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# Xiao-Dong Yu

Postdoc

Room: B-106

Phone:

## Preprints

See also arxiv

Ye-Chao Liu, Xiao-Dong Yu, Jiangwei Shang, Huangjun Zhu and Xiangdong Zhang
Efficient verification of Dicke states
arXiv:1904.01979

Among various multipartite entangled states, Dicke states stand out because their entanglement is maximally persistent and robust under particle losses. Although much attention has been attracted for their potential applications in quantum information processing and foundational studies, the characterization of Dicke states remains as a challenging task in experiments. Here, we propose efficient and practical protocols for verifying arbitrary $n$-qubit Dicke states in both adaptive and nonadaptive ways. Our protocols require only two distinct settings based on Pauli measurements besides permutations of the qubits. To achieve infidelity $\epsilon$ and confidence level $1-\delta$, the total number of tests required is only $O(n\epsilon^{-1}\ln\delta^{-1})$. This performance is much more efficient than all known protocols based on local measurements, including quantum state tomography and direct fidelity estimation, and is comparable to the best global strategy. Our protocols are readily applicable with current experimental techniques and are able to verify Dicke states of hundreds of qubits.

Xiao-Dong Yu, Jiangwei Shang and Otfried Gühne
Optimal verification of general bipartite pure states
arXiv:1901.09856

The efficient and reliable verification of quantum states plays a crucial role in various quantum information processing tasks. We consider the task of verifying entangled states using one-way and two-way classical communication and completely characterize the optimal strategies via convex optimization. We solve these optimization problems using both analytical and numerical methods, and the optimal strategies can be constructed for any bipartite pure state. Compared with the nonadaptive approach, our adaptive strategies significantly improve the efficiency of quantum state verification. Moreover, these strategies are experimentally feasible, as only few local projective measurements are required.

## Publications

Jiang Zhang, Xiao-Dong Yu, Gui-Lu Long and Qi-Kun Xue
Topological Dynamical Decoupling
SCIENCE CHINA Physics, Mechanics & Astronomy 62, 12036 (2019), arXiv:1909.10697

We show that topological equivalence classes of circles in a two-dimensional square lattice can be used to design dynamical decoupling procedures to protect qubits attached on the edges of the lattice. Based on the circles of the topologically trivial class in the original and the dual lattices, we devise a procedure which removes all kinds of local Hamiltonians from the dynamics of the qubits while keeping information stored in the homological degrees of freedom unchanged. If only the linearly independent interaction and nearest-neighbor two-qubit interactions are concerned, a much simpler procedure which involves the four equivalence classes of circles can be designed. This procedure is compatible with Eulerian and concatenated dynamical decouplings, which make it possible to implement the procedure with bounded-strength controls and for a long time period. As an application, it is shown that our method can be directly generalized to finite square lattices to suppress uncorrectable errors in surface codes.

C. L. Liu, Xiao-Dong Yu and D. M. Tong
Flag Additivity in Quantum Resource Theories
Phys. Rev. A 99, 04232 (2019), arXiv:1904.07627

Quantum resource theories offer a powerful framework for studying various phenomena in quantum physics. Despite considerable effort has been devoted to developing a unified framework of resource theories, there are few common properties that hold for all quantum resources. In this paper, we fill this gap by introducing the flag additivity based on the tensor product structure and the flag basis for the general quantum resources. To illustrate the usefulness of flag additivity, we show that flag additivity can be used to derive other nontrivial properties in quantum resource theories, e.g., strong monotonicity, convexity, and full additivity.

Roope Uola, Tristan Kraft, Jiangwei Shang, Xiao-Dong Yu and Otfried Gühne
Quantifying quantum resources with conic programming
Phys. Rev. Lett. 122, 130404 (2019), arXiv:1812.09216

Resource theories can be used to formalize the quantification and manipulation of resources in quantum information processing such as entanglement, asymmetry and coherence of quantum states, and incompatibility of quantum measurements. Given a certain state or measurement, one can ask whether there is a task in which it performs better than any resourceless state or measurement. Using conic programming, we prove that any general robustness measure (with respect to a convex set of free states or measurements) can be seen as a quantifier of such outperformance in some discrimination task. We apply the technique to various examples, e.g. joint measurability, POVMs simulable by projective measurements, and state assemblages preparable with a given Schmidt number.

Timo Simnacher, Nikolai Wyderka, Cornelia Spee, Xiao-Dong Yu and Otfried Gühne
Certifying quantum memories with coherence
Phys. Rev. A 99, 062319 (2019), arXiv:1809.03403

Quantum memories are an important building block for quantum information processing. Ideally, these memories preserve the quantum properties of the input. We present general criteria for measures to evaluate the quality of quantum memories. Then, we introduce a quality measure based on coherence satisfying these criteria, which we characterize in detail for the qubit case. The measure can be estimated from sparse experimental data and may be generalized to characterize other building blocks, such as quantum gates and teleportation schemes.

Xiao-Dong Yu and Otfried Gühne
Detecting coherence via spectrum estimation
Phys. Rev. A 99, 062310 (2019), arXiv:1808.08884

Coherence is a basic phenomenon in quantum mechanics and considered to be an essential resource in quantum information processing. Although the quantification of coherence has attracted a lot of interest, the lack of efficient methods to measure the coherence in experiments limits the applications. We address this problem by introducing an experiment-friendly method for coherence and spectrum estimation. This method is based on the theory of majorization and can not only be used to prove the presence of coherence, but also result in a rather precise lower bound of the amount of coherence. As an illustration, we show how to characterize the freezing phenomenon of coherence with only two local measurements for any $N$-qubit quantum systems. Our approach also has other applications in quantum information processing, such as the characterization of distillability and entanglement transformations.

Da-Jian Zhang, C. L. Liu, Xiao-Dong Yu and D. M. Tong
Estimating coherence measures from limited experimental data available
Phys. Rev. Lett. 120, 170501 (2018), arXiv:1707.02966

Quantifying coherence has received increasing attention, and considerable work has been directed towards finding coherence measures. While various coherence measures have been proposed in theory, an important issue following is how to estimate these coherence measures in experiments. This is a challenging task, since the state of a system is often unknown in practical applications and the accessible measurements in a real experiment are typically limited. In this Letter, we put forward an approach to estimate coherence measures of an unknown state from any limited experimental data available. Our approach is not only applicable to coherence measures but can be extended to other resource measures.

C. L. Liu, Da-Jian Zhang, Xiao-Dong Yu, Qi-Ming Ding and Longjiang Liu
A new coherence measure based on fidelity
Quantum Inf Process 16:19, (2017), arXiv:1706.07941

Quantifying coherence is an essential endeavor for both quantum foundations and quantum technologies. In this paper, we put forward a quantitative measure of coherence by following the axiomatic definition of coherence measures introduced in [T. Baumgratz, M. Cramer, and M. B. Plenio, Phys. Rev. Lett. 113, 140401 (2014)]. Our measure is based on fidelity and analytically computable for arbitrary states of a qubit. As one of its applications, we show that our measure can be used to examine whether a pure qubit state can be transformed into another pure or mixed qubit state only by incoherent operations.

Da-Jian Zhang, Xiao-Dong Yu, Hua-Lin Huang and D. M. Tong
Universal freezing of asymmetry
Phys. Rev. A 95, 022323 (2017), arXiv:1608.08046

Asymmetry of quantum states is a useful resource in applications such as quantum metrology, quantum communication, and reference frame alignment. However, asymmetry of a state tends to be degraded in physical scenarios where environment-induced noise is described by covariant operations, e.g., open systems constrained by superselection rules, and such degradations weaken the abilities of the state to implement quantum information processing tasks. In this paper, we investigate under which dynamical conditions asymmetry of a state is totally unaffected by the noise described by covariant operations. We find that all asymmetry measures are frozen for a state under a covariant operation if and only if the relative entropy of asymmetry is frozen for the state. Our finding reveals the existence of universal freezing of asymmetry, and provides a necessary and sufficient condition under which asymmetry is totally unaffected by the noise.

Da-Jian Zhang, Xiao-Dong Yu, Hua-Lin Huang and D. M. Tong
General approach to find steady-state manifolds in Markovian and non-Markovian systems
Phys. Rev. A 94, 052132 (2016), arXiv:1611.02800

Steady-state manifolds of open quantum systems, such as decoherence-free subspaces and noiseless subsystems, are of great practical importance to the end of quantum information processing. Yet, it is a difficult problem to find steady-state manifolds of open quantum systems, especially of non-Markovian systems. In this paper, we propose an approach to find the steady-state manifolds, which is generally applicable to both Markovian and non-Markovian systems. Our approach is based on an arbitrarily given steady state, and by following the standard steps of the approach, the steady-state manifold on the support subspace of the given state can be obtained. Our work reduces the problem of finding a manifold of steady states to that of finding only one steady state, which is indeed an interesting progress towards completely solving the difficult problem. Besides, in deriving our approach, we introduce the notions of the modified noise algebra and its commutant, and prove two theorems on the structure of steady-state manifolds of general open systems, which themselves are interesting findings too.

Xiao-Dong Yu, Da-Jian Zhang, G. F. Xu and D. M. Tong
Alternative framework for quantifying coherence
Phys. Rev. A 94, 060302 (2016), arXiv:1606.03181

We propose an alternative framework for quantifying coherence. The framework is based on a natural property of coherence, the additivity of coherence for subspace-independent states, which is described by an operation-independent equality rather than operation-dependent inequalities and therefore applicable to various physical contexts. Our framework is compatible with all the known results on coherence measures but much more flexible and convenient for applications, and by using it many open questions can be resolved.

Xiao-Dong Yu, Da-Jian Zhang, C. L. Liu and D. M. Tong
Measure-Independent Freezing of Quantum Coherence
Phys. Rev. A 93, 060303(R) (2016), arXiv:1603.01124

We find that all measures of coherence are frozen for an initial state in a strictly incoherent channel if and only if the relative entropy of coherence is frozen for the state. Our finding reveals the existence of measure-independent freezing of coherence, and provides an entropy-based dynamical condition in which the coherence of an open quantum system is totally unaffected by noise.

C. L. Liu, Xiao-Dong Yu, G. F. Xu and D. M. Tong
Ordering states with coherence measures
Quantum Inf Process 15(10), 418 (2016), arXiv:1601.03936

The quantification of quantum coherence has attracted a growing attention, and based on various physical contexts, several coherence measures have been put forward. An interesting question is whether these coherence measures give the same ordering when they are used to quantify the coherence of quantum states. In this paper, we consider the two well-known coherence measures, the $l_1$ norm of coherence and the relative entropy of coherence, to show that there are the states for which the two measures give a different ordering. Our analysis can be extended to other coherence measures, and as an illustration of the extension we further consider the formation of coherence to show that the $l_1$ norm of coherence and the formation of coherence, as well as the relative entropy of coherence and the coherence of formation, do not give the same ordering too.

Xiao-Dong Yu, Yan-Qing Guo and D. M. Tong
A proof of the Kochen-Specker theorem can always be converted to a state-independent noncontextuality inequality
New J. Phys. 17, 093001 (2015), arXiv:1505.02603

Quantum contextuality is one of the fundamental notions in quantum mechanics. Proofs of the Kochen-Specker theorem and noncontextuality inequalities are two means for revealing the contextuality phenomenon in quantum mechanics. It has been found that some proofs of the Kochen-Specker theorem, such as those based on rays, can be converted to a state-independent noncontextuality inequality, but it remains open whether it is true in general, i.e., whether any proof of the Kochen-Specker theorem can always be converted to a noncontextuality inequality. In this paper, we address this issue. We prove that all kinds of proofs of the Kochen-Specker theorem, based on rays or any other observables, can always be converted to state-independent noncontextuality inequalities. Besides, our constructive proof also provides a general approach for deriving a state-independent noncontextuality inequality from a proof of the Kochen-Specker theorem.

Da-Jian Zhang, Xiao-Dong Yu and D. M. Tong
Theorem on the existence of a nonzero energy gap in adiabatic quantum computation
Phys. Rev. A 90, 0423321 (2014), arXiv:1410.3562

Adiabatic quantum computation, based on the adiabatic theorem, is a promising alternative to conventional quantum computation. The validity of an adiabatic algorithm depends on the existence of a nonzero energy gap between the ground and excited states. However, it is difficult to ascertain the exact value of the energy gap. In this paper, we put forward a theorem on the existence of nonzero energy gap for the Hamiltonians used in adiabatic quantum computation. It can help to effectively identify a large class of the Hamiltonians without energy-level crossing between the ground and excited states.

Xiao-Dong Yu and D. M. Tong
Coexistence of Kochen-Specker inequalities and noncontextuality inequalities
Phys. Rev. A 89, 010101 (Rapid Communications) (2014), arXiv:1402.5200

Two types of inequalities, Kochen-Specker inequalities and noncontextuality inequalities, are both used to demonstrate the incompatibility between the noncontextual hidden variable model and quantum mechanics. It has been thought that noncontextuality inequalities are much more potent than Kochen-Specker inequalities, since the latter are constrained by the Kochen-Specker rules, which are regarded as an extra constraint imposed on the noncontextual hidden variable model. However, we find that a noncontextuality inequality exists in a ray set if and only if a Kochen-Specker inequality exists in the same ray set. This provides an effect approach both for constructing noncontextuality inequalities in a Kochen-Specker set and for converting a Kochen-Specker inequality to a noncontextuality inequality in any ray set.