arXiv subjects

Hrachya Zakaryan

Publications and source records attributed to Hrachya Zakaryan.

3 recordsLinked to original sources

arXiv2025

Orbit classification and analysis of qutrit graph states under local complementation and local scaling

Graph states and their entanglement properties are pivotal for the development of quantum computing and technologies. For qubits, local complementation, a graphical rule that connects all the equivalent states under Local Clifford (LC) operations, was used for the complete characterization of all the LC equivalence classes up until 12 particles, assisting applications in quantum error correction and state preparation protocols optimization. This concept has been extended for qudits. In this work, we provide a complete characterization of the entanglement classes up until 7 qutrits, mapping each class into an orbit. The graph-theoretic properties of the orbits are studied, illuminating the rich structure they have. Clear connections between the connectivity of the orbits and the entanglement properties are observed. The correlations between the graph-theoretic properties and the Schmidt measure provide useful insights regarding qudit state preparation and fault-tolerance. This work is accompanied by a repository consisting of the code to extract the orbits and perform the presented statistical analysis. The strong interplay between quantum theory and graph theory is well-known and extensively studied for qubits. Our work provides practical tools and results to assist this endeavor for the qudit case.

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arXiv2025

$χ$-Colorable Graph States: Closed-Form Expressions and Quantum Orthogonal Arrays

Graph states are a fundamental class of multipartite entangled quantum states with wide-ranging applications in quantum information and computation. In this work, we develop a systematic framework for constructing and analyzing $χ$-colorable graph states, deriving explicit closed-form expressions for arbitrary $χ$. For two- and a broad family of three-colorable graph states, the representations obtained using only local operations, require a minimal number of terms in the Z-eigenbasis. We prove that every two-colorable graph state is local Clifford (LC) equivalent to a state expressible as a summation of rows of an orthogonal array (OA), providing a structured approach to writing highly entangled states. For graph states with $χ> 2$, we show that they are LC-equivalent to quantum orthogonal arrays (QOAs), establishing a direct combinatorial connection between multipartite entanglement and structured quantum states. Additionally, the derived closed-form expression has the minimal Schmidt measure for every two-colorable and a broad family of three-colorable graph states. Furthermore, the upper and lower bounds of the Schmidt measure are also discussed. Our results offer an efficient and practical method for systematically constructing graph states, optimizing their representation in quantum circuits, and identifying structured forms of multipartite entanglement. This framework also connects graph states to $k$-uniform and absolutely maximally entangled (AME) states, motivating further exploration of the structure of entangled states and their applications in quantum networks, quantum error correction, and measurement based quantum computing.

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arXiv2025

Non-symmetric GHZ states: weighted hypergraph and controlled-unitary graph representations

Non-symmetric GHZ states ($n$-GHZ$_α$), defined by unequal superpositions of $|00...0>$ and $|11...1>$, naturally emerge in experiments due to decoherence, control errors, and state preparation imperfections. Despite their relevance in quantum communication, relativistic quantum information, and quantum teleportation, these states lack a stabilizer formalism and a graph representation, hindering their theoretical and experimental analysis. We establish a graph-theoretic framework for non-symmetric GHZ states, proving their local unitary (LU) equivalence to two structures: fully connected weighted hypergraphs with controlled-phase interactions and star-shaped controlled-unitary (CU) graphs. While weighted hypergraphs generally lack stabilizer descriptions, we demonstrate that non-symmetric GHZ states can be efficiently stabilized using local operations and a single ancilla, independent of system size. We extend this framework to qudit systems, constructing LU-equivalent weighted qudit hypergraphs and showing that general non-symmetric qudit GHZ states can be described as star-shaped CU graphs. Our results provide a systematic approach to characterizing and stabilizing non-symmetric multipartite entanglement in both qubit and qudit systems, with implications for quantum error correction and networked quantum protocols.

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