arXiv subjects

John Martin

Publications and source records attributed to John Martin.

At least 19 recordsLinked to original sources

arXiv2026

Universality in fidelity-based quantum metrology

We consider the problem of identifying the quantum spin states that are the optimal sensors of a given transformation, averaged over all possible orientations of the spin system. Our geometric approach to the problem is based on a fidelity criterion and is entirely general, encompassing any unitary transformation. This formalism leads to a universality result: For any value of the spin, there exists a zero-measure subset of states that can be the optimal sensors for certain transformations and the worst sensors for others, and this set does not depend on the transformation under consideration. In other words, some spin states are simply the best (or worst) sensors, regardless of what they detect.

quant-ph↗

arXiv2026

Total, quantum, and classical measures of anticoherence for mixed spin states

Anticoherent spin states have isotropic low-order spin moments and are relevant to direction-independent metrology and quantum reference-frame alignment. In contrast to pure states, for mixed states such isotropy may originate either from genuine quantum correlations or from classical statistical mixing. We introduce an axiomatic framework for mixed-state $t$-anticoherence based on the symmetric qubit embedding. We distinguish total $t$-anticoherence, non-decreasing under SU(2)-covariant channels, from quantum $t$-anticoherence, defined as a resource monotone relative to a chosen total measure and constrained to coincide with it on pure states. This yields a classical contribution as their difference. We construct total measures based on reduced-state purity, Hilbert-Schmidt distance, and cumulative multipoles, and we discuss fidelity-based total candidates. We construct quantum counterparts via convex-roof extensions of pure-state functionals tied to bipartite entanglement in the symmetric sector. We provide explicit mixed-state examples, identify states with maximal quantum anticoherence supported on anticoherent subspaces, study robustness under particle loss for different types of states, and characterize the trade-off between purity and the maximal achievable anticoherence order.

quant-ph↗

arXiv2026

Dynamical decoupling and quantum error correction with SU(d) symmetries

Dynamical decoupling is a long-established and effective way to suppress unwanted interactions in qubit systems, enabling advances in fields ranging from quantum metrology to quantum computing. For general qudit systems, however, comparable protocols remain rare, mainly because Hamiltonian engineering in higher dimensions lacks the geometric intuition available for qubits. Here we present a general framework for dynamical decoupling in qudit systems, based on Lie group representation theory. By extending the group theory approach to dynamical decoupling, we show how decoupling groups can be systematically identified among the finite subgroups of SU(d) by analyzing their access to the irreducible components of the operator space. As an application, we construct new pulse sequences for interacting qutrit systems based on finite subgroups of SU(3), and show how subgroup factorizations and group orientations can be exploited to obtain shorter and more experimentally practical protocols for spin-1 systems with large zero-field splitting. We further show that the same symmetry-based framework yields quantum error-correcting codes: whenever a finite subgroup of SU(d) acts as a decoupling group for the relevant set of operators, the associated one-dimensional symmetry sectors define codespaces satisfying the Knill-Laflamme conditions, thereby unifying dynamical decoupling and quantum error correction in multi-level quantum systems.

quant-ph↗

arXiv2026

Symmetric Resourceful Steady States via Non-Markovian Dissipation

We prove a no-go theorem for symmetry-based dissipative engineering of collective-spin steady states: in spin-only Lindblad dynamics with jump operators linear in the collective-spin operators, any unique steady state exhibiting at least $\mathbb{Z}_2 \times \mathbb{Z}_2$ symmetry is necessarily the maximally mixed state. We then show that bath memory lifts this obstruction, enabling unique entangled steady states with a prescribed symmetry and a metrological gain, and providing a steady-state witness of non-Markovianity. Notably, this framework is largely insensitive to the microscopic details of the bath.

quant-ph↗

arXiv2026

Multiqubit monogamy relations beyond shadow inequalities

Multipartite quantum systems are subject to monogamy relations that impose fundamental constraints on the distribution of quantum correlations between subsystems. These constraints can be studied quantitatively through sector lengths, defined as the average value of $m$-body correlations, which have applications in quantum information theory and coding theory. In this work, we derive a set of monogamy inequalities that complement the shadow inequalities, enabling a complete characterization of the numerical range of sector lengths for systems with $N\leq 5$ qubits in a pure state. This range forms a convex polytope, facilitating the efficient extremization of key physical quantities, such as the linear entropy of entanglement and the quantum shadow enumerators, by a simple evaluation at the polytope vertices. For larger systems ($N\geq 6$), we highlight a significant increase in complexity that neither our inequalities nor the shadow inequalities can fully capture.

quant-ph↗

arXiv2025

Coherent Generation and Protection of Anticoherent Spin States

We report the first protocol specifically designed to generate anticoherent spin-$j$ states at different orders. The protocol consists of cycles of a rotation pulse about an axis followed by a squeezing pulse in a perpendicular direction. To protect these states, we develop dynamical decoupling techniques using group-based sequence design and the dynamically corrected gate formalism. We analyze key sources of dephasing, disorder, and dipole-dipole interactions and assess the effectiveness of our methods in preserving coherence. Potential applications of the produced anticoherent spin states include quantum sensing and studies related to quantum entanglement.

quant-ph↗

arXiv2025

Dynamical decoupling of interacting spins through group factorization

Dynamical decoupling (DD) is a well-known open-loop protocol for suppressing unwanted interactions in a quantum system, thereby drastically extending the coherence time of useful quantum states. In the original framework of evolution symmetrization, a DD sequence was shown to enforce a symmetry on the unwanted Hamiltonian, thereby suppressing it if the symmetry was inaccessible. In this work, we show how symmetries already present in the undesired Hamiltonian can be harnessed to reduce the complexity of decoupling sequences and to construct nested protocols that correct dominant errors at shorter timescales, using the factorization of DD symmetry groups into a product of its subgroups. We provide many relevant examples in various spin systems, using the Majorana constellation and point-group factorization to identify and exploit symmetries in the interaction Hamiltonian. Our framework recovers tailored pulse sequences developed in the context of NMR, including the classical Lee-Goldburg protocol, and further produces novel short and robust sequences capable of suppressing on-site disorder, dipole-dipole interactions, and more exotic many-body interactions in spin ensembles.

quant-ph↗

arXiv2025

The role of non-Markovian dissipation in quantum phase transitions: tricriticality, spin squeezing, and directional symmetry breaking

Understanding how to control phase transitions in quantum systems is at the forefront of research for the development of new quantum materials and technologies. Here, we study how the coupling of a quantum system to a non-Markovian environment, i.e., an environment with a frequency-dependent spectral density inducing memory effects, can be used to generate and reshape phase transitions and squeezing in matter phases. Focusing on a Lipkin-Meshkov-Glick model, we demonstrate that non-Markovian dissipation can be leveraged to engineer tricriticality via the fusion of $2^{\mathrm{nd}}$-order and $1^{\mathrm{st}}$-order critical points. We identify phases that arise from different ways of breaking the single weak symmetry of our model, which led us to introduce the concept of \textit{directional spontaneous symmetry breaking} (DSSB) as a general framework to understand this phenomenon. We show that signatures of DSSB can be seen in the emergence of spin squeezing along different directions, and that the latter is controllable via non-Markovian effects, opening up possibilities for applications in quantum metrology. Finally, we propose an experimental implementation of our non-Markovian model in cavity QED. Our work features non-Markovianity as a resource for controlling phase transitions in general systems, and highlights shortcomings of the Markovian limit in this context.

quant-ph↗

arXiv2025

Nonequivalence between absolute separability and positive partial transposition in the symmetric subspace

The equivalence between absolutely separable states and absolutely positive partial transposed (PPT) states in general remains an open problem in quantum entanglement theory. In this work, we study an analogous question for symmetric multiqubit states. We show that symmetric absolutely PPT (SAPPT) states (symmetric states that remain PPT after any symmetry-preserving unitary evolution) are not always symmetric absolutely separable by providing explicit counterexamples. More precisely, we construct a family of entangled five-qubit SAPPT states. Similar counterexamples for larger odd numbers of qubits are identified.

quant-ph↗

arXiv2025

Platonic dynamical decoupling sequences for interacting spin systems

In the NISQ era, where quantum information processing is hindered by the decoherence and dissipation of elementary quantum systems, developing new protocols to extend the lifetime of quantum states is of considerable practical and theoretical importance. A well-known technique, known as dynamical decoupling, uses a carefully designed sequence of pulses applied to a quantum system, such as a spin-$j$ (which represents a qudit with $d=2j+1$ levels), to suppress the coupling Hamiltonian between the system and its environment, thereby mitigating dissipation. While dynamical decoupling of qubit systems has been widely studied, the decoupling of qudit systems has been far less explored and often involves complex sequences and operations. In this work, we design efficient decoupling sequences composed solely of global $\mathrm{SU}(2)$ rotations and based on tetrahedral, octahedral, and icosahedral point groups, which we call Platonic sequences. We extend the Majorana representation for Hamiltonians to develop a simple framework that establishes the decoupling properties of each Platonic sequence and show its effectiveness on many examples. These sequences are universal in their ability to cancel any type of interaction with the environment for single spin-$j$ with spin quantum number $j\leqslant 5/2$, and they are capable of decoupling up to $5$-body interactions in an ensemble of interacting spin-$1/2$ with only global pulses, provided that the interaction Hamiltonian has no isotropic component, with the exception of the global identity. We also discuss their inherent robustness to finite pulse duration and a wide range of pulse errors, as well as their potential application as building blocks for dynamically corrected gates.

quant-ph↗

arXiv2025

Quantum metrology of rotations with mixed spin states

The efficiency of a quantum metrology protocol can be significantly diminished by the interaction of the system with its environment, leading to a loss of purity and, as a result, a mixed state for the probing system. An example is the measurement of a magnetic field through the rotation of a spin that is subject to decoherence due to its coupling to a surrounding spin or bosonic bath. In this work, we define mixed optimal quantum rotosensors (OQRs) as mixed spin-$j$ states that achieve maximum sensitivity to estimate infinitesimal rotations, when the rotation axis is unknown. We study two scenarios, where the probe states saturate the averaged fidelity or the averaged quantum Cramér-Rao bound, the latter giving the ultimate sensitivity. We find that mixed OQRs can achieve sensitivity equal to that of pure states and are obtained by mixing states from linear subspaces of anticoherent states. We present several examples of mixed OQRs and their associated anticoherent subspaces. We also show that OQRs maximize entanglement in a specific sense, preserving the known relation between entanglement and optimal rotation sensitivity for pure states, even in the context of mixed states. Our results highlight the interconnection between quantum metrology of rotations, anticoherence and entanglement in mixed spin states.

quant-ph↗

arXiv2025

Critical Dynamics of the Anderson Transition on Small-World Graphs

The Anderson transition on random graphs draws interest through its resemblance to the many-body localization (MBL) transition with similarly debated properties. In this Letter, we construct a unitary Anderson model on Small-World graphs to characterize long time and large size wave-packet dynamics across the Anderson transition. We reveal the logarithmically slow non-ergodic dynamics in the critical regime, confirming recent random matrix predictions. Our data clearly indicate two localization times: an average localization time that diverges, while the typical one saturates. In the delocalized regime, the dynamics are initially non-ergodic but cross over to ergodic diffusion at long times and large distances. Finite-time scaling then allows us to characterize the critical dynamical properties: the logarithm of the average localization time diverges algebraically, while the ergodic time diverges exponentially. Our results could be used to clarify the dynamical properties of MBL and could guide future experiments with quantum simulators.

cond-mat.dis-nn↗

arXiv2025

The Physics-Informed Neural Network Gravity Model: Generation III

Scientific machine learning and the advent of the Physics-Informed Neural Network (PINN) have shown high potential in their ability to solve complex differential equations. One example is the use of PINNs to solve the gravity field modeling problem -- learning convenient representations of the gravitational potential from position and acceleration data. These PINN gravity models, or PINN-GMs, have demonstrated advantages in model compactness, robustness to noise, and sample efficiency when compared to popular alternatives; however, further investigation has revealed various failure modes for these and other machine learning gravity models which this manuscript aims to address. Specifically, this paper introduces the third generation Physics-Informed Neural Network Gravity Model (PINN-GM-III) which includes design changes that solve the problems of feature divergence, bias towards low-altitude samples, numerical instability, and extrapolation error. Six evaluation metrics are proposed to expose these past pitfalls and illustrate the PINN-GM-III's robustness to them. This study concludes by evaluating the PINN-GM-III modeling accuracy on a heterogeneous density asteroid, and comparing its performance to other analytic and machine learning gravity models.

cs.LG↗

arXiv2024

Polytopes of Absolutely Wigner Bounded Spin States

Quasiprobability has become an increasingly popular notion for characterising non-classicality in quantum information, thermodynamics, and metrology. Two important distributions with non-positive quasiprobability are the Wigner function and the Glauber-Sudarshan function. Here we study properties of the spin Wigner function for finite-dimensional quantum systems and draw comparisons with its infinite-dimensional analog, focusing in particular on the relation to the Glauber-Sudarshan function and the existence of absolutely Wigner-bounded states. More precisely, we investigate unitary orbits of mixed spin states that are characterized by Wigner functions lower-bounded by a specified value. To this end, we extend a characterization of the set of absolutely Wigner positive states as a set of linear eigenvalue constraints, which together define a polytope centred on the maximally mixed state in the simplex of spin-$j$ states. The lower bound determines the relative size of such absolutely Wigner bounded (AWB) polytopes and we study their geometric characteristics. In each dimension a Hilbert-Schmidt ball representing a tight purity-based sufficient condition to be AWB is exactly determined, while another ball representing a necessary condition to be AWB is conjectured. Special attention is given to the case where the polytope separates orbits containing only positive Wigner functions from other orbits because of the use of Wigner negativity as a witness of non-classicality. Comparisons are made to absolute symmetric state separability and spin Glauber-Sudarshan positivity, with additional details given for low spin quantum numbers.

quant-ph↗

arXiv2024

Spectral theory of non-Markovian dissipative phase transitions

Dissipative phase transitions in quantum systems have been largely studied under the so-called Markovian approximation, where the environments to which the systems are coupled are memoryless. Here, we present a generalization of the spectral theory of dissipative phase transitions to non-Markovian systems, encompassing a much broader class of quantum materials and experiments and opening many possibilities for non-Markovian engineering of matter phases such as, as explored in the companion Letter [Debecker et. al., Phys. Rev. Lett. 133, 140403 (2024)], reshaping of phase boundaries and triggering of phase transitions. We first prove several statements about the connections between the spectrum of the generator of the non-Markovian dynamics of general systems and dissipative phase transitions. Then, as a benchmark, we show that our framework can capture all the expected signatures of the superradiant phase transition appearing in a challenging $U(1)$-symmetric two-mode Dicke model from a reduced description of the dynamics of the atoms only, a task for which all other methods have failed so far.

quant-ph↗

arXiv2024

Controlling Matter Phases beyond Markov

Controlling phase transitions in quantum systems via coupling to reservoirs has been mostly studied for idealized memory-less environments under the so-called Markov approximation. Yet, most quantum materials and experiments in the solid state, atomic, molecular and optical physics are coupled to reservoirs with finite memory times. Here, using the spectral theory of non-Markovian dissipative phase transitions developed in the companion paper [Debecker et al., Phys. Rev. A 110, 042201 (2024)], we show that memory effects can be leveraged to reshape matter phase boundaries, but also reveal the existence of dissipative phase transitions genuinely triggered by non-Markovian effects.

quant-ph↗

arXiv2024

Dissipative phase transition: from qubits to qudits

We investigate the fate of dissipative phase transitions in quantum many-body systems when the individual constituents are qudits ($d$-level systems) instead of qubits. As an example system, we employ a permutation-invariant $XY$ model of $N$ infinite-range interacting $d$-level spins undergoing individual and collective dissipation. In the mean-field limit, we identify a dissipative phase transition, whose critical point is independent of $d$ after a suitable rescaling of parameters. When the decay rates between all adjacent levels are identical and $d\geq 4$, the critical point expands, in terms of the ratio between dissipation and interaction strengths, to a critical region in which two phases coexist and which increases as $d$ grows. In addition, a larger $d$ leads to a more pronounced change in spin expectation values at the critical point. Numerical investigations for finite $N$ reveal symmetry breaking signatures in the Liouvillian spectrum at the phase transition. The phase transition is furthermore marked by maximum entanglement negativity and a significant purity change of the steady state, which become more pronounced as $d$ increases. Considering qudits instead of qubits thus opens new perspectives on accessing rich phase diagrams in open many-body systems.

quant-ph↗

arXiv2024

Absolute separability witnesses for symmetric multiqubit states

The persistent separability of certain quantum states, known as symmetric absolutely separable (SAS), under symmetry-preserving global unitary transformations is of key significance in the context of quantum resources for bosonic systems. In this work, we develop criteria for detecting SAS states of any number of qubits. Our approach is based on the Glauber-Sudarshan $P$ representation for finite-dimensional quantum systems. We introduce three families of SAS witnesses, one linear and two nonlinear in the eigenvalues of the state, formulated respectively as an algebraic inequality or a quadratic optimization problem. These witnesses are capable of identifying more SAS states than previously known counterparts. We also explore the geometric properties of the subsets of SAS states detected by our witnesses, shedding light on their distinctions.

quant-ph↗