29 papers
Malleability of transformations on the ciphertext in noisy Quantum public key encryption
Pete Rigas
We characterize a noisy variant of a Quantum public encryption protocol recently introduced by Malavolta and Walter which demonstrated that the notion of everlasting security can b…
Multiplayer parallel repetition without dependency-breaking and anchoring variables: monotonic, concave amplification
Pete Rigas
We obtain quantitative estimates on the decay of the multiplayer optimal value under parallel repetition. In comparison to a previous work of the author in 2025 (arXiv: 2508.09380)…
Eve's forgery probability from her false acceptance probability: interactive authentication, Holevo information and the min-entropy
Pete Rigas
We obtain estimates for Eve's forgery probability, namely the probability that she is able to forge a message which Alice or Bob mistakenly accept over a noisy Quantum channel for…
Composable, unconditional security without a Quantum secret key: public broadcast channels and their conceptualizations, adaptive bit transmission rates, fidelity pruning under wiretaps
Pete Rigas
We examine public broadcast, forward conceptual, and backward conceptual, Quantum channels in the context of communication protocols that are independent of secret keys. Given rese…
Quantum Optimality in the Odd-Cycle game: the topological odd-blocker, marked connected components of the giant, consistency of pearls, vanishing homotopy
Pete Rigas
We characterize optimality of Quantum strategies for the Odd-Cycle game. Separate from other game-theoretic settings, parallel repetition for the Odd-Cycle game is related to the f…
Probability distributions over CSS codes: two-universality, QKD hashing, collision bounds, security
Pete Rigas
We characterize novel probability distributions for CSS codes. Such classes of error correcting codes, originally introduced by Calderbank, Shor, and Steane, are of great significa…
Parallel repetition of expanded, and multiplayer, Quantum games: anchoring, optimal values, generalized error bounds, dependency-breaking as symmetry-breaking
Pete Rigas
We demonstrate that parallel repetition of the multiplayer anchored optimal value, , decays exponentially. Central to our approach are several pr…
Error correction, authentication, and false acceptance, probabilities for communication over noisy quantum channels: converse upper bounds on the bit transmission rate
Pete Rigas
We obtain strict upper bounds on the bit transmission rate for communication of Classical bit codewords over Quantum channels. Albeit previous arguments in arXiv: 1804.01797 which…
Quantum strategies, error bounds, optimality, and duality gaps for multiplayer XOR, , compiled XOR, , and strong parallel repetiton of XOR, , and FFL games
Pete Rigas
We characterize exact, and approximate, optimality of games that players can interact with using quantum strategies. In comparison to a previous work of the author, arXiv: 2311.128…
Exact solvability of an Ising-type model, and exact solvability of the 6-vertex, and 8-vertex, models
Pete Rigas
We compute the action-angle coordinates for an Ising type model whose L-operator has been previously studied in the literature by Bazhanov and Sergeev. In comparison to computation…
Intertwining vectors, and Boltzmann weight matrices, of a Solid-on-Solid model from the 20-vertex model
Pete Rigas
We initiate a new study on the correspondence between the 20-vertex model and a SOS (Solid-on-Solid) model. In comparison to two previous works of the author in 2024 which characte…
Poisson structure of the 4-vertex model, and the higher-spin XXX chain, and Yang-Baxter algebras
Pete Rigas
We implement the quantum inverse scattering method for the 4-vertex model. In comparison to previous works of the author which examined the 6-vertex, and 20-vertex, models, the 4-v…
The emptiness formation probability, and representations for nonlocal correlation functions, of the 20-vertex model
Pete Rigas
We study the emptiness formation probability, along with various representations for nonlocal correlation functions, of the 20-vertex model. In doing so, we leverage previous argum…
Quantum inverse scattering for the 20-vertex model up to Dynkin automorphism: 3D Poisson structure, triangular height functions, weak integrability
Pete Rigas
We initiate a novel application of the quantum inverse scattering method for the 20-vertex model, building upon seminal work from Faddeev and Takhtajan on the study of Hamiltonian…
Scaling limit of the triangular kinetic prudent walk
Pete Rigas
Expressions for scaling limits of random walks, such as those obtained in several areas of the Probability theory literature, are of great significance in characterizing long term,…
Optimal, and approximately optimal, quantum strategies for and games
Pete Rigas
We analyze optimal, and approximately optimal, quantum strategies in two non-local settings based upon previous investigations of the XOR and CHSH games. By building upon previous…
Open boundary conditions of the spin chain and sectors of conformal field theories
Pete Rigas
We study open boundary conditions for the spin chain, which shares connections with the six-vertex model, under staggering, and also to the antiferromagnetic Potts mode…
Poisson structure and Integrability of a Hamiltonian flow for the inhomogeneous six-vertex model
Pete Rigas
We compute the action-angle variables for a Hamiltonian flow of the inhomogeneous six-vertex model, from a formulation introduced in a 2022 work due to Keating, Reshetikhin, and Sr…
Operator formalism for discretely holomorphic parafermions of the two-color Ashkin-Teller, loop , staggered eight-vertex, odd eight-vertex, and abelian sandpile models
Pete Rigas
We extend an operator formalism, developed by Hongler, Kytölä, and Zahabi in 2012 for the Ising model, to the Ashkin-Teller and loop models. The formalism is pr…
Eigenvalue attraction in open quantum systems, biophysical systems, and Parity-Time symmetric materials
Pete Rigas
We investigate eigenvalue attraction for open quantum systems, biophysical systems, and for Parity-Time symmetric materials. To determine whether an eigenvalue and its complex conj…
Phase transition of the long range Ising model in lower dimensions, for , with a Peierls argument
Pete Rigas
We extend previous results due to Ding and Zhuang in order to prove that a phase transition occurs for the long range Ising model in lower dimensions. By making use of a recent arg…
Eigenvectors of Toeplitz matrices from Fisher-Hartwig symbols with greater than, or equal to, one singularity
Pete Rigas
Asymptotically, we analytically derive the form of eigenvectors for two Fisher-Hartwig symbols besides those which were previously investigated in a work due to Movassagh an…
The phase transition for the Gaussian free field is sharp
Pete Rigas
We prove that the phase transition for the Gaussian free field (GFF) is sharp. In comparison to a previous argument due to Rodriguez in 2017 which characterized a law for the…
Kesten's incipient infinite cluster for the three-dimensional, metric-graph Gaussian free field, from critical level-set percolation, and for the Villain model, from random cluster geometries and a Swendsen-Wang type algorithm
Pete Rigas
We address one open problem in a recent work due to Ding and Wirth, the first version of which was available in , relating to level-set percolation on metric-graphs for the G…