arXiv subjects

Jun-Yi Wu

Publications and source records attributed to Jun-Yi Wu.

At least 19 recordsLinked to original sources

arXiv2026

Reduced State Stabilizer R\'enyi Entropy as a Probe of Quantum Phase Transitions in Frustrated J_1-J_2 Spin Models

We investigate whether the second-order purity-corrected stabilizer R\'enyi entropy (SRE) of reduced two-qubit density matrices can serve as a reliable local indicator of quantum phase transitions (QPTs) in frustrated quantum spin systems. We consider the one-dimensional isotropic $J_1-J_2$ Heisenberg model, the one-dimensional XXZ $J_1-J_2$ model, and the two-dimensional $J_1-J_2$ Heisenberg model on a $4\times4$ square lattice. Unlike several previously studied quantum information measures, which fail to detect QPTs in the ground state of these frustrated systems, the reduced ground-state purity-corrected SRE successfully identifies most transitions. For the remaining cases, we consider a low temperature subjacent state, modeled as a statistical mixture of the ground and first excited states with a Maxwell--Boltzmann-type occupation probability. For the 1D isotropic model, the subjacent-state SRE shows a discontinuity at the critical point, yielding $\alpha_c(\infty)=0.24116$, in excellent agreement with established values; the ground-state SRE shows a point of inflection, yielding $\alpha_c(\infty)=0.2681$. For the 1D XXZ model, the subjacent-state SRE reproduces the full anisotropy dependent phase diagram, while the ground-state SRE captures transitions only at low anisotropy. For the 2D model, the subjacent-state SRE detects two transitions, at $\alpha_c(4\times4)=0.40781$ and $0.6208$, while the ground-state SRE identifies the second at $0.6230$. Compared with conventional two-qubit entanglement, purity-corrected SRE shows a clear advantage in revealing otherwise-invisible phase transitions, establishing it as a robust, efficient, local probe of frustrated quantum criticality.

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arXiv2026

Reduced-State Stabilizer Rényi Entropy as a Probe of Quantum Criticality in the Transverse ANNNI Model and the Quantum Compass Model

We investigate the effectiveness of the stabilizer Rényi entropy (SRE), a quantifier associated with non-stabilizer resources (quantum magic), as an indicator of quantum phase transitions. Specifically, we analyze the behavior of the purity-corrected SRE of reduced density matrices in the ground states of two one-dimensional spin models: the transverse axial next-nearest-neighbor Ising (TANNNI) model and the quantum compass model (QCM). The ground state of the TANNNI model is obtained using exact diagonalization techniques, while the QCM is analyzed using the Jordan--Wigner (JW) transformation followed by Bogoliubov diagonalization of the resulting quadratic fermionic Hamiltonian. For the TANNNI model, the purity-corrected SRE successfully detects the antiphase--floating phase transition in the high-frustration regime, while in the low-frustration regime the raw (purity-uncorrected) SRE reproduces the known ferromagnetic--paramagnetic phase boundaries more accurately. For the QCM, the purity-corrected SRE exhibits a clear signature near the isotropic point $J_x/J_z=1$, where the system undergoes a first-order quantum phase transition. Our results establish SRE of reduced states as a complementary probe of quantum criticality and provide further insight into the role of non-stabilizer resources in many-body quantum phase transitions.

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arXiv2026

Entanglement-assisted circuit knitting: Distributed quantum computing using limited entanglement resources

Distributed quantum computing (DQC) provides a promising route toward scalable quantum computation, where entanglement-assisted LOCC and circuit knitting represent two complementary approaches. The former deterministically realizes nonlocal operations but demands extensive entanglement resources, whereas the latter requires no entanglement yet suffers from exponential sampling overhead. Here, we propose a hybrid framework called entanglement-assisted circuit knitting that integrates these two paradigms by performing circuit knitting assisted with a limited amount of entanglement. We establish a general theoretical framework for entanglement-assisted circuit knitting. Optimal sampling overhead is achieved for Choi-stretchable unitaries with general entanglement resources, while for general unitaries we derive both lower and upper bounds for one-Bell-pair-assisted circuit knitting. We further extend the framework to the black-box setting, which can be treated as a class of quantum combs. This extension releases the need for explicit knowledge of the global unitary of a whole quantum circuit, enables a more flexible embedding structure, and broadens its applicability. Within this framework, we develop constructive protocols utilizing different resources, including entanglement, local operations, and classical communication. We derive the optimal mixed configuration among these protocols and provide an algorithm for its determination. Under dynamically probabilistic entanglement distribution, we reveal a trade-off between sampling overhead and entanglement cost in entanglement-assisted circuit knitting. This hybrid approach can thus be viewed as a form of hybrid classical-quantum computation, balancing sampling and entanglement efficiency, and enabling more resource-efficient implementations of distributed quantum computing.

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arXiv2025

Characterizing Space-Constrained Implementability of Quantum Instruments via Signaling Conditions

Scaling up the number of qubits available on quantum processors remains technically demanding even in the long term; it is therefore crucial to clarify the number of qubits required to implement a given quantum operation. For the most general class of quantum operations, known as quantum instruments, the qubit requirements are not well understood, especially when mid-circuit measurements and delayed input preparation are permitted. In this work, we characterize lower and upper bounds on the number of qubits required to implement a given quantum instrument in terms of the causal structure of the instrument. We further apply our results to entanglement distillation protocols based on stabilizer codes and show that, in these cases, the lower and upper bounds coincide, so the optimal qubit requirement is determined. In particular, we compute that the optimal number of qubits is 3 for the $[[9,1,3]]$-code-based protocol and 4 for the $[[5,1,3]]$-code-based protocol.

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arXiv2025

Two-detector reconstruction of multiphoton states in linear optical networks

We propose a method for partial state reconstruction of multiphoton states in multimode ($N$-photon $M$-mode) linear optical networks (LONs) employing only two bucket photon-number-resolving (PNR) detectors. The reconstructed Heisenberg-Weyl-reduced density matrix captures quantum coherence and symmetry with respect to Heisenberg-Weyl operators. Employing deterministic quantum computing with one qubit (DQC1) circuits, we reduce the detector requirement from $M$ to $2$, while the requirement on measurement configurations is retained $2M^{3}-2M$. To ensure physicality, maximum likelihood estimation (MLE) is incorporated into the DQC1 reconstruction process, with numerical simulations demonstrating the efficiency of our approach and its robustness against interferometer noises. This method offers a resource-efficient solution for state characterization in large-scale LONs to advance photonic quantum technologies.

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arXiv2025

Linear-optical approach to encoding qubits into harmonic-oscillator modes via quantum walks

We propose a linear-optical scheme that allows encoding grid-state quantum bits (qubits) into a bosonic mode using cat state and post-selection as sources of non-Gaussianity in the encoding. As a linear-optical realization of the quantum-walk encoding scheme in [Lin {\em et al.}, Quantum Info. Processing {\bf 19}, 272 (2020)], we employ the cat state as a quantum coin that enables encoding approximate Gottesman-Kitaev-Preskill (GKP) qubits through quantum walk of a squeezed vacuum state in phase space. We show that the conditional phase-space displacement necessary for the encoding can be realized through a Mach-Zehnder interferometer (MZI) assisted with ancillary cat-state input under appropriate parameter regimes. By analyzing the fidelity of the MZI-based displacement operation, we identify the region of parameter space over which the proposed linear-optical scheme can generate grid-state qubits with high fidelity. With adequate parameter setting, our proposal should be accessible to current optical and superconducting-circuit platforms in preparing grid-state qubits for bosonic modes in the, respectively, optical and microwave domains.

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arXiv2024

Scalability enhancement of quantum computing under limited connectivity through distributed quantum computing

We employ quantum-volume random-circuit sampling to benchmark the two-QPU entanglement-assisted distributed quantum computing (DQC) and compare it with single-QPU quantum computing. We first specify a single-qubit depolarizing noise model in the random circuit. Based on this error model, we show the one-to-one correspondence of three figures of merits, namely average gate fidelity, heavy output probability, and linear cross-entropy. We derive an analytical approximation of the average gate fidelity under the specified noise model, which is shown to align with numerical simulations. The approximation is calculated based on a noise propagation matrix obtained from the extended connectivity graph of a DQC device. In numerical simulation, we unveil the scalability enhancement in DQC for the QPUs with limited connectivity. Furthermore, we provide a simple formula to estimate the average gate fidelity, which also provides us with a heuristic method to evaluate the scalability enhancement in DQC, and a guide to optimize the structure of a DQC configuration.

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arXiv2024

Fidelity and Entanglement of Random Bipartite Pure States: Insights and Applications

We investigate the fidelity of Haar random bipartite pure states from a fixed reference quantum state and their bipartite entanglement. By plotting the fidelity and entanglement on perpendicular axes, we observe that the resulting plots exhibit non-uniform distributions. The distribution depends on the entanglement of the fixed reference quantum state used to quantify the fidelity of the random pure bipartite states. We find that the average fidelity of typical random pure bipartite qubits within a narrow entanglement range with respect to a randomly chosen fixed bipartite qubit is $\frac{1}{4}$. Extending our study to higher dimensional bipartite qudits, we find that the average fidelity of typical random pure bipartite qudits with respect to a randomly chosen fixed bipartite qudit remains constant within a narrow entanglement range. The values of these constants are $\frac{1}{d^2}$, with d being the dimension of the local Hilbert space of the bipartite qudit system, suggesting a consistent relationship between entanglement and fidelity across different dimensions. The probability distribution functions of fidelity with respect to a product state are analytically studied and used as a reference for the benchmarking of distributed quantum computing devices.

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arXiv2023

Entanglement-efficient bipartite-distributed quantum computing

In noisy intermediate-scale quantum computing, the limited scalability of a single quantum processing unit (QPU) can be extended through distributed quantum computing (DQC), in which one can implement global operations over two QPUs by entanglement-assisted local operations and classical communication. To facilitate this type of DQC in experiments, we need an entanglement-efficient protocol. To this end, we extend the protocol in [Eisert et. al., PRA, 62:052317(2000)] implementing each nonlocal controlled-unitary gate locally with one maximally entangled pair to a packing protocol, which can pack multiple nonlocal controlled-unitary gates locally using one maximally entangled pair. In particular, two types of packing processes are introduced as the building blocks, namely the distributing processes and embedding processes. Each distributing process distributes corresponding gates locally with one entangled pair. The efficiency of entanglement is then enhanced by embedding processes, which merge two non-sequential distributing processes and hence save the entanglement cost. We show that the structure of distributability and embeddability of a quantum circuit can be fully represented by the corresponding packing graphs and conflict graphs. Based on these graphs, we derive heuristic algorithms for finding an entanglement-efficient packing of distributing processes for a given quantum circuit to be implemented by two parties. These algorithms can determine the required number of local auxiliary qubits in the DQC. We apply these algorithms for bipartite DQC of unitary coupled-cluster circuits and find a significant reduction of entanglement cost through embeddings. This method can determine a constructive upper bound on the entanglement cost for the DQC of quantum circuits.

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arXiv2023

Distributing circuits over heterogeneous, modular quantum computing network architectures

We consider a heterogeneous network of quantum computing modules, sparsely connected via Bell states. Operations across these connections constitute a computational bottleneck and they are likely to add more noise to the computation than operations performed within a module. We introduce several techniques for transforming a given quantum circuit into one implementable on a network of the aforementioned type, minimising the number of Bell states required to do so. We extend previous works on circuit distribution over fully connected networks to the case of heterogeneous networks. On the one hand, we extend the hypergraph approach of [Andres-Martinez & Heunen. 2019] to arbitrary network topologies. We additionally make use of Steiner trees to find efficient realisations of the entanglement sharing within the network, reusing already established connections as often as possible. On the other hand, we extend the embedding techniques of [Wu, et al. 2022] to networks with more than two modules. Furthermore, we discuss how these two seemingly incompatible approaches can be made to cooperate. Our proposal is implemented and benchmarked; the results confirming that, when orchestrated, the two approaches complement each other's weaknesses.

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arXiv2023

Quantum correlations on the no-signaling boundary: self-testing and more

In device-independent quantum information, correlations between local measurement outcomes observed by spatially separated parties in a Bell test play a fundamental role. Even though it is long-known that the set of correlations allowed in quantum theory lies strictly between the Bell-local set and the no-signaling set, many questions concerning the geometry of the quantum set remain unanswered. Here, we revisit the problem of when the boundary of the quantum set coincides with the no-signaling set in the simplest Bell scenario. In particular, for each Class of these common boundaries containing $k$ zero probabilities, we provide a $(5-k)$-parameter family of quantum strategies realizing these (extremal) correlations. We further prove that self-testing is possible in all nontrivial Classes beyond the known examples of Hardy-type correlations, and provide numerical evidence supporting the robustness of these self-testing results. Candidates of one-parameter families of self-testing correlations from some of these Classes are identified. As a byproduct of our investigation, if the qubit strategies leading to an extremal nonlocal correlation are local-unitarily equivalent, a self-testing statement provably follows. Interestingly, all these self-testing correlations found on the no-signaling boundary are provably non-exposed. An analogous characterization for the set $\mathcal{M}$ of quantum correlations arising from finite-dimensional maximally entangled states is also provided. En route to establishing this last result, we show that all correlations of $\mathcal{M}$ in the simplest Bell scenario are attainable as convex combinations of those achievable using a Bell pair and projective measurements. In turn, we obtain the maximal Clauser-Horne-Shimony-Holt Bell inequality violation by any maximally entangled two-qudit state and a no-go theorem regarding the self-testing of such states.

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arXiv2022

Generation and evaluation of multipartite entanglement with multi-rail encoding in linear optics networks

A linear optics network is a multimode interferometer system, where indistinguishable photon inputs can create nonclassical interference that can not be simulated with classical computers. Such nonclassical interference implies the existence of entanglement among its subsystems, if we divide its modes into different parties. Entanglement in such systems is naturally encoded in multi-rail (multi-mode) quantum registers. For bipartite entanglement, a generation and detection scheme with multi-rail encoding has been theoretically proposed [NJP 19(10):103032, 2017] and experimentally realized [Optica, 7(11):1517, 2020]. In this paper, we will take a step further to establish a theory for the detection of multi-rail-encoded discrete-variable genuine multipartite entanglement (GME) in fixed local-photon-number subspaces of linear optics networks. We also propose a scheme for GME generation with both discrete-variable (single photons) and continuous-variable (squeezed states) light sources. This scheme allows us to reveal the discrete-variable GME in continuous-variable systems. The effect of photon losses is also numerically analyzed for the generation scheme based on continuous-variable inputs.

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arXiv2020

Complementary properties of multiphoton quantum states in linear optics networks

We have developed a theory for accessing quantum coherences in mutually unbiased bases associated with generalized Pauli operators in multiphoton multimode linear optics networks (LONs). We show a way to construct complementary Pauli measurements in multiphoton LONs and establish a theory for evaluation of their photonic measurement statistics without dealing with the computational complexity of Boson samplings. This theory extends characterization of complementary properties in single-photon LONs to multiphoton LONs employing convex-roof extension. It allows us to detect quantum properties such as entanglement using complementary Pauli measurements, which reveals the physical significance of entanglement between modes in bipartite multiphoton LONs.

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arXiv2020

Adaptive State Fidelity Estimation for Higher Dimensional Bipartite Entanglement

An adaptive method for quantum state fidelity estimation in bipartite higher dimensional systems is established. This method employs state verifier operators which are constructed by local POVM operators and adapted to the measurement statistics in the computational basis. Employing this method, the state verifier operators that stabilize Bell-type entangled states are constructed explicitly. Together with an error operator in the computational basis, one can estimate the lower and upper bounds on the state fidelity for Bell-type entangled states in few measurement configurations. These bounds can be tighter than the fidelity bounds derived in [Bavaresco et.al., Nature Physics (2018), 14, 1032~1037], if one constructs more than one local POVM measurements additional to the measurement in the computational basis.

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arXiv2019

Quantum enhancement of sensitivity achieved by photon-number-resolving detection in the dark port of a two-path interferometer operating at high intensities

It is shown that the maximal phase sensitivity of a two-path interferometer with high-intensity coherent light and squeezed vacuum in the input ports can be achieved by photon-number-resolving detection of only a small number of photons in a dark output port. It is then possible to achieve the quantum Cramér-Rao bound of the two-path interferometer using only the field displacement dependence of the photon number statistics in the single mode output of the dark port represented by a field-displaced squeezed vacuum state. We find that, at small field displacements, it is not sufficient to use the average photon number as the estimator, indicating that an optimal phase estimation depends critically on measurements of the precise photon number. We therefore analyze the effect of detection efficiency on the Fisher information and show that there is a transition from low robustness against photon losses associated with quantum interference effects at low field displacements to high robustness against photon losses at high field displacements. The transition between the two regimes occurs at field shifts proportional to the third power of the squeezing factor, indicating that squeezing greatly enhances the phase interval in which quantum effects are relevant in optimal phase estimations using photon resolving detectors. The case under study could thus be understood as a `missing link' between genuine multiphoton interference and the straightforward suppression of noise usually associated with squeezed light.

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arXiv2018

Derivation of the statistics of quantum measurements from the action of unitary dynamics

Quantum statistics is defined by Hilbert space products between the eigenstates associated with state preparation and measurement. The same Hilbert space products also describe the dynamics generated by a Hamiltonian when one of the states is an eigenstate of energy E and the other represents an observable B. In this paper, we investigate this relation between the observable time evolution of quantum systems and the coherence of Hilbert space products in detail. It is shown that the times of arrival for a specific value of B observed with states that have finite energy uncertainties can be used to derive the Hilbert space product between eigenstates of energy E and eigenstates of the dynamical variable B. In these Hilbert space products, quantum phases and interference effects appear in the form of an action that relates energy to time in the experimentally observable dynamics of localized states. Quantum effects emerge in the measurement statistics when the precise control of energy in quantum state preparation results in a coherent randomization of the dynamics, such that two different arrival times contribute to the quantum statistics of the same measurement outcome B. The non-classical features associated with quantum interference can thus be explained as a consequence of quantum dynamics and its role in state preparation and measurement, indicating that the apparent randomness of control described by the energy-time uncertainties is not merely a technical problem but rather originates from the fundamental nature of interactions between physical systems.

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arXiv2017

Evaluation of bipartite entanglement between two optical multi-mode systems using mode translation symmetry

Optical multi-mode systems provide large scale Hilbert spaces that can be accessed and controlled using single photon sources, linear optics and photon detection. Here, we consider the bipartite entanglement generated by coherently distributing $M$ photons in $M$ modes to two separate locations, where linear optics and photon detection is used to verify the non-classical correlations between the two $M$-mode systems. We show that the entangled state is symmetric under mode shift operations performed in the two systems and use this symmetry to derive correlations between photon number distributions detected after a discrete Fourier transform (DFT) of the modes. The experimentally observable correlations can be explained by a simple and intuitive rule that relates the sum of the output mode indices to the eigenvalue of the input state under the mode shift operation. Since the photon number operators after the DFT do not commute with the initial photon number operators, entanglement is necessary to achieve strong correlations in both the initial mode photon numbers and the photon numbers observed after the DFT. We can therefore derive entanglement witnesses based on the experimentally observable correlations in both photon number distributions, providing a practical criterion for the evaluation of large scale entanglement in optical multi-mode systems. Our method thus demonstrates how non-classical signatures in large scale optical quantum circuits can be accessed experimentally by choosing an appropriate combination of modes in which to detect the photon number distributions that characterize the quantum coherences of the state.

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arXiv2016

Quantum effects in the interference of photon number states

Multi-photon interference results in modulations of output probabilities with phase shift periods that are much shorter than 2 Pi. Here, we investigate the physics behind these statistical patterns in the case of well-defined photon numbers in the input and output modes of a two-path interferometer. We show that the periodicity of the multi-photon interference is related to the weak value of the unobserved intensity difference between the two arms of the interferometer. This means that the operator relations between the photon number differences in input, path, and output can be used to determine the periodicity of the experimentally observed quantum interference, establishing an important link between the classical causality of random phase interference and quantum effects that depend on the superposition of classically distinct possibilities.

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