arXiv subjects

Moein Naseri

Publications and source records attributed to Moein Naseri.

8 recordsLinked to original sources

arXiv2026

Polytopic Quantum Resource Theories: Geometry and Structures

Quantum resource theories provide a unifying framework to quantify, compare, and manipulate quantum resources under well-defined operational constraints. Here, we consider any resource theory where the set of free states can be expressed as a convex combination of a set of quantum states, referred to as extremal states and name them as polytopic quantum resource theories (PQRT). These include some of the most studied resource theories, such as coherence and magic. We formulate a novel tensorial representation of PQRTs that reveals the underlying geometry of these theories and provides insight into the origin of the resources. We further address a fundamental question in resource theories that when two theories should be regarded as physically equivalent, and to this purpose we introduce notions of homomorphism and isomorphism that compare both the structure of free states and the allowed transformations. Using the tools we develop, we find results revealing the geometrical and structural foundations of such theories. Interestingly, we find that all polytopic resource theories with a fixed number of pure extremal points are equivalent under a physical map, up to normalisation. Additionally, we introduce linearly independent polytopic resource theories (resource theory of ``basis-non-convexity''), where the set of extremal free states forms a basis of the quantum density operators. We further study the categorical structures of PQRTs beyond single systems.

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arXiv2025

Entanglement Generation via Hamiltonian Dynamics Having Limited Resources

We investigate the fundamental limits of entanglement generation under bipartite Hamiltonian dynamics when only finite physical resources-specifically, bounded energy variance-are available. Using the relative entropy of entanglement, we derive a closed analytical expression for the instantaneous entanglement generation rate for arbitrary pure states and Hamiltonians expressed in the Schmidt basis. We find that constraints based solely on the mean energy of the Hamiltonian are insufficient to bound the entanglement generation rate, whereas imposing a variance constraint ensures a finite and well-defined maximum. We fully characterize the Hamiltonians that achieve this optimal rate, establishing a direct relation between their imaginary components in the Schmidt basis and the structure of the optimal initial states. For systems without ancillas, we obtain a closed-form expression for the maximal rate in terms of the surprisal variance of the Schmidt coefficients and identify the family of optimal states and Hamiltonians. We further extend our analysis to scenarios where Alice and Bob may employ local ancillary systems: using a matrix-analytic framework and a refined description of the Hamiltonians allowed by the physical constraints, we derive an explicit optimization formula and characterize the attainable enhancement in entanglement generation.

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arXiv2025

Local Purity Distillation in Quantum Systems: Exploring the Complementarity Between Purity and Entanglement

Quantum thermodynamics and quantum entanglement represent two pivotal quantum resource theories with significant relevance in quantum information science. Despite their importance, the intricate relationship between these two theories is still not fully understood. Here, we delve into the interplay between entanglement and thermodynamics, particularly in the context of local cooling processes. We introduce and develop the framework of Gibbs-preserving local operations and classical communication. Within this framework, we explore strategies enabling remote parties to effectively cool their local systems to the ground state. Our analysis is centered on scenarios where only a single copy of a quantum state is accessible, with the ideal performance defined by the highest possible fidelity to the ground state achievable under these constraints. We focus on systems with fully degenerate local Hamiltonians, where local cooling aligns with the extraction of local purity. In this context, we establish a powerful link between the efficiency of local purity extraction and the degree of entanglement present in the system, a concept we define as purity-entanglement complementarity. Moreover, we demonstrate that in many pertinent scenarios, the optimal performance can be precisely determined through semidefinite programming techniques. Our findings open doors to various practical applications, including techniques for entanglement detection and estimation. We demonstrate this by evaluating the amount of entanglement for a class of bound entangled states.

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arXiv2024

Scalable noisy quantum circuits for biased-noise qubits

In this work, we consider biased-noise qubits affected only by bit-flip errors, which is motivated by existing systems of stabilized cat qubits. This property allows us to design a class of noisy Hadamard-tests involving entangling and certain non-Clifford gates, which can be conducted reliably with only a polynomial overhead in algorithm repetitions. On the flip side we also found classical algorithms able to efficiently simulate both the noisy and noiseless versions of our specific variants of Hadamard test. We propose to use these algorithms as a simple benchmark of the biasness of the noise at the scale of large circuits. The bias being checked on a full computational task, it makes our benchmark sensitive to crosstalk or time-correlated errors, which are usually invisible from individual gate tomography. For realistic noise models, phase-flip will not be negligible, but in the Pauli-Twirling approximation, we show that our benchmark could check the correctness of circuits containing up to $10^6$ gates, several orders of magnitudes larger than circuits not exploiting a noise-bias. Our benchmark is applicable for an arbitrary noise-bias, beyond Pauli models.

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arXiv2024

Coherence generation with Hamiltonians

We explore methods to generate quantum coherence through unitary evolutions, by introducing and studying the coherence generating capacity of Hamiltonians. This quantity is defined as the maximum derivative of coherence that can be achieved by a Hamiltonian. By adopting the relative entropy of coherence as our figure of merit, we evaluate the maximal coherence generating capacity with the constraint of a bounded Hilbert-Schmidt norm for the Hamiltonian. Our investigation yields closed-form expressions for both Hamiltonians and quantum states that induce the maximal derivative of coherence under these conditions. Specifically, for qubit systems, we solve this problem comprehensively for any given Hamiltonian, identifying the quantum states that lead to the largest coherence derivative induced by the Hamiltonian. Our investigation enables a precise identification of conditions under which quantum coherence is optimally enhanced, offering valuable insights for the manipulation and control of quantum coherence in quantum systems.

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arXiv2022

Quantum Speed Limit for Change of Basis

Quantum speed limits provide ultimate bounds on the time required to transform one quantum state into another. Here, we extend the notion of quantum speed limits to collections of quantum states, investigating the time for converting a basis of states into an unbiased one. We provide tight bounds for systems of dimension smaller than 5, and general bounds for multi-qubit systems and Hilbert space dimension $d$. For two-qubit systems, we show that the fastest transformation implements two Hadamards and a swap of the qubits simultaneously. We further prove that for qutrit systems the evolution time depends on the particular type of the unbiased basis. We also investigate speed limits for coherence generation, providing the minimal time to establish a certain amount of coherence with a unitary evolution.

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arXiv2022

Entanglement and coherence in Bernstein-Vazirani algorithm

Quantum algorithms allow to outperform their classical counterparts in various tasks, most prominent example being Shor's algorithm for efficient prime factorization on a quantum computer. It is clear that one of the reasons for the speedup is the superposition principle of quantum mechanics, which allows a quantum processor to be in a superposition of different states at the same time. While such superposition can lead to entanglement across different qubits of the processors, there also exists quantum algorithms which outperform classical ones using superpositions of individual qubits without entangling them. As an example, the Bernstein-Vazirani algorithm allows one to determine a bit string encoded into an oracle. While the classical version of the algorithm requires multiple calls of the oracle to learn the bit string, a single query of the oracle is enough in the quantum case. In this Letter, we analyze in detail the quantum resources in the Bernstein-Vazirani algorithm. For this, we introduce and study its probabilistic version, where the goal is to guess the bit string after a single call of the oracle. We show that in the absence of entanglement, the performance of the algorithm is directly related to the amount of quantum coherence in the initial state. We further demonstrate that a large amount of entanglement in the initial state prevents the algorithm from achieving optimal performance. We also apply our methods to quantum computation with mixed states, proving that pseudopure states achieve optimal performance for a given purity in the Bernstein-Vazirani algorithm. We further investigate quantum resources in the one clean qubit model, showing that the model can exhibit speedup over any known classical algorithm even with arbitrary little amount of multipartite entanglement, general quantum correlations, and coherence.

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arXiv2020

Coherence Based Characterization of Macroscopic Quantumness

One of the most elusive problems in quantum mechanics is the transition between classical and quantum physics. This problem can be traced back to the Schrödinger's cat. A key element that lies at the center of this problem is the lack of a clear understanding and characterization of macroscopic quantum states. Our understanding of Macroscopic Quantumness relies on states such as the Greenberger-Horne-Zeilinger(GHZ) or the NOON state. Here we take a first principle approach to this problem. We start from coherence as the key quantity that captures the notion of quantumness and demand the quantumness to be collective and macroscopic. To this end, we introduce macroscopic coherence which is the coherence between macroscopically distinct quantum states. We construct a measure that quantifies how global and collective the coherence of the state is. Our work also provides a first-principle way to derive well-established states like the GHZ and the NOON state as the states that maximize our measure. This new approach paves the way towards a better understanding of the Quantum-to-Classical transition.

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