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Zhaofang Bai

Publications and source records attributed to Zhaofang Bai.

At least 19 recordsLinked to original sources
arXiv2025

Features of preparable entangled states in Gaussian quantum networks

Large-scale quantum networks have been employed to overcome practical constraints on transmission and storage for single entangled systems. The deterministic preparation of entangled states is one of the key factors for realization of quantum networks. There is no efficient method to verify whether single multipartite entanglement can be prepared by multisource quantum networks. Here, we theoretically analysize under what conditions entangled states can be prepared in three kinds of basic Gaussian quantum networks, named triangle networks, star-shaped networks and chain-type networks. Some necessity criteria are derived for all preparable entangled Gaussian states in such networks. It shows that the network structure imposes strong constraints on the set of preparable entangled Gaussian states, which is fundamentally different with the standard single multipartite entanglement. This takes the first step towards understanding network mechanism for preparing entangled Gaussian states.

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arXiv2025

Measure-independent description of wave-particle duality via coherence

Wave-particle duality as one of the expression of Bohr complementarity is a significant concept in the field of quantum mechanics. Quantitative analysis of wave-particle duality aims to establish a complementary relation between the particle and wave properties. Beyond the conventional quantitative analysis depending on special choice of quantum information measures, we are aimed to provide a measure-independent complementary relation via coherence. By employing maximally coherent states in the set of all states with fixed diagonal elements, a measure-independent complementary relation is proposed. Based on this, we give a measure-independent description of wave-particle-mixedness triality in d-path interferometers. Our complementary relations reveal the relationship between wave-particle duality and quantum coherence, and also give a justification to coherence as it truly brings out the wave nature of quantum systems at its heart.

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arXiv2025

Quantifying imaginarity in terms of pure-state imaginarity

Complex numbers are widely used in quantum physics and are indispensable components for describing quantum systems and their dynamical behavior. The resource theory of imaginarity has been built recently, enabling a systematic research of complex numbers in quantum information theory. In this work, we develop two theoretical methods for quantifying imaginarity, motivated by recent progress within resource theories of entanglement and coherence. We provide quantifiers of imaginarity by the convex roof construction and quantifiers of the imaginarity by the least imaginarity of the input pure states under real operations. We also apply these tools to study the state conversion problem in resource theory of imaginarity.

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arXiv2024

State convertibility under genuinely incoherent operations

State convertibility is fundamental in the study of resource theory of quantum coherence. It is aimed at identifying when it is possible to convert a given coherent state to another using only incoherent operations. In this paper, we give a complete characterization of state convertibility under genuinely incoherent operations. It is found that convexity of the robustness of coherence plays a central role. Based on this, the majorization condition of determining convertibility from pure states to mixed states under strictly incoherent operations is provided. Moreover, maximally coherent states in the set of all states with fixed diagonal elements are determined. It is somewhat surprising that convexity of the robustness of coherence can also decide conversion between off-diagonal parts of coherent states. This might be a big step to answer completely the question of state convertibility for mixed states under incoherent operations.

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arXiv2024

Frozen condition of quantum coherence

Quantum coherence as an important physical resource plays the key role in implementing various quantum tasks, whereas quantum coherence is often deteriorated due to the noise. In this paper, we analyse under which dynamical conditions the $l_1$-norm or the relative entropy of coherence can remain unchanged during the whole evolution (freezing coherence). For single qubit systems, a nice formula is given to realize freezing coherence. Conversely, for a $d\ (d>2)$ dimensional system, we identify universal geometric conditions of freezing coherence. This offers an affirmative answer to the open question: how can one determine whether a unital quantum operation can be decomposed as a convex combination of unitary operations [M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, (Cambridge University Press, Cambridge, 2000)]. Based on this analysis, we also give a complete classification of coherent states from operational coherence theory. This builds the counterpart of entanglement classification under LOCC.

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arXiv2024

Network mechanism for generating genuinely correlative Gaussian states

Generating a long-distance quantum state with genuine quantum correlation (GQC) is one of the most essential functions of quantum networks to support quantum communication. Here, we provide a deterministic scheme for generating multimode Gaussian states with certain GQC (including genuine entanglement). Efficient algorithms of generating multimode states are also proposed. Our scheme is useful for resolving the bottleneck in generating some multimode Gaussian states and may pave the way towards real world applications of preparing multipartite quantum states in current quantum technologies.

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arXiv2022

Incoherent Gaussian equivalence of $m-$mode Gaussian states

Necessary and sufficient conditions for arbitrary multimode (pure or mixed) Gaussian states to be equivalent under incoherent Gaussian operations are derived. We show that two Gaussian states are incoherent equivalence if and only if they are related by incoherent unitaries. This builds the counterpart of the celebrated result that two pure entangled states are equivalent under LOCC if and only if they are related by local unitaries. Furthermore, incoherent equivalence of Gaussian states is equivalent to frozen coherence [Phys. Rev. Lett. \textbf{114}, 210401 (2015)]. Basing this as foundation, we find all measures of coherence are frozen for an initial Gaussian state under strongly incoherent Gaussian operations if and only if the relative entropy measure of coherence is frozen for the state. This gives an entropy-based dynamical condition in which the coherence of an open quantum system is totally unaffected by noise.

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arXiv2022

Conversion of Gaussian states under incoherent Gaussian operations

The coherence resource theory needs to study the operational value and efficiency which can be broadly formulated as the question: when can one coherent state be converted into another under incoherent operations. We answer this question completely for one-mode continuous-variable systems by characterizing conversion of coherent Gaussian states under incoherent Gaussian operations in terms of their first and second moments. The no-go theorem of purification of coherent Gaussian states is also built. The structure of incoherent Gaussian operations of two-mode continuous-variable systems is discussed further and is applied to coherent conversion for pure Gaussian states with standard second moments. The standard second moments are images of all second moments under local linear unitary Bogoliubov operations. As concrete applications, we obtain some peculiarities of a Gaussian system: (1) There does not exist a maximally coherent Gaussian state which can generate all coherent Gaussian states; (2) The conversion between pure Gaussian states is reversible; (3) The coherence of input pure state and the coherence of output pure state are equal.

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arXiv2020

Strictly incoherent operations for one-qubit systems

Strictly incoherent operations (SIO) proposed in [Phys. Rev. Lett. 116, 120404 (2016)] are promising to be a good candidate of free operations in the resource theory of quantum coherence, setting against the central role of local operations and classical communication in the resource theory of quantum entanglement. An important open problem is an efficient description for strictly incoherent operations in physical region. Such a description plays key role for axiomatic study of resource theory of quantum coherence. We are aimed to give a structural characterization of bistochastic SIOs in terms of Pauli operators and the Phase operator for one-qubit systems. Some applications of our results are also sketched in reconstructing quantum thermal averages via a quantum computer and in coherence manipulation.

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arXiv2020

Coherent preorder of quantum states

As an important quantum resource, quantum coherence play key role in quantum information processing. It is often concerned with manipulation of families of quantum states rather than individual states in isolation. Given two pairs of coherent states $(ρ_1,ρ_2)$ and $(σ_1,σ_2)$, we are aimed to study how can we determine if there exists a strictly incoherent operation $Φ$ such that $Φ(ρ_i) =σ_i,i = 1,2$. This is also a classic question in quantum hypothesis testing. In this note, structural characterization of coherent preorder under strongly incoherent operations is provided. Basing on the characterization, we propose an approach to realize coherence distillation from rank-two mixed coherent states to $q$-level maximally coherent states. In addition, one scheme of coherence manipulation between rank-two mixed states is also presented.

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arXiv2016

Conditions for coherence transformations under incoherent operations

We build the counterpart of the celebrated Nielsen's theorem for coherence manipulation in this paper. This offers an affirmative answer to the open question: whether, given two states $ρ$ and $σ$, either $ρ$ can be transformed into $σ$ or vice versa under incoherent operations [Phys. Rev. Lett. \textbf{113}, 140401(2014)]. As a consequence, we find that there exist essentially different types of coherence. Moreover, incoherent operations can be enhanced in the presence of certain coherent states. These extra states are coherent catalysts: they allow uncertain incoherent operations to be realized, without being consumed in any way. Our main result also sheds a new light on the construction of coherence measures.

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arXiv2015

Coherence measures and optimal conversion for coherent states

We discuss a general strategy to construct coherence measures. One can build an important class of coherence measures which cover the relative entropy measure for pure states, the $l_1$-norm measure for pure states and the $α$-entropy measure. The optimal conversion of coherent states under incoherent operations is presented which sheds some light on the coherence of a single copy of a pure state.

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arXiv2015

Maximally coherent states

Relative entropy measure quantifying coherence, a key property of quantum system, is proposed recently. In this note, we investigate the maximally coherent state (MCS) with respect to relative entropy measure. %(denoted by $\mathcal C_{RE}$)%. We show that there are not mixed maximally coherent states and give a complete characterization of pure maximally coherent states. Based on this characterization, for a bipartite MCS with $d_A=d_B$, we obtain that the super-additivity equality of relative entropy measure holds if and only if the state is a product state of its reduced states. From the viewpoint of resource in quantum information, we find there exists a MCS with maximal entanglement. Originated from the behaviour of quantum correlation under the influence of noisy operations, we further classify the incoherent operations which send maximally coherent states to themselves.

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arXiv2015

Coherence convertibility for mixed states

In this paper, by providing a class of coherence measures in finite dimensional systems, a sufficient and necessary condition for the existence of coherence transformations that convert one probability distribution of any pure states into another one is obtained.

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arXiv2014

When quantum channel preserves product states

Product states are always considered as the states that don't contain quantum correlation. We discuss here when a quantum channel sends the product states to themselves. The exact forms of such channels are proposed. It is shown that such a quantum channel is a local quantum channel, a composition of a local quantum channel and a flip operation, or such that one of the local states is fixed. Both finite- and infinite-dimensional systems are considered.

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