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众所周知,2维 Hadamard 矩阵的阶数必须是1或2或4t(此处 t 是某个正整数).反过来,著名的 Hadamard 猜想则说:“对任意正整数 t,至少存在一个2维4t 阶的Hadamard 矩阵.”此猜想至今已有近百年的历史了,虽然许多数学家都曾经或正在为此猜想而绞尽脑汁,但是仍然没人能证明或否定它.1979年美国学者 P.J.Shlichta 将Hadamard 矩阵的理论从2维推广到高维情形,并提出了这样一个高维 Hadamard 猜想:“高维 Hadamard 矩阵的阶数不受4t 的限制,即有可能存在阶数为2s(?)4t(s 是奇数)的高维 Hadamard 矩阵.”最近杨义先已在[2]中证明了上述高维 Hadamard 猜想是正确的.在本文中我们将再给出一个更简单、更有力的新证明.最后我们还得出了如下 相似文献
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Recently, deterministic joint remote state preparation (JRSP) schemes have been proposed to achieve 100% success probability. In this paper, we propose a new version of deterministic JRSP scheme of an arbitrary two-qubit state by using the six-qubit cluster state as shared quantum resource. Compared with previous schemes, our scheme has high efficiency since less quantum resource is required, some additional unitary operations and measurements are unnecessary. We point out that the existing two types of deterministic JRSP schemes based on GHZ states and EPR pairs are equivalent. 相似文献
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We propose a scheme to realize quantum cloning of an unknown M-qudit equatorial-like entangled state. The first stage of the protocol requires teleportation. After the teleportation is accomplished, the receiver can reestablish the original state. In the second stage of the protocol, with the assistance (through a single-particle projective measurement) of the preparer, the perfect copy of an original state can be produced at the site of the sender. Our scheme requires a single maximally entangled qudit pair as the quantum channel and three dits classical communication. The scheme is feasible at the expense of consuming local resources which include M - 1 ancillary qudits introduced by the receiver and additional bi-qudit operations. Moreover, we construct a sort of unitary transformations which ensure ancillary qudits are not necessarily introduced by the sender. Comparing to the previous protocols, the proposed protocol is economical due to that the cost of both quantum nonlocal resources and classical communication is lowest. 相似文献
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We propose a scheme where one can exploit auxiliary resources to achieve quantum multicast communication with network coding over the butterfly network.In this paper,we propose the quantum 2-pair multicast communication scheme,and extend it to k-pair multicast communication over the extended butterfly network.Firstly,an EPR pair is shared between each adjacent node on the butterfly network,and make use of local operation and classical communication to generate entangled relationship between non-adjacent nodes.Secondly,each sender adds auxiliary particles according to the multicast number k,in which the CNOT operations are applied to form the multi-particle entangled state.Finally,combined with network coding and free classical communication,quantum multicast communication based on quantum measurements is completed over the extended butterfly network.Not only the bottleneck problem is solved,but also quantum multicast communication can be completed in our scheme.At the same time,regardless of multicast number k,the maximum capacity of classical channel is 2 bits,and quantum channel is used only once. 相似文献
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Xiu-Bo Chen 《中国物理 B》2022,31(4):40305-040305
Fault-tolerant error-correction (FTEC) circuit is the foundation for achieving reliable quantum computation and remote communication. However, designing a fault-tolerant error correction scheme with a solid error-correction ability and low overhead remains a significant challenge. In this paper, a low-overhead fault-tolerant error correction scheme is proposed for quantum communication systems. Firstly, syndrome ancillas are prepared into Bell states to detect errors caused by channel noise. We propose a detection approach that reduces the propagation path of quantum gate fault and reduces the circuit depth by splitting the stabilizer generator into X-type and Z-type. Additionally, a syndrome extraction circuit is equipped with two flag qubits to detect quantum gate faults, which may also introduce errors into the code block during the error detection process. Finally, analytical results are provided to demonstrate the fault-tolerant performance of the proposed FTEC scheme with the lower overhead of the ancillary qubits and circuit depth. 相似文献
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From 1986 to 1991, based on AMSAA model, Zhou Yuan-quan and Weng Zhao-xi presented AMSAA-BISE model to estimate reliability
growth for multiple systems development, for the case that more than one system of the same type is put into reliability growth
test, once a Type B failure mode is seen during test, corrective action will be taken to all systems. It is shown that there
is something wrong with AMSAA-BISE model. According to AMSAA-BISE model, the maximum likelihood estimation of MTBF for multiple
systems reliability growth test is much larger than that according to AMSAA model for a single system; The more systems is
put into test, the larger the estimation of MTBF. An example is given, and an approximate method is presented.
Biography: Mei Wen-hua (1965-), Senior Engineer, Doctor 相似文献
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