Seth Lloyd, Vittorio Giovannetti, Lorenzo Maccone
We study the transmission of classical information in quantum channels. We present a decoding procedure that is very simple but still achieves the channel capacity. It is used to give an alternative straightforward proof that the classical capacity is given by the regularized Holevo bound. This procedure uses only projective measurements and is based on successive "yes"/"no" tests only.
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The relation between projective measurements and generalized quantum measurements is a fundamental problem in quantum physics, and clarifying this issue is also important to quantum technologies. While it has been intuitively known that projective measurements can be constructed from sequential generalized or weak measurements, there is still lack of a proof of this hypothesis in general cases. Here we prove it from the perspective of quantum channels. We show that projective measurements naturally arise from sequential generalized measurements in the asymptotic limit. Specifically, a selectiv…
We present two new quantum union bounds for sequential projective measurements. These bounds estimate the disturbance accumulation and probability of outcomes when the measurements are performed sequentially. These results are based on a trigonometric representation of quantum states and should have wide application in quantum information theory for information processing tasks such as communication and state discrimination, and perhaps even in the analysis of quantum algorithms.
This work analyzes correlations arising from quantum systems subject to sequential projective measurements to certify that the system in question has a quantum dimension greater than some $d$. We refine previous known methods and show that dimension greater than two can be certified in scenarios which are considerably simpler than the ones presented before and, for the first time in this sequential projective scenario, we certify quantum systems with dimension strictly greater than three. We also perform a systematic numerical analysis in terms of robustness and conclude that performing random…
Sharing tripartite nonlocality sequentially using only projective measurements
本文研究仅用投影测量和共享经典随机性共享三方非定域性，发现无偏测量下两个Charlie可共享标准非定域性，有偏测量可将共享真正非定域性的Charlie增至两个。
Causal-Order Identification of Memoryless Sequential Quantum Processes from Restricted Projective Data
本文研究了从受限投影数据中识别无记忆顺序量子过程因果顺序的充要条件，通过引入代数一致性要求完善了基于伪密度矩阵的判据。
Projective measurements are sufficient for recycling nonlocality
针对顺序观察者共享纠缠态的非定域性回收问题，本文证明无需非锐测量或量子辅助系统，仅用投影测量即可实现，并给出 CHSH 情形下的最优权衡与更大顺序违背。
Decoding the Projective Transverse Field Ising Model
本研究探讨投影横向场伊辛模型作为量子纠错码的能力，发现存在有限阈值，低于该阈值量子信息可被可靠检索，且纠错阈值不同于纠缠跃迁。
Sequential decoding of the XYZ$^2$ hexagonal stabilizer code
本文研究蜂窝晶格上的XYZ$^2$拓扑稳定子码，将其视为[[2,1,1]]相位翻转奇偶校验码与YZZY表面码的级联，提出顺序译码方案，在偏置噪声下取得接近最优的阈值，展示了级联码的两种利用策略。
In this paper, we study the power of sequential decoding strategies for several channels with classical input and quantum output. In our sequential decoding strategies, the receiver loops through all candidate messages trying to project the received state onto a `typical' subspace for the candidate message under consideration, stopping if the projection succeeds for a message, which is then declared as the guess of the receiver for the sent message. We show that even such a conceptually simple strategy can be used to achieve rates up to the mutual information for a single sender single receive…
Constructions and decoding procedures for quantum CSS codes
该研究提出量子纠错CSS码的新构造方法，基于Sloane经典线性码组合方法处理自正交线性码场景，同时提出新的代数译码技术并在多类经典码构造的CSS码上验证。
Unbounded Sharing of Nonlocality Using Projective Measurements
本研究提出局部随机性辅助的投影测量协议，突破投影测量破坏纠缠的认知，实现任意数量顺序观察者与单一爱丽丝共享非局域性，揭示双方不相容性相互作用，为量子非局域性研究及信息处理提供新范式。
Learning-Based List Sequential Belief Propagation Decoding of Quantum LDPC Codes
提出强化学习列表顺序BP译码器，通过列表搜索扩展学习顺序调度，结合路径度量剪枝，在去极化信道下提升QLDPC码译码性能。
Learned Parallel Bit-Flipping Sequential Belief Propagation Decoding of Quantum LDPC Codes
针对量子LDPC码，提出一种结合四元评分与并行比特翻转的序贯BP解码器，通过并行候选延续提升学习型序贯BP的可靠性，并保持低延迟。
Since a quantum measurement generally disturbs the state of a quantum system, one might think that it should not be possible for a sender and receiver to communicate reliably when the receiver performs a large number of sequential measurements to determine the message of the sender. We show here that this intuition is not true, by demonstrating that a sequential decoding strategy works well even in the most general "one-shot" regime, where we are given a single instance of a channel and wish to determine the maximal number of bits that can be communicated up to a small failure probability. Thi…
Quantifying the intrinsic randomness in sequential measurements
本文严格定义了序列测量中的量子内禀随机性，在CGLMP序列场景下量化了混合态与任意量子态在序列投影测量和序列POVM下的随机性，并利用NPA层级给出最大纠缠态与最大违背态的随机性下界。
Due to their fast decoding algorithms, quantum generalizations of low-density parity check, or LDPC, codes have been investigated as a solution to the problem of decoherence in fragile quantum states. However, the additional twisted inner product requirements of quantum stabilizer codes force four-cycles and eliminate the possibility of randomly generated quantum LDPC codes. Moreover, the classes of quantum LDPC codes discovered thus far generally have unknown or small minimum distance, or a fixed rate. This paper presents several new classes of quantum LDPC codes constructed from finite proje…
Quantum correlation is a fundamental property which distinguishes quantum systems from classical ones, and it is also a fragile resource under projective measurement. Recently, it has been shown that a subsystem in entangled pairs can share nonlocality with multiple observers in sequence. Here we present a new steering scenario where both subsystems are accessible by multiple observers. And it is found that the two qubits in singlet state can be simultaneously steered by two sequential observers, respectively.
Recovery of resources through sequential noisy measurements
本文提出在量子网络中利用辅助量子比特序贯执行最优非锐利噪声测量，可像投影测量一样实现节点间纠缠局域化并缓解噪声影响，为制备量子资源态及提升安全通信控制权提供了新方法。
Patchwork: automated lattice surgery and space-time partitioning for real-time decoding
该研究提出了名为Patchwork的自动格手术编译器，通过几何规则与波前算法实现窄走廊二维表面码的实时解码，模拟显示其分阶段解码性能接近整体解码，为容错格手术提供了自动框架。
Encoding and decoding quantum information in a multipartite quantum system are indispensable for quantum error correction and also play crucial roles in multiparty tasks in distributed quantum information processing such as quantum secret sharing. To quantitatively characterize nonlocal properties of multipartite quantum transformations for encoding and decoding, we analyze entanglement costs of encoding and decoding quantum information in a multipartite quantum system distributed among spatially separated parties connected by a network. This analysis generalizes previous studies of entangleme…
Faster Optimal Decoder for Graph Codes with a Single Logical Qubit
本文提出了一种基于图码结构的高效分层解码方法，通过多项式时间解码实现最优性能，避免了传统最大似然解码的复杂性。
Sharing Bell nonlocality of bipartite high-dimensional pure states using only projective measurements
本文证明仅使用投影测量即可共享任意高维纯两体态的Bell非定域性，推广了已有两量子比特纯态的结果，深化了对高维量子态非定域性共享的理解。
In the past few years it has been shown that universal quantum computation can be obtained by projective measurements alone, with no need for unitary gates. This suggests that the underlying logic of quantum computing may be an algebra of sequences of quantum measurements rather than an algebra of products of unitary operators. Such a Sequential Quantum Logic (SQL) was developed in the late 70's and has more recently been applied to the consistent histories framework of quantum mechanics as a possible route to the theory of quantum gravity. In this letter, I give a method for deciding the trut…
Quantum nonlocality offers a secure way to produce random numbers: their unpredictability is intrinsic and can be certified just by observing the statistic of the measurement outcomes, without assumptions on how they are produced. To do this, entangled pairs are generated and measured to violate a Bell inequality with the outcome statistics. However, after a projective quantum measurement, entanglement is entirely destroyed and cannot be used again. This fact poses an upper bound to the number of random numbers that can be produced from each quantum state when projective measurements are emplo…
A quantum battery is a work reservoir that stores energy in quantum degrees of freedom. When immersed in an environment an open quantum battery needs to be stabilized against free energy leakage into the environment. For this purpose we here propose a simple protocol that relies on projective measurement and obeys a second-law like inequality for the battery entropy production rate.
We introduce and analyse an efficient decoder for the quantum Tanner codes of that can correct adversarial errors of linear weight. Previous decoders for quantum low-density parity-check codes could only handle adversarial errors of weight $O(\sqrt{n \log n})$. We also work on the link between quantum Tanner codes and the Lifted Product codes of Panteleev and Kalachev, and show that our decoder can be adapted to the latter. The decoding algorithm alternates between sequential and parallel procedures and converges in linear time.
Projective measurements can probe non-classical work extraction and time-correlations
本研究提出无需辅助系统的投影测量技术表征非经典多时间关联，在金刚石氮-空位中心实验中观测到五倍于常规方案的功提取峰值，并用准概率负性的反常能量交换解释该现象。
We explore the use of weak quantum measurements for single-qubit quantum state tomography processes. Weak measurements are those where the coupling between the qubit and the measurement apparatus is weak; this results in the quantum state being disturbed less than in the case of a projective measurement. We employ a weak measurement tomography protocol developed by Das and Arvind, which they claim offers a new method of extracting information from quantum systems. We test the Das-Arvind scheme for various measurement strengths, and ensemble sizes, and reproduce their results using a sequential…
Quantum information recovery from black hole with projective measurement
本文在 Hayden-Preskill 思想实验中引入局部投影测量，系统考察黑洞信息恢复、终态提议、解码协议及退相干等问题，为理解量子黑洞非微扰性质提供新视角。
We introduce sequential and parallel decoders for quantum Tanner codes. When the Tanner code construction is applied to a sufficiently expanding square complex with robust local codes, we obtain a family of asymptotically good quantum low-density parity-check codes. In this case, our decoders provably correct arbitrary errors of weight linear in the code length, respectively in linear or logarithmic time. The same decoders are easily adapted to the expander lifted product codes of Panteleev and Kalachev. Along the way, we exploit recently established bounds on the robustness of random tensor c…
We present a new decoding procedure to transmit classical information in a quantum channel which, saturating asymptotically the Holevo bound, achieves the optimal rate of the communication line. Differently from previous proposals, it is based on performing a sequence of (projective) YES/NO measurements which in N steps determines which codeword was sent by the sender (N being the number of the codewords). Our analysis shows that as long as N is below the limit imposed by the Holevo bound the error probability can be sent to zero asymptotically in the length of the codewords.
Hierarchy of emergent cluster states by measurement from symmetry-protected-topological states with large symmetry to subsystem cat state
本文提出了一种通过顺序子系统投影测量在关联态中产生测量层级的方法，发现对大对称性SPT簇态进行测量可产生对称性约化的广义簇态和GHZ态，并利用稳定子形式算法和数值模拟验证了该层级结构。
We define a simple rule that allows to describe sequences of projective measurements for a broad class of generalized probabilistic models. This class embraces quantum mechanics and classical probability theory, but, for example, also the hypothetical Popescu-Rohrlich box. For quantum mechanics, the definition yields the established Lüders's rule, which is the standard rule how to update the quantum state after a measurement. In the general case it can be seen as the least disturbing or most coherent way to perform sequential measurements. As example we show that Spekkens's toy model is an ins…
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