How to achieve an arbitrary real-valued probability amplitude in the general single-partite or multipartite quantum system without measuring any other quantum state's probability amplitude? How to achieve an arbitrary real-valued probability amplitude with the deterministic polynomial time's complexity under a small given error? In this paper, one novel quantum measurement scheme is proposed to solve these questions based on the idea of binary searching. First, the measurement algorithm with the exponential speed-up on the quantum state with one single qubit is well-designed. Then, the measurement algorithm is extended to the quantum states in the general multipartite quantum system and the special multipartite quantum system. The theoretical analysis proves that the proposed quantum measurement scheme has the performance in quantum information processing with twofold advantages: separable measurement and exponential speed up.
In this paper we present a method for representing continuous signals with high precision by interpolating quantum state amplitudes. The method is inspired by the Nyquist-Shannon sampling theorem, which links continuous and discrete time signals. This method extends our previous method of computing generalized inner products from integer-valued functions to real-valued functions.
Positive operator valued measurements (POVMs) play an important role in efficient quantum communication and computation. While optical systems are one of the strongest candidates for long distance quantum communication and information processing, efficient methods to implement POVMs in these systems are scarce. Here we propose an all-optical scheme to implement an arbitrary POVM using linear optical components on m-dimensional Hilbert space of internal degrees of freedom. Linear optical nature of the proposed scheme makes it efficient and robust. We show how the scheme can be applied for state…
The Inverse Born Rule Equivalence. On the Informational Limits of Real-Valued Amplitude Encodings and the Measurement of Quantum Advantage in Data Embeddings
Military University of Technology（军事理工大学）；Enquanted；Deakin University（迪肯大学）；Institute of Physics, University of Silesia in Katowice（卡托维兹西里西亚大学物理研究所）；Cardinal Stefan Wyszynski University in Warsaw（华沙卡罗尔·斯特凡·维辛斯基大学）
We tackle the dynamical description of the quantum measurement process, by explicitly addressing the interaction between the system under investigation with the measurement apparatus, the latter ultimately considered as macroscopic quantum object. We consider arbitrary Positive Operator Valued Measures (POVMs), such that the orthogonality constraint on the measurement operators is relaxed. We show that, likewise the well-known von-Neumann scheme for projective measurements, it is possible to build up a dynamical model holding a unitary propagator characterized by a single time-independent Hami…
Solution to the Mean King's problem with mutually unbiased bases for arbitrary levels
本文重新考虑了任意d-水平系统的互无偏基的平均王问题。Hayashi，Horibe和Hashimoto [Phys. Rev. A 71，052331（2005）]将问题与d-1相互正交拉丁方的最大集合的存在性相关，在其限制设置中，仅允许测量投影值测度。然而，我们无法找到解决问题的方法，例如，d=6或d=10。在对比他们的结果，我们表明，国王的问题总是有一个解决方案的任意水平，如果我们也允许积极的运营商价值的措施。在构造解时，我们使用组合设计理论中的正交表。
The Precise Formula in a Sine Function Form of the norm of the Amplitude and the Necessary and Sufficient Phase Condition for Any Quantum Algorithm with Arbitrary Phase Rotations
The Clauser-Horne-Shimony and Holt inequality applies when measurements with binary outcomes are performed on physical systems under the assumption of local realism. Testing such inequalities in the quantum realm usually involves either measurements of two--valued quantum observables or pre-defining a context dependent binning procedure. Here we establish the conditions to test the Clauser-Horne-Shimony and Holt inequality using any quantum observable. Our result applies to observables with an arbitrary spectrum and no prior knowledge of their underlying Hilbert space's dimension is required. …
We study the performance of a partially correlated amplitude damping channel acting on two qubits. We derive lower bounds for the single-shot classical capacity by studying two kinds of quantum ensembles, one which allows to maximize the Holevo quantity for the memoryless channel and the other allowing the same task but for the full-memory channel. In these two cases, we also show the amount of entanglement which is involved in achieving the maximum of the Holevo quantity. For the single-shot quantum capacity we discuss both a lower and an upper bound, achieving a good estimate for high values…
The process of nonlinear electron-positron pair production by an electron colliding with an arbitrary plane wave electromagnetic field (nonlinear trident pair production) is studied analytically and numerically. Special emphasis is put on the properties of the transition amplitude. In fact, its original expression as resulting from applying the Wick's theorem turns out to be divergent and not to manifestly fulfill gauge invariance. By restoring the latter, the amplitude is regularized and investigated in different regimes. In particular, the amplitude is divided into a two-step and a one-step …
The squeezed state is important in quantum metrology and quantum information. The most effective generation tool known is the optical parametric oscillator (OPO). Currently, only the squeezed states of lower-order spatial modes can be generated by an OPO. However, the squeezed states of higher-order complex spatial modes are more useful for applications such as quantum metrology, quantum imaging and quantum information. A major challenge for future applications is efficient generation. Here, we use cascaded phase-only spatial light modulators to modulate the amplitude and phase of the incident…
