Quantum watermarking based on threshold segmentation using quantum informational entropy

We propose a new quantum watermarking scheme based on threshold selection using informational entropy of quantum image. The core idea of this scheme is to embed information into object and background of cover image in different ways. First, a threshold method adopting the quantum informational entropy is employed to determine a threshold value. The threshold value can then be further used for segmenting the cover image to a binary image, which is an authentication key for embedding and extraction information. By a careful analysis of the quantum circuits of the scheme, that is, translating into the basic gate sequences which show the low complexity of the scheme. One of the simulation-based experimental results is entropy difference which measures the similarity of two images by calculating the difference in quantum image informational entropy between watermarked image and cover image. Furthermore, the analyses of peak signal-to-noise ratio, histogram and capacity of the scheme are also provided.     

Encoding entanglement-assisted quantum stabilizer codes

We address the problem of encoding entanglement-assisted (EA) quantum error-correcting codes (QECCs) and of the corresponding complexity. We present an iterative algorithm from which a quantum circuit composed of CNOT, H, and S gates can be derived directly with complexity O(n²) to encode the qubits being sent. Moreover, we derive the number of each gate consumed in our algorithm according to which we can design EA QECCs with low encoding complexity. Another advantage brought by our algorithm is the easiness and efficiency of programming on classical computers.     

Quantum Privacy Amplification for a Sequence of Single Qubits

We present a scheme for quantum privacy amplification (QPA) for a sequence of single qubits. The QPA procedure uses a unitary operation with two controlled-not gates and a Hadamard gate. Every two qubits are performed with the unitary gate operation, and a measurement is made on one photon and the other one is retained.The retained qubit carries the state information of the discarded one. In this way, the information leakage is reduced.The procedure can be performed repeatedly so that the information leakage is reduced to any arbitrarily low level. With this QPA scheme, the quantum secure direct communication with single qubits can be implemented with arbitrarily high security. We also exploit this scheme to do privacy amplification on the single qubits in quantum information sharing for long-distance communication with quantum repeaters.     

Quantum Privacy Amplification for a Sequence of Single Qubits

We present a scheme for quantum privacy amplification （QPA） for a sequence of single qubits. The QPA procedure uses a unitary operation with two controlled-not gates and a Hadamard gate. Every two qubits are performed with the unitary gate operation, and a measurement is made on one photon and the other one is retained. The retained qubit carries the state information of the discarded one. In this way, the information leakage is reduced. The procedure can be performed repeatedly so that the information leakage is reduced to any arbitrarily low level. With this QPA scheme, the quantum secure direct communication with single qubits can be implemented with arbitrarily high security. We also exploit this scheme to do privacy amplification on the single qubits in quantum information sharing for long-distance communication with quantum repeaters.     

Normally Ordered Quantum Gate Operators for Continuum Variables as Images of Classical Transforms

We derive normally ordered quantum gate operators for continuum variables by mapping classical transforms onto Fock space. Successive gate operations can be treated in a unified way that is using the technique of integration within an ordered product of operators.     

Quantum computing methods for electronic states of the water molecule

ABSTRACT

We compare recently proposed methods to compute the electronic state energies of the water molecule on a quantum computer. The methods include the phase estimation algorithm based on Trotter decomposition, the phase estimation algorithm based on the direct implementation of the Hamiltonian, direct measurement based on the implementation of the Hamiltonian and a specific variational quantum eigensolver, Pairwise VQE. After deriving the Hamiltonian using STO-3G basis, we first explain how each method works and then compare the simulation results in terms of gate complexity and the number of measurements for the ground state of the water molecule with different O–H bond lengths. Moreover, we present the analytical analyses of the error and the gate-complexity for each method. While the required number of qubits for each method is almost the same, the number of gates and the error vary a lot. In conclusion, among methods based on the phase estimation algorithm, the second-order direct method provides the most efficient circuit implementations in terms of the gate complexity. Moreover, Pairwise VQE serves the most practical method for near-term applications on the current available quantum computers. Finally the possibility of extending the calculation to excited states and resonances is discussed.     

高维辅助的普适量子线路优化

受到Lanyon等(Lanyon B P et al 2008 Nature Physics. 5 134)利用高维Hilbert空间成功简化Toffoli门的启发, 本文将辅助维度应用到普适量子线路中, 结合Cosine-Sine Decomposition(CSD), Quantum Shannon Decomposition(QSD)等矩阵分解方法, 优化了两比特和三比特普适幺正量子线路, 给出了计算n比特普适量子线路复杂度的公式, 并利用线性光学和腔QED系统设计了实验方案. 结果表明, 两比特和三比特量子线路的复杂度已分别接近和优于目前最优结果, 且随着比特数的增加, 本方案的优势愈加明显.     

Non-Geometric Conditional Phase Gate by Quantum Zeno Dynamics in Laser-Excited Nitrogen-Vacancy Centers

Based on the quantum Zeno dynamics,we propose a two-qubit non-geometric conditional phase gate between two nitrogen-vacancy centers coupled to a whispering-gallery mode cavity.The varying phases design of periodic laser can be used for realizing non-geometric conditional phase gate,and the cavity mode is virtually excited during the gate operation.Thus,the fidelity of the gate operation is insensitive to cavity decay and the fluctuation of the preset laser intensity.The numerical simulation with a realistic set of experimental parameters shows that the gate fidelity 0.987 can be within reached in the near future.     

Polarization-Dependent Mode Analyzer and Controlled-Z Gate in Ti:LiNbO3 Quantum Photonic Circuits

Abstract

On-chip integrated photonic circuits are crucial for further progress toward quantum technologies and in the science of quantum optics. The quantum controlled-Z gate is an example of the maximally entangling gate, which is universal for quantum computing when coupled with single-qubit gates. This article demonstrates a deterministic controlled-Z photonic quantum gate based on titanium in-diffused channel waveguides in which polarization and modal degrees of freedom of a single photon are used for encoding the control and target qubits, respectively.     

Detecting and quantifying temporal correlations in stochastic resonance via information theory measures

We show that Information Theory quantifiers are suitable tools for detecting and for quantifying noise-induced temporal correlations in stochastic resonance phenomena. We use the Bandt & Pompe (BP) method [Phys. Rev. Lett. 88, 174102 (2002)] to define a probability distribution, P, that fully characterizes temporal correlations. The BP method is based on a comparison of neighboring values, and here is applied to the temporal sequence of residence-time intervals generated by the paradigmatic model of a Brownian particle in a sinusoidally modulated bistable potential. The probability distribution P generated via the BP method has associated a normalized Shannon entropy, H[P], and a statistical complexity measure, C[P], which is defined as proposed by Rosso et al. [Phys. Rev. Lett. 99, 154102 (2007)]. The statistical complexity quantifies not only randomness but also the presence of correlational structures, the two extreme circumstances of maximum knowledge (“perfect order") and maximum ignorance (“complete randomness") being regarded an “trivial", and in consequence, having complexity C = 0. We show that both, H and C, display resonant features as a function of the noise intensity, i.e., for an optimal level of noise the entropy displays a minimum and the complexity, a maximum. This resonant behavior indicates noise-enhanced temporal correlations in the sequence of residence-time intervals. The methodology proposed here has great potential for the precise detection of subtle signatures of noise-induced temporal correlations in real-world complex signals.     

Towards optimization of quantum circuits

Any unitary operation in quantum information processing can be implemented via a sequence of simpler steps — quantum gates. However, actual implementation of a quantum gate is always imperfect and takes a finite time. Therefore, searching for a short sequence of gates — efficient quantum circuit for a given operation, is an important task. We contribute to this issue by proposing optimization of the well-known universal procedure proposed by Barenco et al. [Phys. Rev. A 52, 3457 (1995)]. We also created a computer program which realizes both Barenco’s decomposition and the proposed optimization. Furthermore, our optimization can be applied to any quantum circuit containing generalized Toffoli gates, including basic quantum gate circuits.      

Error-detected three-photon hyperparallel Toffoli gate with state-selective reflection

We present an error-detected hyperparallel Toffoli (hyper-Toffoli) gate for a three-photon system based on the interface between polarized photon and cavity-nitrogen-vacancy (NV) center system. This hyper-Toffoli gate can be used to perform double Toffoli gate operations simultaneously on both the polarization and spatial-mode degrees of freedom (DoFs) of a three-photon system with a low decoherence, shorten operation time, and less quantum resources required, in compared with those on two independent three-photon systems in one DoF only. As the imperfect cavity-NV-center interactions are transformed into the detectable failures rather than infidelity based on the heralding mechanism of detectors, a near-unit fidelity of the quantum hyper-Toffoli gate can be implemented. By recycling the procedures, the efficiency of our protocol for the hyper-Toffoli gate is improved further. Meanwhile, the evaluation of gate performance with achieved experiment parameters shows that it is feasible with current experimental technology and provides a promising building block for quantum compute.     

Unconventional Geometric Phase-Shift Gates Based on Superconducting Quantum Interference Devices Coupled to a Single-Mode Cavity

We present a scheme to realize geometric phase-shift gate for two superconducting quantum interference device (SQUID) qubits coupled to a single-mode microwave field. The geometric phase-shift gate operation is performed transitions during the gate operation. Thus, the docoherence due to energy spontaneous emission based on the levels of SQUIDs are suppressed. The gate is insensitive to the cavity decay throughout the operation since the cavity mode is displaced along a circle in the phase space, acquiring a phase conditional upon the two lower flux states of the SQUID qubits, and the cavity mode is still in the original vacuum state. Based on the SQUID qubits interacting with the cavity mode, our proposed approach may open promising prospects for quantum logic in SQUID-system.     

Remote interactions between two d-dimensional distributed quantum systems： nonlocal generalized quantum control-NOT gate and entanglement swapping

We present a systematic simple method to implement a generalized quantum control-NOT （CNOT） gate on two d-dimensional distributed systems. First, we show how the nonlocal generalized quantum CNOT gate can be implemented with unity fidelity and unity probability by using a maximally entangled pair of qudits as a quantum channel. We also put forward a scheme for probabilistically implementing the nonlocal operation with unity fidelity by employing a partially entangled qudit pair as a quantum channel. Analysis of the scheme indicates that the use of partially entangled quantum channel for implementing the nonlocal generalized quantum CNOT gate leads to the problem of ＇the general optimal information extraction＇. We also point out that the nonlocal generalized quantum CNOT gate can be used in the entanglement swapping between particles belonging to distant users in a communication network and distributed quantum computer.[第一段]     

Consideration for Affects of an XOR in a Random Number Generator Using Ring Oscillators

A cloud service to offer entropy has been paid much attention to. As one of the entropy sources, a physical random number generator is used as a true random number generator, relying on its irreproducibility. This paper focuses on a physical random number generator using a field-programmable gate array as an entropy source by employing ring oscillator circuits as a representative true random number generator. This paper investigates the effects of an XOR gate in the oscillation circuit by observing the output signal period. It aims to reveal the relationship between inputs and the output through the XOR gate in the target generator. The authors conduct two experiments to consider the relevance. It is confirmed that combining two ring oscillators with an XOR gate increases the complexity of the output cycle. In addition, verification using state transitions showed that the probability of the state transitions was evenly distributed by increasing the number of ring oscillator circuits.     

功能磁共振成像的基本尺度熵分析

人体大脑活动的复杂度随年龄变化而变化, 并且和性别有一定的联系, 通过对功能磁共振成像复杂度的分析有助于发现人脑活动和性别年龄之间关系的规律. 本文提出需要根据年龄段的变化对基本尺度熵的参数做适当的调整, 以便获得良好的信号区分效果. 本文研究了人脑活动和性别年龄之间存在的关系. 结果证明, 同龄男女的基本尺度熵值存在一定的差异, 并且随年龄段的不同发生相应的变化, 另外基本尺度熵中的参数在数据分析中也随年龄变化存在一定规律的变化. 通过对fMRI数据的分析表明, 基本尺度熵能够有效地区分不同人群fMRI数据特征, 为进一步信号复杂度分析提供方便. 关键词： 功能磁共振成像 基本尺度熵 复杂度     

Unconventional Geometric Phase-Shift Gates Based on Superconducting Quantum Interference Devices Coupled to a Single-Mode Cavity

We present a scheme to realize geometric phase-shift gate for two superconducting quantum interference device （SQUID） qubits coupled to a single-mode microwave field. The geometric phase-shift gate operation is performed in two lower flux states, and the excited state [2〉 would not participate in the procedure. The SQUIDs undergo no transitions during the gate operation. Thus, the docoherence due to energy spontaneous emission based on the levels of SQUIDs are suppressed. The gate is insensitive to the cavity decay throughout the operation since the cavity mode is displaced along a circle in the phase space, acquiring a phase conditional upon the two lower flux states of the SQUID qubits, and the cavity mode is still in the original vacuum state. Based on the SQUID qubits interacting with the cavity mode, our proposed approach may open promising prospects for quantum iogic in SQUID-system.     

Quantum Statistic Entropy of Three-Dimensional BTZ Black Hole

Using the new equation of state density motivated by the generalized uncertainty relation in the quantum gravity, we investigate entropy of a black line on the background of the three-dimensional BTZ. In our calculation, we need not introduce cutoff and can remove the divergent term in the original brick-wall method via the new equation of state density. And it is obtained that the entropy of the black line is proportional to the area of the horizon (perimeter). Further it is shown the entropy of black line is the entropy of quantum state on the surface of horizon (perimeter). The black line entropy is the intrinsic property of the black hole. The entropy is a quantum effect. By using quantum statistical method, we directly obtain the partition function of Bose field and fermi field on the background of the black line. The difficulty to solve wave equation of various particles is avoided. We offer a new simple and direct way for calculating the entropy of various spacetime black holes (black plane, black line and black column). PACS 04.20.Dw; 97.60.Lf     

Quantum Work Statistics with Initial Coherence

The two-point measurement scheme for computing the thermodynamic work performed on a system requires it to be initially in equilibrium. The Margenau–Hill scheme, among others, extends the previous approach to allow for a non-equilibrium initial state. We establish a quantitative comparison between both schemes in terms of the amount of coherence present in the initial state of the system, as quantified by the l1-coherence measure. We show that the difference between the two first moments of work, the variances of work, and the average entropy production obtained in both schemes can be cast in terms of such initial coherence. Moreover, we prove that the average entropy production can take negative values in the Margenau–Hill framework.