arXiv subjects

Lijinzhi Lin

Publications and source records attributed to Lijinzhi Lin.

6 recordsLinked to original sources

arXiv2024

Certifying bipartite pure quantum states efficiently using untrusted devices

It has been known that all bipartite pure quantum states can be certified by quantum self-testing, i.e., any such states can be pinned down completely based on the statistics produced by local quantum measurements. A notable feature of quantum self-testing is that the conclusions remain reliable even when the quantum measurements involved are untrusted, where quantum nonlocality is crucial. This necessitates that each party conducts at least two different quantum measurements to produce the desired correlation. Here, we prove that when the underlying Hilbert space dimension is known beforehand, which is very common in quantum experiments, an arbitrary $d\times d$ bipartite pure state can be certified completely (up to local unitaries) by a certain correlation generated with a single measurement setting on each party, where each measurement yields only $2d$ or even $d+1$ outcomes. We also prove the robustness of our protocols to quantum noises and experimental imperfections. Compared with quantum self-testing, our protocols do not hinge on quantum nonlocality and are much more efficient, yet they maintain the essential feature of not requiring additional assumptions about the quantum devices involved. This advancement could offer significant convenience when certifying bipartite quantum states using untrusted quantum devices in future quantum industries.

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arXiv2024

The Generations of Classical Correlations via Quantum Schemes

Suppose two separated parties, Alice and Bob, share a bipartite quantum state or a classical correlation called a \emph{seed}, and they try to generate a target classical correlation by performing local quantum or classical operations on the seed, i.e., any communications are not allowed. We consider the following fundamental problem about this setting: whether Alice and Bob can use a given seed to generate a target classical correlation. We show that this problem has rich mathematical structures. Firstly, we prove that even if the seed is a pure bipartite state, the above decision problem is already NP-hard and a similar conclusion can also be drawn when the seed is also a classical correlation, implying that this problem is hard to solve generally. Furthermore, we prove that when the seed is a pure quantum state, solving the problem is equivalent to finding out whether the target classical correlation has some diagonal form of positive semi-definite factorizations that matches the seed pure state, revealing an interesting connection between the current problem and optimization theory. Based on this observation and other insights, we give several necessary conditions where the seed pure state has to satisfy to generate the target classical correlation, and it turns out that these conditions can also be generalized to the case that the seed is a mixed quantum state. Lastly, since diagonal forms of positive semi-definite factorizations play a crucial role in solving the problem, we develop an algorithm that can compute them for an arbitrary classical correlation, which has decent performance on the cases we test.

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arXiv2020

Experimental Entanglement Quantification for Unknown Quantum States in a Semi-Device-Independent Manner

Using the concept of non-degenerate Bell inequality, we show that quantum entanglement, the critical resource for various quantum information processing tasks, can be quantified for any unknown quantum states in a semi-device-independent manner, where the quantification is based on the experimentally obtained probability distribution and beforehand knowledge on quantum dimension only. Specifically, as an application of our approach on multi-level systems, we experimentally quantify the entanglement of formation and the entanglement of distillation for qutrit-qutrit quantum systems. In addition, to demonstrate our approach for multi-partite systems, we further quantify the geometry measure of entanglement of three-qubit quantum systems. Our results supply a general way to reliably quantify entanglement in multi-level and multi-partite systems, thus paving the way to characterize many-body quantum systems by quantifying involved entanglement.

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arXiv2020

Quantifying Multipartite Quantum Entanglement in a Semi-Device-Independent Manner

We propose two semi-device-independent approaches that are able to quantify unknown multipartite quantum entanglement experimentally, where the only information that has to be known beforehand is quantum dimension, and the concept that plays a key role is nondegenerate Bell inequalities. Specifically, using the nondegeneracy of multipartite Bell inequalities, we obtain useful information on the purity of target quantum state. Combined with an estimate of the maximal overlap between the target state and pure product states and a continuous property of the geometric measure of entanglement we shall prove, the information on purity allows us to give a lower bound for this entanglement measure. In addition, we show that a different combination of the above results also converts to a lower bound for the relative entropy of entanglement. As a demonstration, we apply our approach on 5-partite qubit systems with the MABK inequality, and show that useful lower bounds for the geometric measure of entanglement can be obtained if the Bell value is larger than 3.60, and those for the relative entropy of entanglement can be given if the Bell value is larger than 3.80, where the Tsirelson bound is 4.

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arXiv2020

Testing the Structure of Multipartite Entanglement with Hardy's Nonlocality

Multipartite quantum states may exhibit different types of quantum entanglement in that they cannot be converted into each other by local quantum operations only, and fully understanding mathematical structures of different types of multipartite entanglement is a very challenging task. In this paper, from the viewpoint of Hardy's nonlocality, we compare W and GHZ states and show a couple of crucial different behaviors between them. Particularly, by developing a geometric model for the Hardy's nonlocality problem of W states, we derive an upper bound for its maximal violation probability, which turns out to be strictly smaller than the corresponding probability of GHZ state. This gives us a new comparison between these two quantum states, and the result is also consistent with our intuition that GHZ states is more entangled. Furthermore, we generalize our approach to obtain an asymptotic characterization for general $N$-qubit W states, revealing that when $N$ goes up, the speed that the maximum violation probabilities decay is exponentially slower than that of general $N$-qubit GHZ states. We provide some numerical simulations to verify our theoretical results.

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arXiv2019

Analytic Semi-device-independent Entanglement Quantification for Bipartite Quantum States

We define a property called nondegeneracy for Bell inequalities, which describes the situation that in a Bell setting, if a Bell inequality and involved local measurements are chosen and fixed, any quantum state with a given dimension and its orthogonal quantum state cannot violate the inequality remarkably at the same time. By choosing a proper nondegenerate Bell inequality, we prove that for a unknown bipartite quantum state of a given dimension, based on the measurement statistics only, we can provide an analytic lower bound for the entanglement of formation or even for the distillable entanglement, making the whole process semi-device-independent. We characterize the mathematical structure of nondegenerate Bell inequalities, and prove that quite a lot of well-known Bell inequalities are nondegenerate. We demonstrate our approach by quantifying entanglement for qutrit-qutrit states based on their violation to the CGLMP inequality.

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