arXiv subjects

Sean Prudhoe

Publications and source records attributed to Sean Prudhoe.

4 recordsLinked to original sources

arXiv2025

Entanglement Breaking Structure of Cartan-Covariant Quantum Channels

Cartan-covariant quantum channels are introduced and studied using the Choi-Jamio{\l}kowski isomorphism. The channels are Cartan-covariant as the covariance groups considered form symmetric pairs with the special unitary group SU($n$), and their associated Cartan involution provides a route to exactly compute the eigenspectrum of their Choi states and the partial transpose for any $n\in \mathbb{N}$. These channels include previously studied SO$(n)$-covariant channels, and further include Sp$(\frac{n}{2})$-covariant channels (when $n$ is even) and S(U($p$) $\times$ U($q$))-covariant channels (where $n\!=\!p\!+\!q$). We show that all Cartan-covariant channels satisfy the PPT$^{2}$-conjecture and further demonstrate the nontrivial nature of this result for the class of Sp$(\frac{n}{2})$-covariant and ${\rm S}({\rm U}(p) \!\times\!{\rm U}(q))$-covariant channels

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arXiv2024

Effective dynamics of qubit networks via phase-covariant quantum ensembles

We derive a new constructive procedure to rapidly generate ensembles of phase-covariant dynamical maps that may be associated to the individual spins of a closed quantum system. We do this by first computing the single-spin dynamical maps in small XXZ networks and chains, specialized to the class of initial states that guarantees phase-covariant dynamics for each spin. Since the dynamics in any small, closed system contains oscillatory features associated to the system size, we define an averaging procedure to extract time-homogeneous dynamics. We use the the average map and the set of deviations from the average map in the exactly derived ensembles to motivate the form of distributional functions for map parameters. The distributions then straightforwardly generate arbitrary-sized ensembles of channels, constrained by a few global properties. This procedure can also generate ensembles where individual maps are not phase-covariant although the average map is, corresponding to realizations of disordered, or noisy, Hamiltonians. The construction procedure suggests new ways to realize random families of open-system dynamics, subject to constraints that require the ensemble to approximate a partition of a closed system.

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arXiv2023

Spontaneously interacting qubits from Gauss-Bonnet

Building on previous constructions examining how a collection of small, locally interacting quantum systems might emerge via spontaneous symmetry breaking from a single-particle system of high dimension, we consider a larger family of geometric loss functionals and explicitly construct several classes of critical metrics which "know about qubits" (KAQ). The loss functional consists of the Ricci scalar with the addition of the Gauss-Bonnet term, which introduces an order parameter that allows for spontaneous symmetry breaking. The appeal of this method is two-fold: (i) the Ricci scalar has already been shown to have KAQ critical metrics and (ii) exact equations of motions are known for loss functionals with generic curvature terms up to two derivatives. We show that KAQ critical metrics, which are solutions to the equations of motion in the space of left-invariant metrics with fixed determinant, exist for loss functionals that include the Gauss-Bonnet term. We find that exploiting the subalgebra structure leads us to natural classes of KAQ metrics which contain the familiar distributions (GUE, GOE, GSE) for random Hamiltonians. We introduce tools for this analysis that will allow for straightfoward, although numerically intensive, extension to other loss functionals and higher-dimension systems.

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arXiv2022

Classifying the non-time-local and entangling dynamics of an open qubit system

We study families of dynamical maps generated from interactions with varying degrees of symmetry. For a family of time-independent Hamiltonians, we demonstrate the relationship between symmetry, strong-coupling, perfect entanglers, non-Markovian features, and non-time-locality. We show that by perturbing the initial environment state, effective time-local descriptions can be obtained that are non-singular yet capture essential non-unitary features of the reduced dynamics. We then consider a time-dependent Hamiltonian that changes the degree of symmetry by activating a dormant degree of freedom. In this example we find that the one-qubit reduced dynamics changes dramatically. These results can inform the construction of effective theories of open systems when the larger system dynamics is unknown.

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