W. Dür, G. Vidal, J. I. Cirac
We analyze the problem of quantum data compression of commuting density operators in the visible case. We show that the lower bound for the compression factor given by the Levitin--Holevo function is reached by providing an explicit protocol.
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We provide a rate distortion interpretation of the problem of quantum data compression of ensembles of mixed states with commuting density operators. There are two versions of this problem. In the visible case the sequence of states is available to the encoder and in the blind or hidden case the encoder may access only a sequence of measurements. We find the exact optimal compression rates for both the visible and hidden cases. Our analysis includes the scenario in which asymptotic reconstruction is imperfect.
Entanglement of purification was introduced by Terhal et al. for characterizing the bound of the generation of correlated states from maximally entangled states with sublinear size of classical communication. On the other hand, M. Horodecki obtained the optimal compression rate with a mixed states ensemble in the visible setting. In this paper, we prove that the optimal visible compression rate for mixed states is equal to the limit of the regularized entanglement of purification of the state corresponding to the given ensemble. This result gives a new interpretation to the entanglement of pur…
We consider the problem of the optimal compression rate in the case of the source producing mixed signal states within the {\it visible} scheme (where Alice, who is to compress the signal, can know the identities of the produced states). We show that a simple strategy based on replacing the signal states with their {\it extensions} gives {\it optimal} compression. As a result we obtain a considerable simplification of the formula for optimal compression rate within visible scheme.
Nonlocal Games, Compression Theorems, and the Arithmetical Hierarchy
本文证明判定双人非局域博弈的量子值是否恰好为1对算术层级第二层Π_2完全，并借助适用于量子与交换算子策略的无间隙压缩定理统一解释非局域博弈复杂度结果。
We consider visible compression for discrete memoryless sources of mixed quantum states when only classical information can be sent from Alice to Bob. We assume that Bob knows the source statistics, and that Alice and Bob have identical random number generators. We put in an information theoretic framework some recent results on visible compression for sources of states with commuting density operators, and remove the commutativity requirement. We derive a general achievable compression rate, which is for the noncommutative case still higher than the known lower bound. We also present several …
Learning to generate high-dimensional distributions with low-dimensional quantum Boltzmann machines
本文证明低维全可见量子玻尔兹曼机可学习生成通常与高维系统相关的分布，并通过人工数据集和高能物理喷注事件生成实验验证非对易项与哈密顿量连通性对学习能力的提升作用。
This thesis addresses problems in the field of quantum information theory. The first part of the thesis is opened with concrete definitions of general quantum source models and their compression, and each subsequent chapter addresses the compression of a specific source model as a special case of the initially defined general models. First, we find the optimal compression rate of a general mixed state source which includes as special cases all the previously studied models such as Schumacher's pure and ensemble sources and other mixed state ensemble models. For an interpolation between the vis…
Contour-integral and Fourier transform based multivariable quantum eigenvalue transformation for commuting matrices
本文提出两种基于围道积分和高维傅里叶变换的量子算法，用于实现交换矩阵元组的多变量特征值变换，并分析复杂度及混合变体，证明多项式实现无需额外次数依赖。
Strong Converse Bounds for Compression of Mixed States
本文研究混合态可见与盲压缩的强逆界，定义新的Rényi推广量，证明可扩展态下纯化纠缠可加性，并给出一般态在超单位解码器下的强逆界。
Commuting Embeddings for Parallel Strategies in Non-local Games
通过引入代数嵌入和交换嵌入条件，提出两种压缩方法以减少并行非局域游戏所需的量子比特资源，并利用李理论中的Cartan分解实现构造。
Hybrid quantum networks rely on efficient interfacing of dissimilar quantum nodes, since elements based on parametric down-conversion sources, quantum dots, color centres or atoms are fundamentally different in their frequencies and bandwidths. While pulse manipulation has been demonstrated in very different systems, to date no interface exists that provides both an efficient bandwidth compression and a substantial frequency translation at the same time. Here, we demonstrate an engineered sum-frequency-conversion process in Lithium Niobate that achieves both goals. We convert pure photons at t…
Expressive equivalence of classical and quantum restricted Boltzmann machines
针对现有量子受限玻尔兹曼机梯度计算成本高的问题，提出半量子受限玻尔兹曼机sqRBM，证明其与经典RBM表达能力关联，可大幅降低量子资源需求。
Ask how the quantum compression of ensembles of pure states is affected by the availability of entanglement, and in settings where the encoder has access to side information. We find the optimal asymptotic quantum rate and the optimal tradeoff (rate region) of quantum and entanglement rates. It turns out that the amount by which the quantum rate beats the Schumacher limit, the entropy of the source, is precisely half the entropy of classical information that can be extracted from the source and side information states without disturbing them at all ("reversible extraction of classical informat…
We study the visible compression of a source E of pure quantum signal states, or, more formally, the minimal resources per signal required to represent arbitrarily long strings of signals with arbitrarily high fidelity, when the compressor is given the identity of the input state sequence as classical information. According to the quantum source coding theorem, the optimal quantum rate is the von Neumann entropy S(E) qubits per signal. We develop a refinement of this theorem in order to analyze the situation in which the states are coded into classical and quantum bits that are quantified sepa…
We show that any language in nondeterministic time $\exp(\exp(\cdots \exp(n)))$, where the number of iterated exponentials is an arbitrary function $R(n)$, can be decided by a multiprover interactive proof system with a classical polynomial-time verifier and a constant number of quantum entangled provers, with completeness $1$ and soundness $1 - \exp(-C\exp(\cdots\exp(n)))$, where the number of iterated exponentials is $R(n)-1$ and $C>0$ is a universal constant. The result was previously known for $R=1$ and $R=2$; we obtain it for any time-constructible function $R$. The result is based on a c…
Rate-Distortion Theory for Mixed States
本文研究带边信息的混合量子态系综压缩的率失真问题，推导了不同纠缠辅助场景下的率失真函数与完整率区域，压缩方案可适配多种压缩模型。
State-Dependent Visibility of Non-Commutative Ordering in Quantum Dynamics
本文研究量子动力学中非阿贝尔序信息的态依赖可见性，通过定义操作可见性揭示其在不同量子态及量子相变中的可见性变化，表明动力学阿贝尔化是态依赖过程的属性。
In blind compression of quantum states, a sender Alice is given a specimen of a quantum state $ρ$ drawn from a known ensemble (but without knowing what $ρ$ is), and she transmits sufficient quantum data to a receiver Bob so that he can decode a near perfect specimen of $ρ$. For many such states drawn iid from the ensemble, the asymptotically achievable rate is the number of qubits required to be transmitted per state. The Holevo information is a lower bound for the achievable rate, and is attained for pure state ensembles, or in the related scenario of entanglement-assisted visible compression…
该研究证明MIP*类等于RE类，整合多项测试与框架得出推论，反驳了Connes嵌入猜想并解答Tsirelson问题。
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