantage is unbounded across the class of noisy two-outcome qubit measurements, as the number of uses of the device increases. As part of this work, we devise and use methods for finding optimal measurement circuits in both the non-adaptive and adaptive cases. In addition, we prove general results about the limits of such circuits, both in measuring a qubit, and more generally, a qudit.

quant-ph↗

arXiv2026

Resource theory of interactive quantum instruments

Quantum instruments describe both the classical outcome and the updated quantum state in a measurement process. To do this in a non-trivial way, instruments must have the capability to interact coherently with the state that they measure. Here, we develop a resource theory for instruments. We consider a relevant quantifier of the separation between interactive and non-interactive instruments and show that it admits three distinct operational interpretations in terms of quantum information tasks. These concern (i) the preservation of maximally entangled states after a local measurement, (ii) the average ability to preserve random states after measurement, and (iii) the ability to recover the classical information generated from measuring half of a maximally entangled state. We also introduce a natural set of allowed operations and show that the third task fully characterises the resource content of instruments. Our general framework reproduces as special cases established resource theories for channels and measurements.

quant-ph↗

arXiv2026

Characterizing entanglement at finite temperature: how does a "classical" paramagnet become a quantum spin liquid?

Quantum spin liquids (QSL) are phases of matter which are distinguished not by the symmetries they break, but rather by the patterns of entanglement within them. Although these entanglement properties have been widely discussed for ground states, the way in which QSL form at finite temperature remains an open question. Here we introduce a method of characterizing both the depth and spatial structure of entanglement, and use this to explore how patterns of entanglement form as temperature is reduced in two widely studied models of QSL, the Kitaev honeycomb model, and the spin-1/2 Heisenberg antiferromagnet on a Kagome lattice. These results enable us to evaluate both the temperature at which spins within the high-temperature paramagnet first become entangled, and the temperature at which the system first develops the structured, multipartite entanglement characteristic of its QSL ground state.

cond-mat.str-el↗

arXiv2026

Automated quantum circuit optimization with randomized replacements

Quantum circuit optimization - the process of transforming a quantum circuit into an equivalent one with reduced time and space requirements - is crucial for maximizing the utility of current and near-future quantum devices. While most automated optimization techniques focus on transforming circuits into equivalent ones that implement the same unitary, we show that substantial new opportunities for resource reduction can be achieved by (1) allowing approximate local transformations and (2) employing mixed quantum channels to approximate pure circuits. Our novel automated protocol for approximate circuit rewriting is a refined evolution of automated optimization techniques based on the ZX-calculus, where we add a greedy strategy that selectively replaces ZX-diagrams with small phase angles with stochastic mixtures of the identity and carefully chosen over-rotations, which are designed to reduce the overall gate count in expectation while staying within a strict error budget. This approach yields modest two-qubit gate count reduction in random quantum circuits, and achieves a substantial reduction in structured circuits such as the quantum Fourier transform. Fundamentally, our protocol converts experimental noise due to gate applications into deliberately engineered random noise, outperforming many other approximation methods on average. These results highlight the potential of mixed-channel approximations to enhance future quantum circuit performance, suggesting new directions for resource-aware automated quantum compilation beyond pure unitary channels.

quant-ph↗

arXiv2025

Unspeakable Coherence Concentration

Unspeakable coherence is a key feature separating quantum and classical physics. Modelled as asymmetry with respect to a continuous transformation generated by a physically relevant observable, such as the Hamiltonian or angular moment, unspeakable coherence has been shown to be the relevant notion of coherence for achieving quantum advantage in the tasks of metrology, reference frame alignment and work extraction, among others. A question of both practical and foundational value is: Given some copies of a state with low coherence, can we prepare a more coherent state via coherence non-increasing operations? Here, we study this question in the minimal limiting case: Given two uncorrelated copies of a coherent state, can one, via globally coherence non-increasing unitaries, increase the coherence in a subsystem? We fully solve this problem for qubits, identifying the optimal unitaries and revealing the existence of bound coherence. This is then used to create a completely constructive multi-qubit coherence enhancement protocol, where only effective-qubit unitaries are used. Unexpectedly, in this protocol, we show that there exists states for which the ratio of the input-output coherence can be amplified unboundedly. Extending beyond qubits, we derive two fundamental upper bounds on the amount of local coherence that can be increased and prove a no-go theorem showing that certain global correlations cannot be converted to local coherence.

quant-ph↗

arXiv2025

Activation of post-quantum steering

There are possible physical theories that give greater violations of Bell's inequalities than the corresponding Tsirelson bound, termed post-quantum non-locality. Such theories do not violate special relativity, but could give an advantage in certain information processing tasks. There is another way in which entangled quantum states exhibit non-classical phenomena, with one notable example being Einstein-Podolsky-Rosen (EPR) steering; a violation of a bipartite Bell inequality implies EPR steering, but the converse is not necessarily true. The study of post-quantum EPR steering is more intricate, but it has been shown that it does not always imply post-quantum non-locality in a conventional Bell test. In this work we show how to distribute resources in a larger network that individually do not demonstrate post-quantum non-locality but violate a Tsirelson bound for the network. That is, we show how to activate post-quantum steering so that it can now be witnessed as post-quantum correlations in a Bell scenario. One element of our work that may be of independent interest is we show how to self-test a bipartite quantum assemblage in a network, even assuming post-quantum resources.

quant-ph↗

arXiv2025

All incompatible sets of measurements can generate Buscemi nonlocality

The presence of Bell-nonlocality in the correlations arising from measuring spatially-separated systems guarantees that the sets of measurements used are necessarily incompatible. Not all sets of incompatible measurements can however lead to Bell-nonlocality, as there exist incompatible sets of measurements which can only produce local correlations. In this work we prove that all sets of incompatible measurements are nevertheless able to generate nonlocality in an extended Bell scenario where quantum, instead of classical, measurement inputs are considered. In particular, this holds true for all incompatible-local sets of measurements and, consequently, shows that these sets of measurements posses a form of hidden nonlocality which can be revealed in such a scenario. We furthermore prove that the maximum amount of nonlocality that can be extracted in such a way is limited by the degree of incompatibility of the given set of measurements, thus effectively establishing an achievable upper bound. In order to obtain these results, we introduce a new object which we term a \emph{generalised set of measurements}, which provides a unifying way to study any scenario involving quantum inputs.

quant-ph↗

arXiv2025

The Hadamard gate cannot be replaced by a resource state in universal quantum computation

We consider models of quantum computation that involve operations performed on some fixed resourceful quantum state. Examples that fit this paradigm include magic state injection and measurement-based approaches. We introduce a framework that incorporates both of these cases and focus on the role of coherence (or superposition) in this context, as exemplified through the Hadamard gate. We prove that given access to incoherent unitaries (those that are unable to generate superposition from computational basis states, e.g. CNOT, diagonal gates), classical control, computational basis measurements, and any resourceful ancillary state (of arbitrary dimension), it is not possible to implement any coherent unitary (e.g. Hadamard) exactly with non-zero probability. We also consider the approximate case by providing lower bounds for the induced trace distance between the above operations and $n$ Hadamard gates. To demonstrate the stability of this result, this is then extended to a similar no-go result for the case of using $k$ Hadamard gates to exactly implement $n>k$ Hadamard gates.

quant-ph↗

arXiv2025

Operational Interpretation of the Choi Rank Through k-State Exclusion

The Choi-state is an indispensable tool in the study and analysis of quantum channels. Considering a channel in terms of its associated Choi-state can greatly simplify problems. It also offers an alternative approach to the characterisation of a channel, with properties of the Choi-state providing novel insight into a channel's behaviour. The rank of a Choi-state, termed the Choi-rank, has proven to be an important characterising property, and here, its significance is further elucidated through an operational interpretation. The Choi-rank is shown to provide a universal bound on how successfully two agents, Alice and Bob, can perform an entanglement-assisted exclusion task. The task can be considered an extension of super-dense coding, where Bob can only output information about Alice's encoded bit-string with certainty. Conclusive state exclusion, in place of state discrimination, is therefore considered at the culmination of the super-dense coding protocol. In order to prove this result, a necessary condition for conclusive k-state exclusion of a set of states is presented in order to achieve this result, and the notions of weak and strong exclusion are introduced.

quant-ph↗

arXiv2025

Revising the quantum work fluctuation framework to encompass energy conservation

Work is a process-based quantity, and its measurement typically requires interaction with a measuring device multiple times. While classical systems allow for non-invasive and accurate measurements, quantum systems present unique challenges due to the influence of the measuring device on the final value of work. As recent studies have shown, among these challenges is the impossibility of formulating a universal definition of work that respects energy conservation for coherent quantum systems and is compatible with the Jarzynski equality - a fluctuation relation linking the equilibrium free energy difference to the non-equilibrium work. Here we overcome this challenge by introducing a genuinely quantum, positive correction to the Jarzynski equality stemming from imposing energy conservation. When sufficiently large, this correction forces quantum work to violate the second law more often. Moreover, we construct modified two-point measurement (TPM) schemes for work along with circuit implementations for them. These measurement schemes correctly certify energy conservation and remain consistent with our quantum-corrected fluctuation relation.

quant-ph↗

arXiv2024

Activation of post-quantumness in bipartite generalised EPR scenarios

In a standard bipartite Einstein-Podolsky-Rosen (EPR) scenario, Alice and Bob share a system prepared in an entangled state and Alice performs local measurements. One possible generalisation of this set-up is to allow Bob to also locally process his subsystem. Then, correlations generated in such generalised EPR scenarios are examples of non-signalling bipartite resources, called assemblages, that can exhibit post-quantum behavior, i.e., cannot be generated using solely quantum systems. There exist assemblages that, despite being post-quantum resources, can only generate quantum correlations in bipartite Bell-type scenarios. Here, we present a protocol for activation of post-quantumness in bipartite generalised EPR scenarios such as the so-called Bob-with-input, measurement-device-independent, and channel EPR scenarios. By designing a protocol that involves distributing the assemblages in a larger network, we derive tailored Bell inequalities which can be violated beyond their quantum bound in this new set-up. Our results show that in all of the above generalised scenarios, the post-quantumness of the assemblages can be witnessed at the level of correlations they produce.

quant-ph↗

arXiv2024

Locally inaccessible hidden quantum correlations

We prove, modulo a conjecture on quantum steering ellipsoids being true, the existence of the phenomenon of locally inaccessible hidden quantum correlations. That is, the existence of two-particle states whose hidden quantum correlations cannot be revealed by local filters implemented exclusively on one side of the experiment, but that can still be revealed when both parties cooperate in applying judiciously chosen local filters. The quantum correlations here considered are the violation of the CHSH-inequality for Bell-nonlocality and the violation of the $\rm F_3$-inequality for EPR-steering. Specifically, we provide a necessary criterion for guaranteeing the presence of such phenomenon for arbitrary two-qubit states. This criterion in turn relies on the conjecture that the maximal violation of CHSH-inequality and $\rm F_3$-inequality are both upper bounded by functions that depend on the magnitude of the quantum steering ellipsoid centre. This latter conjecture, although currently lacking an analytical proof, is supported by numerical results. We use this necessary criterion to explicitly show examples of two-qubit states with locally inaccessible hidden quantum correlations and, furthermore, two-qubit states with locally inaccessible maximal hidden quantum correlations.

quant-ph↗

arXiv2024

The Dynamical Resource Theory of Informational Non-Equilibrium

Information is instrumental in our understanding of thermodynamics. Their interplay has been studied through completely degenerate Hamiltonians whereby the informational contributions to thermodynamic transformations can be isolated. In this setting, all states other then the maximally mixed state are considered to be in informational non-equilibrium. An important yet still open question is: how to characterise the ability of quantum dynamics to maintain informational non-equilibrium? Here, the dynamical resource theory of informational non-equilibrium preservability is introduced to begin providing an answer to this question. A characterisation of the allowed operations is given for qubit channels and the n dimensional Weyl-covariant channels - a physically relevant subset of the general channels. An operational interpretation of a state discrimination game with Bell state measurements is given. Finally, an explicit link between a channels classical capacity and its ability to maintain informational non-equilibrium is made.

quant-ph↗

arXiv2023

Maxwell's Demon walks into Wall Street: Stochastic Thermodynamics meets Expected Utility Theory

The interplay between thermodynamics and information theory has a long history, but its quantitative manifestations are still being explored. We import tools from expected utility theory from economics into stochastic thermodynamics. We prove that, in a process obeying Crooks' fluctuation relations, every $α$ Rényi divergence between the forward process and its reverse has the operational meaning of the ``certainty equivalent'' of dissipated work (or, more generally, of entropy production) for a player with risk aversion $r=α-1$. The two known cases $α=1$ and $α=\infty$ are recovered and receive the new interpretation of being associated to a risk-neutral and an extreme risk-averse player respectively. Among the new results, the condition for $α=0$ describes the behavior of a risk-seeking player willing to bet on the transient violations of the second law. Our approach further leads to a generalized Jarzynski equality, and generalizes to a broader class of statistical divergences.

cond-mat.stat-mech↗

arXiv2023

Quantum complementarity: A novel resource for unambiguous exclusion and encryption

Complementarity is a phenomenon explaining several core features of quantum theory, such as the well-known uncertainty principle. Roughly speaking, two objects are said to be complementary if being certain about one of them necessarily forbids useful knowledge about the other. Two quantum measurements that do not commute form an example of complementary measurements, and this phenomenon can also be defined for ensembles of states. Although a key quantum feature, it is unclear whether complementarity can be understood more operationally, as a necessary resource in some quantum information task. Here we show this is the case, and relates to a novel task which we term $η$-unambiguous exclusion. As well as giving complementarity a clear operational definition, this also uncovers the foundational underpinning of unambiguous exclusion tasks for the first time. We further show that a special type of measurement complementarity is equivalent to advantages in certain encryption tasks. Finally, our analysis suggest that complementarity of measurement and state ensemble can be interpreted as strong forms of measurement incompatibility and quantum steering, respectively.

quant-ph↗

arXiv2023

How to use arbitrary measuring devices to perform almost perfect measurements

We consider the problem of reproducing one quantum measurement given the ability to perform another. We give a general framework and specific protocols for this problem. For example, we show how to use available "imperfect" devices a small number of times to implement a target measurement with average error that drops off exponentially with the number of imperfect measurements used. We hope that could be useful in near-term applications as a type of lightweight error mitigation of the measuring devices. As well as the view to practical applications, we consider the question from a general theoretical perspective in the most general setting where both the available and target measurements are arbitrary generalised quantum measurements. We show that this general problem in fact reduces to the ability to reproduce the statistics of (complete) von Neumann measurements, and that in the asymptotic limit of infinitely many uses of the available measurement, a simple protocol based upon `classical cloning' can perfectly achieve this task. We show that asymptotically all (non-trivial) quantum measurements are equivalent. We also study optimal protocols for a fixed number of uses of the available measurement. This includes, but is not limited to, improving both noisy and lossy quantum measurements. Furthermore, we show that, in a setting where we perform multiple measurements in parallel, we can achieve finite-rate measurement reproduction, by using block-coding techniques from classical information theory. Finally, we show that advantages can also be gained by making use of probabilistic protocols.

quant-ph↗

arXiv2023

Semidefinite Programming in Quantum Information Science

Semidefinite programs (SDPs) are a class of optimisation problems that find application in numerous areas of physics, engineering and mathematics. Semidefinite programming is particularly suited to problems in quantum physics and quantum information science. Following a review of the theory of semidefinite programming, the book proceeds to describe how it can be used to address a wide range of important problems from across quantum information science. Specific applications include quantum state, measurement, and channel estimation and discrimination, entanglement detection and quantification, quantum distance measures, and measurement incompatibility. Though SDPs have become an increasingly important tool in quantum information science it's not yet the kind of mathematics students learn routinely. Assuming only a basic knowledge of linear algebra and quantum physics and quantum information, this graduate-level book provides a unified and accessible presentation of one of the key numerical methods used in quantum information science.

quant-ph↗