针对满足 p-可和性条件的序列，确定了量子计算模型中计算序列均值的查询复杂度，解决了 Heinrich (2001) 中遗留的问题。
摘要：
我们考虑量子计算模型中序列均值的计算。我们确定了满足 $1\le p<2$ 的 $p$-可和性条件的序列的查询复杂度。这解决了 Heinrich (2001) 中遗留的一个问题。
英文摘要：
We consider the computation of the mean of sequences in the quantum model of computation. We determine the query complexity in the case of sequences which satisfy a $p$-summability condition for $1\le p<2$. This settles a problem left open in Heinrich (2001).
In this paper, we present a quantum secure multi-party summation protocol, which allows multiple mutually distrustful parties to securely compute the summation of their secret data. In the presented protocol, a semitrusted third party is introduced to help multiple parties to achieve this secure task. Besides, the entanglement swapping of $d$-level cat states and Bell states is employed to securely transmit message between each party and the semitrusted third party. At last, its security against some common attacks is analyzed, which shows that the presented protocol is secure in theory.
In this paper, a three-party secure semiquantum summation protocol, which can calculate the modulo 2 addition of the private bits from one quantum participant and two classical participants, is constructed by only using single qubits as the initial quantum resource. This protocol needs none of quantum entanglement swapping, the unitary operation or a pre-shared private key. This protocol only requires the quantum participant to perform the Z basis measurements, the X basis measurements and the Bell basis measurements. Compared with the existing only semiquantum summation protocol (Int J Theor …
In this paper, a lightweight three-user secure quantum summation protocol is put forward by using single-particle states, which can accomplish the goal that three users cooperate together to calculate the modulo 2 addition of their private messages without the help of a third party. This protocol only requires single-particle states rather than quantum entangled states as the initial quantum resource, and only needs single-particle measurements and Bell basis measurements. This protocol needs none of quantum entanglement swapping, the Pauli operations, the controlled-not (CNOT) operation, the …
In this paper, we propose a novel secure multi-party quantum summation protocol based on quantum Fourier transform, where the traveling particles are transmitted in a tree-type mode. The party who prepares the initial quantum states is assumed to be semi-honest, which means that she may misbehave on her own but will not conspire with anyone. The proposed protocol can resist both the outside attacks and the participant attacks. Especially, one party cannot obtain other parties' private integer strings; and it is secure for the colluding attack performed by at most n-2 parties, where n is the nu…
Quantum computational path summation for relativistic quantum mechanics and a time dilation relation for a Dirac Hamiltonian generator on a qubit array
Improvements on "Secure multi-party quantum summation based on quantum Fourier transform"
最近，提出了一种基于量子傅里叶变换的量子多方求和协议[Quantum Inf Process 17：129，2018]。该协议声称对外部和参与者的攻击都是安全的。然而，仔细观察就会发现，负责生成所需多体纠缠态的玩家可以发起两种攻击，以了解其他方的私有整数串而不会被捕获。在本文中，我们提出了这些攻击，并提出对策，使协议的安全。改进后的协议不仅可以抵抗这些攻击，而且不需要参与者进行量子傅里叶变换和量子编码操作。
Semi-quantum protocols construct connections between quantum users and ``classical'' users who can only perform certain ``classical'' operations. In this paper, we present a new semi-quantum private comparison protocol based on entangled states and single particles, which does not require pre-shared keys between the ``classical'' users to guarantee the security of their private data. By utilizing multi-particle entangled states and single particles, our protocol can be easily extended to multi-party scenarios to meet the requirements of multiple ``classical'' users who want to compare their pr…
The understanding of complex quantum many-body systems has been vastly boosted by tensor network (TN) methods. Among others, excitation spectrum and long-range interacting systems can be studied using TNs, where one however confronts the intricate summation over an extensive number of tensor diagrams. Here, we introduce a set of generating functions, which encode the diagrammatic summations as leading order series expansion coefficients. Combined with automatic differentiation, the generating function allows us to solve the problem of TN diagrammatic summation. We illustrate this scheme by com…
On the basis of the method of iterative summation of path integrals (ISPI), we develop a numerically exact transfer-matrix method to describe the nonequilibrium properties of interacting quantum-dot systems. For this, we map the ISPI scheme to a transfer-matrix approach, which is more accessible to physical interpretation, allows for a more transparent formulation of the theory, and substantially improves the efficiency. In particular, the stationary limit is directly implemented, without the need of extrapolation. The resulting new method, referred to as "transfer-matrix summation of path int…
A Unified Poisson Summation Framework for Generalized Quantum Matrix Transformations
Origin Quantum Computing Technology (Hefei) Co., Ltd.（本源量子计算科技（合肥）有限公司）；Laboratory of Quantum Information, University of Science and Technology of China（中国科学技术大学量子信息实验室）；Institute of Artificial Intelligence, Hefei Comprehensive National Science Center（合肥综合性国家科学中心人工智能研究院）
The metric-adjusted skew information establishes a connection between the geometrical formulation of quantum statistics and the measures of quantum information. We study uncertainty relations in product and summation forms of metric-adjusted skew information. We present lower bounds on product and summation uncertainty inequalities based on metric-adjusted skew information via operator representation of observables. Explicit examples are provided to back our claims.
