arXiv subjects

Pete Rigas

Publications and source records attributed to Pete Rigas.

At least 19 recordsLinked to original sources

arXiv2026

Malleability of transformations on the ciphertext in noisy Quantum public key encryption

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 be rigorously formulated for Quantum key distribution after two rounds of interaction between Alice and Bob. To address one possible direction of research that is related to injecting noise in the cryptographic protocol related to Quantum key distribution we formulate arguments for further examining the notion of everlasting security through malleability assumptions on transformations of the ciphertext. Assumptions surrounding malleability were introduced by Maurer and Tackmann for the purposes of comparing how authenticate then encrypt, and encrypt then authenticate, protocols behave through a variety of expressions for the forwarding error, deleting error, and reconstruction probabilities. Such probabilities are put to further use for obtaining connections between the indistinguishability and security threshold for a cryptographic protocol of interests. To further build upon such associations we demonstrate, through an adaptation of the Gentle Measurement Lemma from Quantum information theory, how upper bounds on the trace distance can be used to generalize the negligibility function obtained by Malavolta and Walter in the noiseless setting. Besides the fact that the negligibility function in the noisy setting is related to a higher security threshold it continues to remain of interest to determine whether computations provided in this work for upper bounding the trace distance can be related to other settings that are centered more on game-theoretic approaches.

quant-ph↗

arXiv2026

Multiplayer parallel repetition without dependency-breaking and anchoring variables: monotonic, concave amplification

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) which sought to generalize dependency-breaking and anchoring variables from two-player Quantum games, being able to establish quantitative estimates on the decay of the optimal value of a multiplayer game under parallel repetition is of interest to establish under different assumptions. Specifically, independently of the dependency-breaking and anchoring variables that have previously been employed to remove correlations from entangled information shared between Alice and Bob (hence removing dependencies), monotonic concave functions can be used in place of such variables to obtain rates of decay on the optimal value. The game-theoretic setting with two players was first analyzed with monotonic concave functions by Lanzenberger and Maurer. For $q_i , x_i > 0$ $\forall 1 \leq i \leq N$ where $N > 0 $ is the total number of players we adddress an open question raised in their work regarding potential generalizations of two-player monotonic concave functions, through amplification functions of the form $\Psi_{\textit{Mult}} \equiv \Psi = N - \underset{1 \leq i \leq N}{\prod} \mathrm{exp} \big[ - q_i x_i \big]$, which in the multiplayer game-theoretic setting have more intricate combinatorial structures.

quant-ph↗

arXiv2026

Eve's forgery probability from her false acceptance probability: interactive authentication, Holevo information and the min-entropy

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 generating a shared Quantum secret key. This probability is related to Eve's success probability obtained in a previous work due to Renner and Wolf, which was obtained from assumptions on the min-entropy for characterizing asymmetric security. To demonstrate that protocols over noisy Quantum channels are dependent upon a single, unified security threshold in comparison to multiple security parameters in the Renner-Wolf interactive authentication protocol framework we upper bound Eve's forgery probability with a Holevo-type quantity that can be made negligibly small. By leveraging estimates for Eve's false acceptance probability that have previously been obtained by the author, we obtain the desired security threshold by bounding the false acceptance probability with a suitably chosen two-universal function which serves as a counterpart to two-universal hashing functions that have previously been examined for cryptographic protocols in Quantum key distribution. As a result the protocol is not only $\epsilon$-secure, for some $\epsilon>0$, but also composable against forgery and key leakage.

quant-ph↗

arXiv2025

Composable, unconditional security without a Quantum secret key: public broadcast channels and their conceptualizations, adaptive bit transmission rates, fidelity pruning under wiretaps

We examine public broadcast, forward conceptual, and backward conceptual, Quantum channels in the context of communication protocols that are independent of secret keys. Given research directions of interest previously identified in arXiv: 1804.01797, besides converse upper bounds on the bit transmission rate obtained by the author in recent work (arXiv: 2507.03035), additional possibilities remain, including: (1) determining whether aspects of QKD dependent protocols can be incorporated into steps of QKD independent protocols; (2) whether there would be any amplification to the Quantum-classical performance gap that Alice and Bob can exploit towards prospective Quantum advantage; (3) formulating the conditions under which secrecy and authentication can be simultaneously achieved. To characterize the conditions for which secrecy can be achieved with high probability, we argue that there not only exists suitable protocols which enable Alice and Bob to map into the authenticated space of bit codewords with high probability, but also that forward conceptual channels, through cascading, can significantly increase Eve's probability of false acceptance. Albeit the fact that secrecy, along with conceputalizations of the public broadcast channel, were initially discussed by Maurer for QKD dependent protocols, determining whether aspects of such protocols can be adapted for unconditional security without the use of a secret key is of great interest to explore. We demonstrate that Eve's error probability, through the cascading procedure, can be analyzed with the Holevo information under an optimal decoder. Furthermore, through post-processing of the outputs of a Completely Positive Trace Preserving (CPTP) map, we also demonstrate how to decrease Holevo sum quantities with data-processing and entropy-continuity bounds.

quant-ph↗

arXiv2025

Quantum Optimality in the Odd-Cycle game: the topological odd-blocker, marked connected components of the giant, consistency of pearls, vanishing homotopy

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 foam problem, which can be formulated through a minimization of the surface area. In comparison to previous works on minimizing the surface area, we quantify how properties of the marked giant connected component can be related to the maximum winning probability using Quantum strategies. Objects that we introduce to formulate such connections include the topological odd-blocker, previous examples of error bounds for other Quantum games that have been formulated by the author, pearls, consistent regions, and the cycle elimination problem.

quant-ph↗

arXiv2025

Probability distributions over CSS codes: two-universality, QKD hashing, collision bounds, security

We characterize novel probability distributions for CSS codes. Such classes of error correcting codes, originally introduced by Calderbank, Shor, and Steane, are of great significance in advancing the fidelity of Quantum computation, with implications for future near term applications. Within the context of Quantum key distribution, such codes, as examined by Ostrev in arXiv: 2109.06709 along with two-universal hashing protocols, have greatly simplified Quantum phases of computation for unconditional security. To further examine novel applications of two-universal hashing protocols, particularly through the structure of parity check matrices, we demonstrate how being able to efficiently compute functions of the parity check matrices relates to marginals of a suitably defined probability measure supported over random matrices. The security of the two-universal QKD hashing protocol will be shown to depend upon the computation of purified states of random matrices, which relates to probabilistic collision bounds between two hashing functions. Central to our approach are the introduction of novel real, simulator, and ideal, isometries, hence allowing for efficient computations of functions of the two parity check matrices. As a result of being able to perform such computations involving parity check matrices, the security of the two-universal hashing protocol is a factor of $2^{ \frac{5}{2} ( 5 - \frac{3}{2} ) + \mathrm{log}_2 \sqrt{C}}$ less secure, for some strictly positive constant $C$.

quant-ph↗

arXiv2025

Parallel repetition of expanded, and multiplayer, Quantum games: anchoring, optimal values, generalized error bounds, dependency-breaking as symmetry-breaking

We demonstrate that parallel repetition of the multiplayer anchored optimal value, $\omega \big( G_{\bot} \big)^{\otimes n}$, decays exponentially. Central to our approach are several probabilistic computations, pertaining to: (1) the computation of expected values for quantifying how the winning probability of the game is likely to change under the anchoring transformation; (2) the computation of positive operator valued measurements, which can be placed into direct correspondence with several probabilistically defined quantities; (3) the computation of Relative, and Relative-min entropies; (4) and lastly, the computation of generalized error bounds, which have previously been analyzed by the author in several multiplayer game-theoretic settings (arXiv: 2505.06322, and arXiv: 2507.03035). This work builds upon observations originally provided by Bavarian, Vidick, and Yuen (arXiv: 1509.07466).

quant-ph↗

arXiv2025

Error correction, authentication, and false acceptance, probabilities for communication over noisy quantum channels: converse upper bounds on the bit transmission rate

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 have demonstrated that lower bounds can be shown to hold for the bit transmission rate without the presence of significant noise over the channel shared by Alice and Bob for the purposes of encoding, decoding, transmission and authentication, the author suggests that upper bounding the bit transmission rate could be of use towards classifying paradoxical aspects of communication protocols, as well as constructing error correcting codes which are resilient to noise. The upper bound that is obtained in this work for the bit transmission rate, as a converse result, is dependent upon the natural logarithm of the size of each player's alphabet, as well as smaller alphabets, which can be leveraged for simultaneously realizing Quantum advantage for maximizing error correction and minimizing false acceptance. Crucially, the upper bound to the bit transmission rate is dependent upon a pruning procedure, which seeks to determine whether letters from player's alphabets can be removed so that prospective Quantum advantage, in order for Alice and Bob to implement error correction protocols with high probability, despite the fact that there is more noise over the channel between Alice and Bob in comparison to that between Bob and Eve.

quant-ph↗

arXiv2025

Quantum strategies, error bounds, optimality, and duality gaps for multiplayer XOR, $\mathrm{XOR}^{}$, compiled XOR, $\mathrm{XOR}^{}$, and strong parallel repetiton of XOR, $\mathrm{XOR}^{*}$, and FFL games

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: 2311.12887, which applied a 2016 framework due to Ostrev for constructing error bounds beyond CHSH and XOR games, in addition to the existence of well-posed semidefinite programs for determining primal feasible solutions, along with quantum-classical duality gaps, it continues to remain of interest to further develop the construction of error bounds, and related objects, to game-theoretic settings with several participants. In such settings, one encounters a rich information theoretic landscape, not only from the fact that there exists a significantly larger combinatorial space of possible strategies for each player, but also several opportunities for pronounced quantum advantage. We conclude this effort by describing other variants of other possible strategies, as proposed sources for quantum advantage, in $\mathrm{XOR}^{*}$, compiled $\mathrm{XOR}^{*}$, and strong parallel repetition variants of $\mathrm{XOR}^{*}$ games.

quant-ph↗

arXiv2024

Exact solvability of an Ising-type model, and exact solvability of the 6-vertex, and 8-vertex, models

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 computations with such operators that have been examined previously by the author for the 4-vertex, 6-vertex, and 20-vertex, models, computations for asymptotically approximating a collection of sixteen identities with the Poisson bracket, which together constitute the Poisson structure of the Ising type model, exhibit dependencies upon nearest neighbor interactions. Inspite of the fact that L-operators for the 20-vertex model are defined in terms of combinatorial, and algebraic, constituents unlike such operators for the 6-vertex model which are defined in terms of projectors and Pauli basis elements, L-operators for the Ising-type model can be used for concluding that a model which interpolates between the 6-vertex, and 8-vertex, models is exactly solvable.

cond-mat.stat-mech↗

arXiv2024

Intertwining vectors, and Boltzmann weight matrices, of a Solid-on-Solid model from the 20-vertex model

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 characterized properties of the transfer, and quantum monodromy, matrices of the 20-vertex model from the perspective of the quantum inverse scattering method, in addition to the structure of nonlocal correlations, the forthcoming approach is an adaptation of a study on the rational 7-vertex model. For the rational 7-vertex model, Antoenneko and Valinevich demonstrated that the intertwining vectors can be used to transform the R-matrix of a vertex model into the Boltzman weight matrix of an SOS model. To further develop perspectives on classes of higher dimensional SOS models, by leveraging previous computations with L-operators due to the author, and by also manipulating q-exponentials, and other related factors from a factorization of the universal R-matrix due to Boos et al, analogs of intertwining vectors for the 20- vertex model can be obtained. In comparison to the system of equations that have been obtained for the rational 7-vertex model, the system that one obtains for the 20-vertex model consists of 9 equations for each entry of the R-matrix. Furthermore, from the fact that the 20-vertex model contains more possible configurations in the sample space than the rational 7-vertex model does, the Boltzman weight matrix of the corresponding SOS model asymptotically depends upon several contributions, a few of which include tensor products of basis elements, and spectral parameters over the triangular lattice.

math-ph↗

arXiv2024

Poisson structure of the 4-vertex model, and the higher-spin XXX chain, and Yang-Baxter algebras

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-vertex model exhibits different characteristics, ranging from L-operators expressed in terms of projectors and Pauli matrices to algebraic and combinatorial properties, including Poisson structure and boxed plane partitions. With far fewer computations with an L-operator provided for the 4-vertex model by Bogoliubov in 2007, in comparison to those for L-operators of the 6, and 20, vertex models, from lower order expansions of the transfer matrix we derive a system of relations from the structure of operators that can be leveraged for studying characteristics of the higher-spin XXX chain in the weak finite volume limit. In comparison to quantum inverse scattering methods for the 6, and 20, vertex models which can be used to further study integrability, and exact solvability, an adaptation of such an approach for the 4-vertex model can be used to approximate, asymptotically in the weak finite volume limit, sixteen brackets which generate the Poisson structure. From explicit relations for operators of the 4-vertex transfer matrix, we conclude by discussing corresponding aspects of the Yang-Baxter algebra, which is closely related to the operators obtained from products of L-operators for approximating the transfer, and quantum monodromy, matrices. The structure of computations from L-operators of the 4-vertex model directly transfers to L-operators of the higher-spin XXX chain, revealing a similar structure of another Yang-Baxter algebra of interest.

math-ph↗

arXiv2024

The emptiness formation probability, and representations for nonlocal correlation functions, of the 20-vertex model

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 arguments for representations of nonlocal correlation functions for the 6-vertex model, under domain-wall boundary conditions, due to Colomo, Di Giulio, and Pronko, in addition to the inhomogeneous, and homogeneous, determinantal representations for the 20-vertex partition function due to Di Francesco, also under domain-wall boundary conditions. By taking a product of row configuration probabilities, we obtain a desired contour integral representation for nonlocal correlations from a determinantal representation. Finally, a counterpart of the emptiness formation probability is introduced for the 20-vertex model.

math-ph↗

arXiv2024

Operator formalism for discretely holomorphic parafermions of the two-color Ashkin-Teller, loop $\mathrm{O} ( 1 )$, staggered eight-vertex, odd eight-vertex, and abelian sandpile models

We extend an operator formalism, developed by Hongler, Kytölä, and Zahabi in 2012 for the Ising model, to the Ashkin-Teller and loop $\mathrm{O} ( n ) $ models. The formalism is primarily dependent upon notions of massive, and massless, s-holomorphicity of the Ising model, which are respectively satisfied at, and below, the critical temperature, hence allowing for rigorous analyses of the transfer matrix, correlation functions, and lattice fermion operators. From results of another paper, by Tanhayi-Ahari and Rouhani in 2012, which demonstrates that parafermionic observables for the staggered eight-vertex model coincide with those of the Ashkin-Teller model, as well as a 2003 paper, by Wu and Kunz, which establishes a correspondence between the staggered eight-vertex and odd eight-vertex models, we establish further associations.

math.PR↗

arXiv2024

From logarithmic delocalization of the six-vertex height function under sloped boundary conditions to weakened crossing probability estimates for the Ashkin-Teller, generalized random-cluster, and $(q_σ,q_τ)$-cubic models

To obtain Russo-Seymour-Welsh estimates for the height function of the six-vertex model under sloped boundary conditions, which can be leveraged to demonstrate that the height function logarithmically delocalizes under a broader class of boundary conditions, we formulate crossing probability estimates in strips of the square lattice and the cylinder, for parameters satisfying $a\equiv b$, $c \in [1,2]$, and $\mathrm{max} \{ a , b \} \leq c$, in which each of the first two conditions respectively relate to invariance under vertical and diagonal reflections enforced through the symmetry $σξ\geq -ξ$ for domains in strips of the square lattice, and satisfaction of FKG, for the height function and for its absolute value. To determine whether arguments for estimating crossing probabilities of the height function for flat boundary conditions from a recent work due to Duminil-Copin, Karila, Manolescu, and Oulamara remain applicable for sloped boundary conditions, from the set of possible slopes given by the interior of the set of rational points from $[-1,1] \times [-1,1]$, we analyze sloped Gibbs states, which do not have infinitely many disjointly oriented circuits. In comparison to Russo-Seymour-Welsh arguments for flat boundary conditions, arguments for sloped boundary conditions present additional complications for both planar and cylindrical settings, in which crossing events that are considered in the strip, and then extended to the annulus and cylinder, must be maintained across rectangles of large aspect ratio, in spite of the fact that some proportion of faces within the strip freeze with positive probability.

math.PR↗

arXiv2024

The phase transition for the Gaussian free field is sharp

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 $0-1$ law for the Massive Gaussian Free Field by analyzing crossing probabilities below a threshold $h_{**}$, we implement a strategy due to Duminil-Copin and Manolescu in 2016, which establishes that two parameters are equal, one of which encapsulates the probability of obtaining an infinite connected component under free boundary conditions, while the other encapsulates the natural logarithm of the probability of obtaining a connected component from the origin to the box of length $n$ which is also taken under free boundary conditions. We quantify the probability of obtaining crossings in easy and hard directions, without imposing conditions that the graph is invariant with respect to reflections, in addition to making use of a differential inequality adapted for the GFF. The sharpness of the phase transition is characterized by the fact that below a certain height parameter of the GFF, the probability of obtaining an infinite cluster a.s. decays exponentially fast, while above the parameter, the probability of obtaining an infinite cluster occurs a.s. with good probability.

math.PR↗

arXiv2024

Eigenvectors of Toeplitz matrices from Fisher-Hartwig symbols with greater than, or equal to, one singularity

Asymptotically, we analytically derive the form of eigenvectors for two Fisher-Hartwig symbols besides those which were previously investigated in a $2016$ work due to Movassagh and Kadanoff, in which the authors characterized the eigenpairs of Toeplitz matrices generated by Fisher-Hartwig symbols with one singularity. To perform such computations, we extend their methods which consists of formulating an eigenvalue problem, obtained by a Wiener-Hopf method, from which a suitable winding number is defined for passing to Fourier space, and introducing a factorization dependent upon the winding number, for other Fisher-Hartwig symbols which have previously been defined in the literature. Following the computations required for the proof after obtaining the asymptotic approximation of the eigenvectors, we provide a table from which eigenvalues of one Fisher-Hartwig symbol for different complex valued functions $b$ can be inferred.

math-ph↗

arXiv2024

Eigenvalue attraction in open quantum systems, biophysical systems, and Parity-Time symmetric materials

We investigate eigenvalue attraction for open quantum systems, biophysical systems, and for Parity-Time symmetric materials. To determine whether an eigenvalue and its complex conjugate of a real matrix attract, we derive expressions for the second derivative of eigenvalues, which is dependent upon contributions from inertial forces, attraction between an eigenvalue and its complex conjugate, as well as the force of the remaining eigenvalues in the spectrum.

quant-ph↗