arXiv subjects

Hyunchul Nha

Publications and source records attributed to Hyunchul Nha.

At least 19 recordsLinked to original sources

arXiv2026

Maximal coherence of quantum measurement and the resource theory of sharpness

A resource theory of quantum measurement can be addressed in terms of quantum coherence and measurement sharpness, respectively. The former analyzes the off-diagonal structure of POVM elements in a predetermined basis while the latter analyzes the deviation from trivial, state-independent, measurements. We establish a direct connection between the two resource theories by identifying measurement sharpness as the maximal coherence that is achievable under all possible unitary changes of the reference basis. For a broad class of POVMs whose elements share a common eigenbasis, we show that the maximal distance-based coherence of measurement coincides exactly with the corresponding distance-based sharpness monotone. We further extend this equivalence, with element-additive distances, to POVMs whose elements admit a common mutually unbiased basis structure. These results provide a measurement-theoretic analogue of the maximal-coherence \& purity correspondence for quantum states. We also show that the maximal coherence of measurement is faithful with respect to trivial measurements and is monotonic under fuzzifying operations for dichotomic measurements, as well as under mixed-unitary and unitarily covariant preprocessing channels. Finally, we illustrate the operational meaning and limitations of the equivalence through qubit POVMs, single-photon phase sensing, and noisy photon-number resolving detection. In particular, the maximal Fisher information in a Mach-Zehnder interferometer is shown to be determined by the squared maximal coherence of the measurement, while in an imperfect photon-number resolving detector the maximal coherence behaves as a proper sharpness monotone, unlike conventional PVM-based unsharpness measures.

quant-ph↗

arXiv2026

Entanglement Structure Across $\mathbb{Z}_n$ Phase Transitions in 1D Rydberg Atom Arrays

Multipartite quantum entanglement plays a crucial role in the emergence of different quantum phases and their transitions in quantum many-body systems. It is of general interest to know what sort of analysis on quantum entanglement can bring us a profound insight to understand the rich dynamics of quantum many-body systems. In this work we study the characteristics of quantum entanglement in relation to $\mathbb{Z}_n$-ordered phases emerging under a varied strength of 1-dim Rydberg interaction. We propose an approach based on the structure of pair-wise entanglement across the Rydberg chain using two-qubit concurrence as an entanglement measure. We define an entanglement-structure factor via Fourier analysis of total concurrence at each site and address $\mathbb{Z}_n$ phase transitions in comparison with the conventional order-parameter based on local density, i.e. magnetization. We also discuss how the required two-qubit concurrence can be measured in analog Rydberg atom arrays using site-selective erasure and parametrized laser pulses. Our investigation suggests that an entanglement-structure-based approach can provide a powerful tool in analyzing symmetry-breaking in quantum phase transitions.

quant-ph↗

arXiv2025

Quantum entanglement and extractable work for Gaussian states

The study of quantum thermodynamics aims to elucidate the role played by quantum principles in the emergent features of quantum thermodynamic processes. Specifically, it is of fundamental importance to understand how quantum correlation among different parties enables thermodynamic features distinguishable from those arising in classical thermodynamics. In this work, we investigate the relation between extractable work and quantum correlations for two-mode Gaussian states. We examine the change in local energy occurring at one party due to a Gaussian measurement performed on the other in relation to the quantum correlations of two-mode states classified as separable, entangled, and steerable states. Our analysis reveals a clear quantitative difference in the extractable work, depending on the class of states to which the two-mode state belongs.

quant-ph↗

arXiv2024

Observable criterion for collective entanglement in Boson-lattice system

An optical lattice with cold trapped atoms represents a quantum system of fundamental importance as it enables the study of quantum many-body system in a controllable way. It is thus necessary to develop theoretical and experimental tools to explore quantum correlation in such systems to advance our understanding of many-body physics. While previous works have identified some profound aspects of quantum entanglement using e.g. entanglement entropy, there exists a critical demand to have an experimentally accessible tool to investigate many-body quantum entanglement in a broad context. We present an entanglement criterion characterizing collective entanglement in Boson lattice systems and enabling experimental observation readily. On applying our approach to the extended Bose-Hubbard model, we show that our criterion witnesses phase transitions such as Mott insulator--superfluid and Mott insulator--charge density wave transitions. Remarkably, it also makes it possible to detect multipartite entanglement among boson lattice sites in a rigorous sense. Our criterion can be experimentally tested via Raman scattering or time-of-flight methods, which are within the reach of current technology.

quant-ph↗

arXiv2024

Non-Gaussian entanglement criteria for atomic homodyne detection

Homodyne measurement is a crucial tool widely used to address continuous variables for bosonic quantum systems. While an ideal homodyne detection provides a powerful analysis, e.g. to effectively measure quadrature amplitudes of light in quantum optics, it relies on the use of a strong reference field, the so-called local oscillator typically in a coherent state. Such a strong coherent local oscillator may not be readily available particularly for a massive quantum system like Bose-Einstein condensate (BEC), posing a substantial challenge in dealing with continuous variables appropriately. It is necessary to establish a practical framework that includes the effects of non-ideal local oscillators for a rigorous assessment of various quantum tests and applications. We here develop entanglement criteria beyond Gaussian regime applicable for this realistic homodyne measurement that do not require assumptions on the state of local oscillators. We discuss the working conditions of homodyne detection to effectively detect non-Gaussian quantum entanglement under various states of local oscillators.

quant-ph↗

arXiv2024

Fundamental limits on concentrating and preserving tensorized quantum resources

Quantum technology offers great advantages in many applications by exploiting quantum resources like nonclassicality, coherence, and entanglement. In practice, an environmental noise unavoidably affects a quantum system and it is thus an important issue to protect quantum resources from noise. In this work, we investigate the manipulation of quantum resources possessing the so-called tensorization property and identify the fundamental limitations on concentrating and preserving those quantum resources. We show that if a resource measure satisfies the tensorization property as well as the monotonicity, it is impossible to concentrate multiple noisy copies into a single better resource by free operations. Furthermore, we show that quantum resources cannot be better protected from channel noises by employing correlated input states on joint channels if the channel output resource exhibits the tensorization property. We address several practical resource measures where our theorems apply and manifest their physical meanings in quantum resource manipulation.

quant-ph↗

arXiv2023

$T$-depth-optimized Quantum Search with Quantum Data-access Machine

Quantum search algorithms offer a remarkable advantage of quadratic reduction in query complexity using quantum superposition principle. However, how an actual architecture may access and handle the database in a quantum superposed state has been largely unexplored so far; the quantum state of data was simply assumed to be prepared and accessed by a black-box operation -- so-called oracle, even though this process, if not appropriately designed, may adversely diminish the quantum query advantage. Here, we introduce an efficient quantum data-access process, dubbed as quantum data-access machine (QDAM), and present a general architecture for quantum search algorithm. We analyze the runtime of our algorithm in view of the fault-tolerant quantum computation (FTQC) consisting of logical qubits within an effective quantum error correction code. Specifically, we introduce a measure involving two computational complexities, i.e. quantum query and $T$-depth complexities, which can be critical to assess performance since the logical non-Clifford gates, such as the $T$ (i.e., $π/8$ rotation) gate, are known to be costliest to implement in FTQC. Our analysis shows that for $N$ searching data, a QDAM model exhibiting a logarithmic, i.e., $O(\log{N})$, growth of the $T$-depth complexity can be constructed. Further analysis reveals that our QDAM-embedded quantum search requires $O(\sqrt{N} \times \log{N})$ runtime cost. Our study thus demonstrates that the quantum data search algorithm can truly speed up over classical approaches with the logarithmic $T$-depth QDAM as a key component.

quant-ph↗

arXiv2021

Verifying single-mode nonclassicality beyond negativity in phase space

While negativity in phase space is a well-known signature of nonclassicality, a wide variety of nonclassical states require their characterization beyond negativity. We establish a framework of nonclassicality in phase space that addresses nonclassical states comprehensively with a direct experimental evidence. This includes the negativity of phase-space distribution as a special case and further analyzes quantum states with positive distributions effectively. We prove that it detects all nonclassical Gaussian states and all non-Gaussian states of arbitrary dimension remarkably by examining three phase-space points only. Our formalism also provides an experimentally accessible lower bound for a nonclassicality measure based on trace distance. Importantly, this foundational approach can be further adapted to constitute practical tests in two directions looking into particle and wave nature of bosonic systems, via an array of nonideal on-off detectors and coarse-grained homodyne measurement, respectively. All these tests are practically powerful in characterizing nonclasssical states reliably against noise, making a versatile tool for a broad range of quantum systems in quantum technologies.

quant-ph↗

arXiv2021

Quantifying non-Gaussianity of a quantum state by the negative entropy of quadrature distributions

We propose a non-Gaussianity measure of a multimode quantum state based on the negentropy of quadrature distributions. Our measure satisfies desirable properties as a non-Gaussianity measure, i.e., faithfulness, invariance under Gaussian unitary operations, and monotonicity under Gaussian channels. Furthermore, we find a quantitative relation between our measure and the previously proposed non-Gaussianity measures defined via quantum relative entropy and the quantum Hilbert-Schmidt distance. This allows us to estimate the non-Gaussianity measures readily by homodyne detection, which would otherwise require a full quantum-state tomography.

quant-ph↗

arXiv2021

Quantum teleportation is a reversal of quantum measurement

We introduce a generalized concept of quantum teleportation in the framework of quantum measurement and reversing operation. Our framework makes it possible to find an optimal protocol for quantum teleportation enabling a faithful transfer of unknown quantum states with maximum success probability up to the fundamental limit of the no-cloning theorem. Moreover, an optimized protocol in this generalized approach allows us to overcome noise in quantum channel beyond the reach of existing teleportation protocols without requiring extra qubit resources. Our proposed framework is applicable to multipartite quantum communications and primitive functionalities in scalable quantum architectures.

quant-ph↗

arXiv2021

Complete Information Balance in Quantum Measurement

Quantum measurement is a basic tool to manifest intrinsic quantum effects from fundamental tests to quantum information applications. While a measurement is typically performed to gain information on a quantum state, its role in quantum technology is indeed manifold. For instance, quantum measurement is a crucial process element in measurement-based quantum computation. It is also used to detect and correct errors thereby protecting quantum information in error-correcting frameworks. It is therefore important to fully characterize the roles of quantum measurement encompassing information gain, state disturbance and reversibility, together with their fundamental relations. Numerous efforts have been made to obtain the trade-off between information gain and state disturbance, which becomes a practical basis for secure information processing. However, a complete information balance is necessary to include the reversibility of quantum measurement, which constitutes an integral part of practical quantum information processing. We here establish all pairs of trade-off relations involving information gain, disturbance, and reversibility, and crucially the one among all of them together. By doing so, we show that the reversibility plays a vital role in completing the information balance. Remarkably, our result can be interpreted as an information-conservation law of quantum measurement in a nontrivial form. We completely identify the conditions for optimal measurements that satisfy the conservation for each tradeoff relation with their potential applications. Our work can provide a useful guideline for designing a quantum measurement in accordance with the aims of quantum information processors.

quant-ph↗

arXiv2020

Quantifying coherence of quantum measurements

In this work we investigate how to quantify the coherence of quantum measurements. First, we establish a resource theoretical framework to address the coherence of measurement and show that any statistical distance can be adopted to define a coherence monotone of measurement. For instance, the relative entropy fulfills all the required properties as a proper monotone. We specifically introduce a coherence monotone of measurement in terms of off-diagonal elements of Positive-Operator-Valued Measure (POVM) components. This quantification provides a lower bound on the robustness of measurement-coherence that has an operational meaning as the maximal advantage over all incoherent measurements in state discrimination tasks. Finally, we propose an experimental scheme to assess our quantification of measurement-coherence and demonstrate it by performing an experiment using a single qubit on IBM Q processor.

quant-ph↗

arXiv2020

Quantum Photovoltaic Cells Driven by Photon Pulses

We investigate the quantum thermodynamics of two quantum systems, a two-level system and a four-level quantum photocell, each driven by photon pulses as a quantum heat engine. We set these systems to be in thermal contact only with a cold reservoir while the heat (energy) source, conventionally given from a hot thermal reservoir, is supplied by a sequence of photon pulses. The dynamics of each system is governed by a coherent interaction due to photon pulses in terms of the Jaynes-Cummings Hamiltonian together with the system-bath interaction described by the Lindblad master equation. We calculate the thermodynamic quantities for the two-level system and the quantum photocell including the change in system energy, power delivered by photon pulses, power output to an external load, heat dissipated to a cold bath, and entropy production. We thereby demonstrate how a quantum photocell in the cold bath can operate as a continuum quantum heat engine with the sequence of photon pulses continuously applied. We specifically introduce the power efficiency of the quantum photocell in terms of the ratio of output power delivered to an external load with current and voltage to the input power delivered by the photon pulse. Our study indicates a possibility that a quantum system driven by external fields can act as an efficient quantum heat engine under non-equilibrium thermodynamics.

quant-ph↗

arXiv2020

Information Fluctuation Theorem for an Open Quantum Bipartite System

We study an arbitrary non-equilibrium dynamics of a quantum bipartite system coupled to a reservoir. For its characterization, we present a fluctuation theorem (FT) that explicitly addresses the quantum correlation of subsystems during the thermodynamic evolution. To our aim, we designate the local and the global states altogether in the time-forward and the time-reversed transition probabilities. In view of the two-point measurement scheme, only the global states are subject to measurements whereas the local states are used only as an augmented information on the composite system. We specifically derive a FT in such a form that relates the entropy production of local systems in the time-forward transition to the change of quantum correlation in the time-reversed transition. This also leads to a useful thermodynamic inequality and we illustrate its advantage by an example of an isothermal process on Werner states.

quant-ph↗

arXiv2020

Entropy, Free Energy, and Work of Restricted Boltzmann Machines

A restricted Boltzmann machine is a generative probabilistic graphic network. A probability of finding the network in a certain configuration is given by the Boltzmann distribution. Given training data, its learning is done by optimizing parameters of the energy function of the network. In this paper, we analyze the training process of the restricted Boltzmann machine in the context of statistical physics. As an illustration, for small size Bar-and-Stripe patterns, we calculate thermodynamic quantities such as entropy, free energy, and internal energy as a function of training epoch. We demonstrate the growth of the correlation between the visible and hidden layers via the subadditivity of entropies as the training proceeds. Using the Monte-Carlo simulation of trajectories of the visible and hidden vectors in configuration space, we also calculate the distribution of the work done on the restricted Boltzmann machine by switching the parameters of the energy function. We discuss the Jarzynski equality which connects the path average of the exponential function of the work and the difference in free energies before and after training.

cond-mat.dis-nn↗

arXiv2019

Faithful measure of Quantum non-Gaussianity via quantum relative entropy

We introduce a measure of quantum non-Gaussianity (QNG) for those quantum states not accessible by a mixture of Gaussian states in terms of quantum relative entropy. Specifically, we employ a convex-roof extension using all possible mixed-state decompositions beyond the usual pure-state decompositions. We prove that this approach brings a QNG measure fulfilling the properties desired as a proper monotone under Gaussian channels and conditional Gaussian operations. As an illustration, we explicitly calculate QNG for the noisy single-photon states and demonstrate that QNG coincides with non-Gaussianity of the state itself when the single-photon fraction is sufficiently large.

quant-ph↗

arXiv2019

Quantum non-Gaussianity and secure quantum communication

No-cloning theorem, a profound fundamental principle of quantum mechanics, also provides a crucial practical basis for secure quantum communication. The security of communication can be ultimately guaranteed if the output fidelity via communication channel is above the no-cloning bound (NCB). In quantum communications using continuous-variable (CV) systems, Gaussian states, more specifically, coherent states have been widely studied as inputs, but less is known for non-Gaussian states. We aim at exploring quantum communication covering CV states comprehensively with distinct sets of unknown states properly defined. Our main results here are (i) to establish the NCB for a broad class of quantum non-Gaussian states including Fock states, their superpositions and Schrodinger-cat states and (ii) to examine the relation between NCB and quantum non-Gaussianity (QNG). We find that NCB typically decreases with QNG. Remarkably, this does not mean that quantum non-Gaussian states are less demanding for secure communication. By extending our study to mixed-state inputs, we demonstrate that QNG specifically in terms of Wigner negativity requires more resources to achieve output fidelity above NCB in CV teleportation. The more non-Gaussian, the harder to achieve secure communication, which can have crucial implications for CV quantum communications.

quant-ph↗

arXiv2019

Entropic Uncertainty Relations via Direct-Sum Majorization Relation for Generalized Measurements

We derive an entropic uncertainty relation for generalized positive-operator-valued measure (POVM) measurements via a direct-sum majorization relation using Schur concavity of entropic quantities in a finite-dimensional Hilbert space. Our approach provides a significant improvement of the uncertainty bound compared with previous majorization-based approaches [S. Friendland, V. Gheorghiu and G. Gour, Phys. Rev. Lett. 111, 230401 (2013); A. E. Rastegin and K. Życzkowski, J. Phys. A, 49, 355301 (2016)], particularly by extending the direct-sum majorization relation first introduced in [Ł. Rudnicki, Z. Puchała and K. Życzkowski, Phys. Rev. A 89, 052115 (2014)]. We illustrate the usefulness of our uncertainty relations by considering a pair of qubit observables in a two-dimensional system and randomly chosen unsharp observables in a three-dimensional system. We also demonstrate that our bound tends to be stronger than the generalized Maassen--Uffink bound with an increase in the unsharpness effect. Furthermore, we extend our approach to the case of multiple POVM measurements, thus making it possible to establish entropic uncertainty relations involving more than two observables.

quant-ph↗