arXiv subjects

Sixia Yu

Publications and source records attributed to Sixia Yu.

At least 19 recordsLinked to original sources

arXiv2026

Saving resources through repeat-until-success positive-operator-valued-measure measurements in quantum computation

We present a quantum computation approach in which computation is guided by positive-operator-valuedmeasure (POVM) measurements following a given computation path in multisteps. In this approach, one ancillary qubit is coupled to a register of working qubits, and a POVM measurement is implemented effectively on the working qubits by applying a unitary operation on the whole system followed by a projective measurement performed on the ancillary qubit. Each step of the computation is a repeat-until-success procedure such that the desired state of the step is obtained deterministically on the working qubits via POVM measurements. The principle of deferred measurement states that measurements can always be moved from an intermediate stage of a quantum circuit to the end of the circuit without affecting the efficiency of the computation.We demonstrate that in our approach, by introducing intermediate measurements on the ancillary qubit in the computation process, both the number of qubits and unitary operations can be reduced polynomially, compared to the case where the intermediate measurements are deferred to the end of the computation. We also provide a method for implementation of the approach.

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arXiv2025

Harnessing Non-convex Quantum Correlations of Independent Qubits

Quantum correlations in Bell and prepare-and-measure experiments are central resources for probing nonclassicality and enabling device-based quantum information protocols. In the absence of shared public randomness (i.e., without run-to-run mixing), even qubit correlation sets are typically non-convex, making standard convex characterizations inadequate. Here we derive qubit-specific constraints from uncertainty relations, yielding a state-independent consistency test for observed statistics in both prepare-and-measure and Bell scenarios. The test captures explicit non-convex boundaries in representative correlation families and enables correlation-based device inference by constraining (and sometimes uniquely determining) unitary-invariant measurement parameters even away from extreme points. Moreover, incorporating the inferred qubit constraints as additional conditions in a moment-matrix relaxation strengthens separability tests and can certify entanglement even for Bell-local correlations within the independent-device model. These tools provide a practical route to characterize and leverage low-dimensional quantum devices, including certification, randomness generation, and entanglement verification.

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arXiv2025

Quantum Estimation with State Symmetry-Induced Optimal Measurements

A central challenge in quantum metrology is identifying optimal measurements that saturate the quantum Cramer-Rao bound under realistic constraints, e.g., local measurements. We show that symmetries of the probe state provide a general principle for identifying optimal measurement strategies. Building on this idea, we demonstrate that when a parameter is encoded in the real coefficients of a fixed-basis expansion, the optimal measurement reduces to projection in that basis, with an application to critical metrology. Under local-measurement constraints, we show that local state symmetries provide a systematic route to constructing optimal local measurements. We illustrate this framework using graph states, explicitly constructing optimal local measurements from their local symmetries. Furthermore, weak and strong connection rules are introduced to generate broader classes of graph states that achieve Heisenberg-scaling precision using local measurements. By relaxing the number of stabilizer generators, graph states are extended to a stabilizer-code subspace. Analytical and numerical results show that coherent states in these subspaces offer multiple metrological advantages: high precision, partial noise resilience, local-measurement accessibility, and built-in error correction. These findings advance the theory of optimal measurements in quantum metrology and underscore the central role of state symmetry.

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arXiv2025

Entanglement Detection Beyond Local Bound with Coarse Calibrated measurements

Bell's test, initially devised to distinguish quantum theory from local hidden variable models through {violations of local bounds}, is also a common tool for detecting entanglement. For this purpose, one can assume the quantum description of devices and use available information to strengthen the bound for separable states, which may go beyond the local bound, enabling more efficient entanglement detection. Here we present a systematic approach for strengthening Bell inequalities for qubit systems, using Mermin-Klyshko-Bell inequalities as examples, by considering measurement devices that are coarsely calibrated only by their ability to generate nonlocal correlations without requiring precise quantum characterization. In the case of bipartite and tripartite systems, we derive trade-offs between upper bounds for separable states and general states in terms of structure functions to optimize the entanglement detection. We then strengthen $n$-partite Bell inequalities for the detection of states exhibiting a diversity of entanglement structures such as genuine multipartite entanglement. For general Bell scenarios with some measurements characterized, we demonstrate that entanglement can also be detected with some local correlations by exploiting the Navascu\'{e}s-Pironio-Ac\'{i}n hierarchy of tests.

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arXiv2025

Specifying the Intrinsic Back-action of a General Measurement

Understanding the invasive nature of quantum measurement and its implications in quantum foundations and information science demands a mathematically rigorous and physically well-grounded characterization of intrinsic back-action in general measurement processes. However, such a framework remains elusive, leaving a critical gap in quantum theory. Here, we address this issue by conceptualizing a general quantum measurement as a reduction of extended projection measurements ensured by Naimark's theorem and, derive a state-updating rule for the concerned measurement as a reduction of the projective measurements postulate. Our framework provides a detailed analysis by explicitly decomposing the disturbance effects into two distinct contributions: those arising from the measurement elements themselves and those resulting from the dilation process. Notably, this formulation naturally recovers the projection postulate in the case of projective measurements. Beyond providing insights into joint measurability, non-disturbance, our rule establishes quantitaive connections between intrinsic disturbance and other fundamental quantum features, such as randomness, uncertainty, and information gain.

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arXiv2025

Exploring the boundary of quantum network states from inside out

Quantum networks with bipartite resources and shared randomness present the simplest infrastructure for implementing a future quantum internet. Here, we shall investigate which kinds of entanglement can or cannot be generated from this kind of quantum network by examining their fidelity with different graph states. On the one hand, based on a standard form of graph states under local complementation and a fine-grained uncertainty relation between two projections, we establish upper bounds of fidelity that improve over previous results by at least $25\%$ as the dimension of local systems tends to infinity. On the other hand, in the triangle network, we propose efficient protocols to generate genuine multipartite entangled states from the network, providing significant nontrivial lower bounds of fidelity with high dimensional GHZ states.

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arXiv2023

Bounding the amount of entanglement from witness operators

We present an approach to estimate the operational distinguishability between an entangled state and any separable state directly from measuring an entanglement witness. We show that this estimation also implies bounds on a variety of other well-known entanglement quantifiers. This approach for entanglement estimation is then extended to to both the measurement-device-independent scenario and the fully device-independent scenario, where we obtain non-trivial but sub-optimal bounds. The procedure requires no numerical optimization and is easy to compute. It offers ways for experimenters to not only detect, but also quantify, entanglement from the standard entanglement witness procedure.

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arXiv2023

Lower-bounding entanglement with nonlocality in a general Bell's scenario

Understanding the quantitative relation between entanglement and Bell nonlocality is a long-standing open problem of fundamental and practical interest. Here, we tackle this problem in a general Bell scenario. {We observe that lying in the center of quantifying these properties are two minimal distances: one from a state to separable states (entanglement), and the other from a correlation to local correlations (nonlocality).} We find that these two distances can be related to each other -- the minimal correlation distance provides a lower bound for the minimal state distance, which allows us to derive nontrivial bounds on many entanglement measures with an arbitrary nonlocal correlation. Moreover, with the on-hand structural knowledge of entanglement and nonlocality in the $(n, 2, 2)$ Bell scenario, we refine our estimate significantly.

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arXiv2023

Quantum network-entanglement measures

Quantum networks are of high interest nowadays and a quantum internet has been long envisioned. Network-entanglement adapts the notion of entanglement to the network scenario and network-entangled states are considered to be a resource to overcome the limitations of a given network structure. In this work, we introduce measures of quantum network-entanglement that are well-defined within the general framework of quantum resource theories, which at the same time have a clear operational interpretation characterizing the extra resources necessary to prepare a targeted quantum state within a given network. In particular, we define the network communication cost and the network round complexity, which turn out to be intimately related to graph-theoretic parameters. We also provide methods to estimate these measures by introducing novel witnesses of network-entanglement.

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arXiv2023

Optimal Local Measurements in Single-Parameter Quantum Metrology

Quantum measurement plays a crucial role in quantum metrology. Due to the limitations of experimental capabilities, collectively measuring multiple copies of probing systems can present significant challenges. Therefore, the concept of locality in quantum measurements must be considered. In this work, we investigate the possibility of achieving the Quantum Cram\'er-Rao Bound (QCRB) through local measurements (LM). We first demonstrate that if there exists a LM to saturate the QCRB for qubit systems, then we can construct another rank-1 local projective measurement to saturate the QCRB. In this sense, rank-1 local projective measurements are sufficient to analyze the problem of saturating the QCRB. For pure qubits, we propose two necessary and sufficient methods to determine whether and how a given parameter estimation model can achieve QCRB through LM. The first method, dubbed iterative matrix partition method (IMP) and based on unitary transformations that render the diagonal entries of a tracless matrix vanish, elucidates the underlying mathematical structure of LM as well as the local measurements with classical communications (LMCC), generalizing the result by [Zhou et al Quantum Sci. Technol. 5, 025005 (2020)], which only holds for the later case. We clarify that the saturation of QCRB through LM for the GHZ-encoded states is actually due to the self-similar structure in this approach. The second method, dubbed hierarchy of orthogonality conditions (HOC) and based on the parametrization of rank-1 measurements for qubit systems, allows us to construct several examples of saturating QCRB, including the three-qubit W states and $N$-qubit W states ($N \geq 3$). Our findings offer insights into achieving optimal performance in quantum metrology when measurement resources are limited.

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arXiv2023

Experimental full network nonlocality with independent sources and strict locality constraints

Nonlocality arising in networks composed of several independent sources gives rise to phenomena radically different from that in standard Bell scenarios. Over the years, the phenomenon of network nonlocality in the entanglement-swapping scenario has been well investigated and demonstrated. However, it is known that violations of the so-called bilocality inequality used in previous experimental demonstrations cannot be used to certify the non-classicality of their sources. This has put forward a stronger concept for nonlocality in networks, called full network nonlocality. Here, we experimentally observe full network nonlocal correlations in a network where the source-independence, locality, and measurement-independence loopholes are closed. This is ensured by employing two independent sources, rapid setting generation, and space-like separations of relevant events. Our experiment violates known inequalities characterizing non-full network nonlocal correlations by over five standard deviations, certifying the absence of classical sources in the realization.

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arXiv2022

Testing Heisenberg's measurement uncertainty relation of three observables

Heisenberg's measurement uncertainty relations (MUR) of two quantum observables are essential for contemporary researches in quantum foundations and quantum information science. Going beyond, here we report the first experimental test of MURs for three quantum observables. Following the proposal of Bush, Lahti, and Werner [Phys. Rev. A 89, 012129 (2014)], we first establish rigorously MURs for triplets of unbiased qubit observables as combined approximation errors lower-bounded by an incompatibility measure. We then develop a convex programming protocol to numerically find the exact value of the incompatibility measure and the corresponding optimal measurements. Furthermore, we propose a novel implementation of optimal joint measurements and experimentally test our MURs using a single-photon qubit. Lastly, we discuss to analytically calculate the exact value of incompatibility measure for some symmetric triplets. We anticipate that this work may stimulate broad interests associated with the Heisenberg's uncertainty relation of multiple observables, enriching our understanding of quantum mechanics and inspiring innovative applications in quantum information science.

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arXiv2022

Measurement uncertainty relation for three observables

In this work we establish rigorously a measurement uncertainty relation (MUR) for three unbiased qubit observables, which was previously shown to hold true under some presumptions. The triplet MUR states that the uncertainty, which is quantified by the total statistic distance between the target observables and the jointly implemented observables, is lower bounded by an incompatibility measure that reflects the joint measurement conditions. We derive a necessary and sufficient condition for the triplet MUR to be saturated and the corresponding optimal measurement. To facilitate experimental tests of MURs we propose a straightforward implementation of the optimal joint measurements. The exact values of incompatibility measure are analytically calculated for some symmetric triplets when the corresponding triplet MURs are not saturated. We anticipate that our work may enrich the understanding of quantum incompatibility in terms of MURs and inspire further applications in quantum information science. This work presents a complete theory relevant to a parallel work [Y.-L. Mao, et al., Testing Heisenberg's measurement uncertainty relation of three observables, arXiv:2211.09389] on experimental tests.

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arXiv2022

Certifying randomness in quantum state collapse

The unpredictable process of state collapse caused by quantum measurements makes the generation of quantum randomness possible. In this paper, we explore the quantitive connection between the randomness generation and the state collapse and provide a randomness verification protocol under the assumptions: (I) independence between the source and the measurement devices and (II) the L\"{u}ders' rule for collapsing state. Without involving heavy mathematical machinery, the amount of genereted quantum randomness can be directly estimated with the disturbance effect originating from the state collapse. In the protocol, we can employ general measurements that are not fully trusted. Equipped with trusted projection measurements, we can further optimize the randomness generation performance. Our protocol also shows a high efficiency and yields a higher randomness generation rate than the one based on uncertainty relation. We expect our results to provide new insights for understanding and generating quantum randomness

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arXiv2022

Experimental demonstration of genuine tripartite nonlocality under strict locality conditions

Nonlocality captures one of the counterintuitive features of nature that defies classical intuition. Recent investigations reveal that our physical world's nonlocality is at least tripartite; i.e., genuinely tripartite nonlocal correlations in nature cannot be reproduced by any causal theory involving bipartite nonclassical resources and unlimited shared randomness. Here, by allowing the fair sampling assumption and postselection, we experimentally demonstrate such genuine tripartite nonlocality in a network under strict locality constraints that are ensured by spacelike separating all relevant events and employing fast quantum random number generators and high-speed polarization measurements. In particular, for a photonic quantum triangular network we observe a locality-loophole-free violation of the Bell-type inequality by 7.57 standard deviations for a postselected tripartite Greenberger-Horne-Zeilinger state of fidelity $(93.13 \pm 0.24)\%$, which convincingly disproves the possibility of simulating genuine tripartite nonlocality by bipartite nonlocal resources with globally shared randomness.

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arXiv2022

Uncertainty-disturbance relations and applications

Uncertainty and intrinsic measurement disturbance, two fundamental concepts in quantum measurement, have conventionally been viewed as distinct and studied separately. In this work, we establish a fundamental connection between them, proving that uncertainty not only serves as a prerequisite for intrinsic disturbance but also bounds it from above. We formalize this connection via uncertainty-disturbance relations (UDRs) with direct applications in quantum information science. We show that for rank-one projective measurements, these UDRs effectively function as uncertainty relations by bounding the uncertainties of incompatible measurements. They also enable the experimental estimation of key quantum resources -- including von Neumann entropy, purity, coherence, and genuine randomness. Our findings thus unify the understanding of uncertainty and disturbance and provide a versatile framework for quantum resource detection.

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arXiv2022

Test of Genuine Multipartite Nonlocality

While Bell nonlocality of a bipartite system is counter-intuitive, multipartite nonlocality in our many-body world turns out to be even more so. Recent theoretical study reveals in a theory-agnostic manner that genuine multipartite nonlocal correlations cannot be explained by any causal theory involving fewer-partite nonclassical resources and global shared randomness. Here we provide a Bell-type inequality as a test for genuine multipartite nonlocality in network by exploiting a matrix representation of the causal structure of a multipartite system. We further present experimental demonstrations that both four-photon GHZ state and generalized four-photon GHZ state significantly violate the inequality, i.e., the observed four-partite correlations resist explanations involving three-way nonlocal resources subject to local operations and common shared randomenss, hence confirming that nature is boundless multipartite nonlocal.

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arXiv2019

Efficient quantum algorithm for solving structured problems via multi-step quantum computation

In classical computation, a problem can be solved in multiple steps where calculated results of each step can be copied and used repeatedly. While in quantum computation, it is difficult to realize a similar multi-step computation process because the no-cloning theorem forbids making copies of an unknown quantum state perfectly. We find a method based on quantum resonant transition to protect and reuse an unknown quantum state that encodes calculated results of an intermediate step without making copies of the state, and present a quantum algorithm that solves a problem via a multi-step quantum computation process. This algorithm can achieve an exponential speedup over classical algorithms in solving a type of structured search problems.

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