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We point out that the main results—the analytic expressions for the Groverian measure of entanglement, in the above mentioned paper are erroneous. The technical mistake of the paper is discussed. It is shown by an explicit example that the formula for calculating the Groverian measure yields $${G(|\psi\rangle)=0}$$ for some entangled states. [ABSTRACT FROM AUTHOR]

This paper presents a quantum image steganography algorithm based on HSI color space embedding technique. To increase the security of sensitive information, a three-dimensional hyperchaotic system incorporating sinusoidal mapping, Henon mapping, and Cubic mapping using the cascade modulation method is first presented. Additionally, a brand-new steganography algorithm built on the HSI color space embedding method is suggested in this study. The effective pixel information of three channels can be concentrated in one intensity channel by converting color images from RGB to HSI, which decreases the null domain steganography algorithm's time and space complexity. In the meantime, a successful quantum steganography circuit is created. The simulation and numerical analysis results show that the algorithm has good invisibility, security, and robustness. [ABSTRACT FROM AUTHOR]

Due to the fact that many classical numerical methods have not yet mature quantum counterparts, quantum circuit design is very important in quantum image processing. In this paper, using the novel enhanced quantum representation (NEQR) model, an image encryption algorithm based on Feistel structure is carried out in quantum computer by giving the encryption quantum circuits. First, the modified Feistel structure for image encryption is proposed. It is a 128-bit block cipher and requires 16-bit subkeys to encrypt the image, and it is a mixture of Feistel and substitution–permutation network; then, the detailed quantum circuits design of the encryption algorithm are given. Through numerical simulation and analysis, it is verified that the proposed quantum image encryption algorithm is effective and can resist statistical attacks effectively. [ABSTRACT FROM AUTHOR]

A novel quantum steganography scheme is investigated based on efficient embedding algorithm of modified exploiting modification direction in this paper, which embeds two 2 n × 2 n binary images (secret information) into a 2 n × 2 n color image (carrier image). To improve the security of the secret information and enhance the robustness of the proposed scheme, a 2 n × 2 n binary image (secret key) is generated according to the exclusive or operation of two secret images. The secret key acts as the control key of choosing two channels from the carrier image's three channels of R, G and B (i.e., R, G or R, B channels chose as the pixel-group) to hide the secret information. In addition, the effective quantum circuits for investigated quantum steganography scheme are illustrated to better understanding the procedure of embedding algorithm. The experiment results simulated on the classical computer with MATLAB environment, and the numerical analyses demonstrate that the presented algorithm has good performance on imperceptibility and security. [ABSTRACT FROM AUTHOR]

Based on the modified flexible representation of quantum images, a novel quantum image encryption algorithm was proposed in this paper. The encryption process performs Arnold scrambling operation to disturb the quantum image information in spatial domain first. Then, quantum wavelet transforms are employed to decompose the scrambled quantum image into multiscale resolution (i.e., a sequence of subimages) in the frequency domain, which are mainly divided into two parts: the low-frequency component (i.e., the approximation) and high-frequency detail information (i.e., the horizontal details, vertical details and diagonal details in each decomposition level). Following that, Arnold scrambling operations are implemented to encrypt the wavelet coefficients within each subimage in the frequency domain once again. Finally, based on inverse quantum wavelet transforms, the encrypted wavelet coefficients can affect the pixel values of the entire reconstructed quantum images. Due to the fact that all the quantum operations are invertible, the decryption process of the encrypted image is performed in a straightforward manner by reversing all of the quantum operations within quantum image encryption process. The proposed encryption algorithm is simulated on a classical computer with MATLAB environments. Experimental results and numerical analysis indicate that the presented algorithm has a good encrypted effect and high security. [ABSTRACT FROM AUTHOR]

This paper is concerned with the feasibility of the classical nearest-neighbor interpolation based on flexible representation of quantum images (FRQI) and novel enhanced quantum representation (NEQR). Firstly, the feasibility of the classical image nearest-neighbor interpolation for quantum images of FRQI and NEQR is proven. Then, by defining the halving operation and by making use of quantum rotation gates, the concrete quantum circuit of the nearest-neighbor interpolation for FRQI is designed for the first time. Furthermore, quantum circuit of the nearest-neighbor interpolation for NEQR is given. The merit of the proposed NEQR circuit lies in their low complexity, which is achieved by utilizing the halving operation and the quantum oracle operator. Finally, in order to further improve the performance of the former circuits, new interpolation circuits for FRQI and NEQR are presented by using Control-NOT gates instead of a halving operation. Simulation results show the effectiveness of the proposed circuits. [ABSTRACT FROM AUTHOR]

Various constraints concerning control fields can be imposed in the realistic implementations of quantum control systems. One of the most important is the restriction on the frequency spectrum of acceptable control parameters. It is important to consider the limitations of experimental equipment when trying to find appropriate control parameters. Therefore, in this paper, we present a general method of obtaining a piecewise-constant controls, which are robust with respect to spectral constraints. We consider here a Heisenberg spin chain; however, the method can be applied to a system with more general interactions. To model experimental restrictions, we apply an ideal low-pass filter to numerically obtained control pulses. The usage of the proposed method has negligible impact on the control quality as opposed to the standard approach, which does not take into account spectral limitations. [ABSTRACT FROM AUTHOR]

Quantum walks subject to decoherence generically suffer the loss of their genuine quantum feature, a quadratically faster spreading compared to classical random walks. This intuitive statement has been verified analytically for certain models and is also supported by numerical studies of a variety of examples. In this paper we analyze the long-time behavior of a particular class of decoherent quantum walks, which, to the best of our knowledge, was only studied at the level of numerical simulations before. We consider a local coin operation which is randomly and independently chosen for each time step and each lattice site and prove that, under rather mild conditions, this leads to classical behavior: With the same scaling as needed for a classical diffusion the position distribution converges to a Gaussian, which is independent of the initial state. Our method is based on non-degenerate perturbation theory and yields an explicit expression for the covariance matrix of the asymptotic Gaussian in terms of the randomness parameters. [ABSTRACT FROM AUTHOR]

We present a quantum-like (QL) model in that contexts (complexes of e.g. mental, social, biological, economic or even political conditions) are represented by complex probability amplitudes. This approach gives the possibility to apply the mathematical quantum formalism to probabilities induced in any domain of science. In our model quantum randomness appears not as irreducible randomness (as it is commonly accepted in conventional quantum mechanics, e.g., by von Neumann and Dirac), but as a consequence of obtaining incomplete information about a system. We pay main attention to the QL description of processing of incomplete information. Our QL model can be useful in cognitive, social and political sciences as well as economics and artificial intelligence. In this paper we consider in a more detail one special application–QL modeling of brain’s functioning. The brain is modeled as a QL-computer. [ABSTRACT FROM AUTHOR]

The system in consideration is a singular simple cubic cell of spins s = 1 2 doped in centre with additional spin S = 1 . The structure is located in external magnetic field and is undergoing dissipative, Markovian evolution. The analysis of system time evolution is focused on the entanglement evaluation and determination of its behaviour over time. We found out the distinct effect of doping the structure with additional spin S = 1 in the time evolution of the bipartite entanglement in | W ⟩ state. We also distinguished the raising and lowering spin interaction with environment and determined its impact on decoherence. Furthermore, we have shown that the entanglement between spins is in the form of a damped superposition of Gaussian functions. Its pulsed nature results from the unitary evolution in spin structure, while the damping is caused by the influence of the environment. [ABSTRACT FROM AUTHOR]

In this paper, we develop a theory of learning nonlinear input–output maps with fading memory by dissipative quantum systems, as a quantum counterpart of the theory of approximating such maps using classical dynamical systems. The theory identifies the properties required for a class of dissipative quantum systems to be universal, in that any input–output map with fading memory can be approximated arbitrarily closely by an element of this class. We then introduce an example class of dissipative quantum systems that is provably universal. Numerical experiments illustrate that with a small number of qubits, this class can achieve comparable performance to classical learning schemes with a large number of tunable parameters. Further numerical analysis suggests that the exponentially increasing Hilbert space presents a potential resource for dissipative quantum systems to surpass classical learning schemes for input–output maps. [ABSTRACT FROM AUTHOR]

In this paper, a polarization-coding scheme for subcarrier multiplexing quantum key distribution (SCM-QKD) is proposed, in which the overall QKD can be substantially increased by relying on parallel sideband channels. The polarization state of each sideband can be randomly and independently synthesized by controlling the phase difference of subcarriers. We derive the mathematical formulas of quantum bit error rate (QBER). Both the theoretical analysis and the numerical results show that an efficient implementation of BB84 protocol is feasible. By the proposed polarization coding in a parallel QKD system, without relying on dispersion compensation, a 6% performance gain in terms of correct bit rate over the conventional BB84 protocol (i.e., without polarization coding) is obtained. More importantly, the proposed polarization-coding-aided SCM-QKD can help achieve a long-distance QKD with a low QBER. [ABSTRACT FROM AUTHOR]

Boson sampling (BS) is an elegant candidate for the proof of quantum supremacy, and the exploration of its practical cryptographic applications is just at the beginning, including one-way functions, private-key cryptography and quantum signature. In order to investigate improvement methods for the combination of cryptography and BS, we propose a quantum hash function with grouped coarse-grained boson sampling (GCGBS) by making full use of the multi-photon characteristics of BS with undiluted conditions, which can eliminate the uncertain outputs, achieve repeatability and reduce the difficulty of experiment. The theoretical analysis and numerical simulation demonstrate an irreversible, anti-collision, anti-brute force search and uniform-distributed GCGBS-based hash function can be achieved with limited resource-consumption. [ABSTRACT FROM AUTHOR]

A scheme is presented for generating steady three- (four-) dimensional entangled states for two atoms trapped in a strongly dissipative single-mode (double-mode) cavity via quantum-jump-based feedback. The cavity decay is no longer undesirable, but plays an integral part in the schemes. Numerical results show that the target states could be obtained from any initial states via quantum-jump-based feedback. Moreover, our scheme is insensitive to moderate fluctuations of experimental parameters and detection inefficiencies without atomic decay since the system can always reach the target state. Nevertheless, the atomic decay still plays a negative role in the current scheme. The scheme can be generalized to realize $$N$$ -dimensional entanglement for two atoms. [ABSTRACT FROM AUTHOR]

By Lyapunov control, we present a protocol to prepare entangled states such as Bell states in the context of cavity QED system. The advantage of our method is of threefold. Firstly, we can only control the phase of classical fields to complete the preparation process. Secondly, the evolution time is sharply shortened when compared to adiabatic control. Thirdly, the final state is steady after removing control fields. The influence of decoherence caused by the atomic spontaneous emission and the cavity decay is discussed. The numerical results show that the control scheme is immune to decoherence, especially for the atomic spontaneous emission from $$|2\rangle $$ to $$|1\rangle $$ . This can be understood as the state staying in an invariant subspace. Finally, we generalize this method in preparation of W state. [ABSTRACT FROM AUTHOR]

Curiously overlooked in physics is its dependence on the transmission of numbers. For example, the transmission of numerical clock readings is implicit in the concept of a coordinate system. The transmission of numbers and other logical distinctions is often achieved over a computer-mediated communications network in the face of an unpredictable environment. By unpredictable we mean something stronger than the spread of probabilities over given possible outcomes, namely an opening to unforeseeable possibilities. Unpredictability, until now overlooked in theoretical physics, makes the transmission of numbers interesting. Based on recent proofs within quantum theory that provide a theoretical foundation to unpredictability, here we show how regularities in physics rest on a background of channels over which numbers are transmitted. As is known to engineers of digital communications, numerical transmissions depend on coordination reminiscent of the cycle of throwing and catching by players tossing a ball back and forth. In digital communications, the players are computers, and the required coordination involves unpredictably adjusting 'live clocks' that step these computers through phases of a cycle. We show how this phasing, which we call logical synchronization, constrains number-carrying networks, and, if a spacetime manifold in invoked, put 'stripes' on spacetime. Via its logically synchronized channels, a network of live clocks serves as a reference against which to locate events. Such a network in any case underpins a coordinate frame, and in some cases the direct use of a network can be tailored to investigate an unpredictable environment. Examples include explorations of gravitational variations near Earth. [ABSTRACT FROM AUTHOR]

The transfer of quantum entanglement (or quantum coherence) is not only fundamental in quantum mechanics but also important in quantum information processing. We here propose a way to achieve the coherent transfer of W-class entangled states of qubits among different cavities. Because no photon is excited in each cavity, decoherence caused by the photon decay is suppressed during the transfer. In addition, only one coupler qubit and one operational step are needed and no classical pulses are used in this proposal; thus, the engineering complexity is much reduced and the operation is greatly simplified. We further give a numerical analysis showing that high-fidelity transfer of a three-qubit W state is feasible within the present circuit QED technique. The proposal can be applied to a wide range of physical implementations with various qubits such as quantum dots, nitrogen vacancy centers, atoms, and superconducting qubits. [ABSTRACT FROM AUTHOR]

Quantum discord Q is a function of density matrix elements. The domain of such a function in the case of two-qubit system with X density matrix may consist of three subdomains at most: two ones where the quantum discord is expressed in closed analytical forms ( $$Q_{\pi /2}$$ and $$Q_0$$ ) and an intermediate subdomain for which, to extract the quantum discord $$Q_{\theta }$$ , it is required to solve numerically a one-dimensional minimization problem to find the optimal measurement angle $$\theta \in (0,\pi /2)$$ . Hence, the quantum discord is given by a piecewise analytical-numerical formula $$Q=\min \{Q_{\pi /2},Q_{\theta },Q_0\}$$ . It is shown that the boundaries between the subdomains consist of bifurcation points. The $$Q_{\theta }$$ subdomains are discovered in the dynamical phase flip channel model, in the anisotropic spin systems at thermal equilibrium, and in the heteronuclear dimers in an external magnetic field. We found that the transitions between $$Q_{\theta }$$ subdomain and $$Q_{\pi /2}$$ and $$Q_0$$ ones occur suddenly, but continuously and smoothly, i.e., nonanalyticity is hidden and can be observed in higher order derivatives of discord function. [ABSTRACT FROM AUTHOR]

Usually, a shared reference frame is indispensable for practical quantum key distribution (QKD) systems. As a result, most QKD systems need active alignment of reference frame due to the unknown and slowly variances of reference frame introduced by environment. Quite interestingly, reference-free-independent (RFI) QKD can generate secret-key bits without alignment of reference frame. However, RFI QKD may be still vulnerable to detector side channel attacks. Here, we propose a new RFI QKD protocol, in which all detector side channels are removed. Furthermore, our protocol can still tolerate unknown and slow variance of reference frame without active alignment. And a numerical simulation shows that long security distance is probable in this protocol. [ABSTRACT FROM AUTHOR]

We characterize and discuss the identifiability condition for quantum process tomography, as well as the minimal experimental resources that ensure a unique solution in the estimation of quantum channels, with both direct and convex optimization methods. A convenient parametrization of the constrained set is used to develop a globally converging Newton-type algorithm that ensures a physically admissible solution to the problem. Numerical simulation is provided to support the results and indicate that the minimal experimental setting is sufficient to guarantee good estimates. [ABSTRACT FROM AUTHOR]

A non-Hermitian quantum optimization algorithm is created and used to find the ground state of an antiferromagnetic Ising chain. We demonstrate analytically and numerically (for up to $$N=1,024$$ spins) that our approach leads to a significant reduction in the annealing time that is proportional to $$\ln N$$ , which is much less than the time (proportional to $$N^2$$ ) required for the quantum annealing based on the corresponding Hermitian algorithm. We propose to use this approach to achieve similar speed-up for NP-complete problems by using classical computers in combination with quantum algorithms. [ABSTRACT FROM AUTHOR]

We present a scheme to implement quantum computation in decoherence-free subspaces (DFSs) with four atoms in a single-mode cavity. A four-dimensional DFS is constituted to protect quantum information when the full symmetry of interaction between system and environment is broken in a specific way, and entangling two-qubit logic gates and noncommuting single-qubit gates are implemented in such DFS. The gate fidelity is numerically calculated, and the feasibility of the approximations taken in this work is verified based on the numerical calculations. [ABSTRACT FROM AUTHOR]

We propose an alternative scalable way to generate multi-color entangled optical beams efficiently utilizing the tripartite entanglement existent between three fields—signal, idler, and pump—from a nondegenerate optical parametric oscillator (NOPO) operating above the threshold. The special case of two cascaded NOPOs is studied, as it is shown that the five beams with very different frequencies are generated by NOPOA (one of the retained signal and idler beams, and the reflected pump beam) and NOPOB (the output signal and idler beams, and the reflected pump beam). These beams are theoretically demonstrated to be continuous variable (CV) entangled with each other by applying the positivity of the partially transposed criterion for the inseparability of multipartite CV entanglement. The symplectic eigenvalues of the partial transposition covariance matrix of the obtained optical entangled state are numerically calculated in terms of experimentally reachable system parameters. The optimal operation conditions to achieve high five-color entanglement are presented. As the cavity parameters and the nonlinear crystals of the two NOPOs can be chosen freely, the frequencies of the submodes in the entangled state thus are adjustable to match the transition frequencies of atoms or low loss fiber-optic communication window. The calculated results provide direct references for future experiment to generate multi-color entangled optical beams efficiently by means of NOPOs operating above the threshold. [ABSTRACT FROM AUTHOR]

We propose two schemes to generate three-qubit decoherence-free state for atoms trapped in a cavity via quantum Zeno dynamics. The influence of various decoherence processes such as spontaneous emission and photon loss on the fidelity of the entangled state is investigated. Numerical results show that the schemes are robust against the cavity decay since the evolution of the system is restricted to a subspace with null-excitation cavity fields. Moreover, no measurement, post selection and auxiliary bits are needed during the whole process. [ABSTRACT FROM AUTHOR]

We propose an efficient scheme for generation of three-atom singlet state in a bimodal cavity based on quantum Zeno dynamics and the large detuning condition. The influence of decoherence induced by cavity decay and atomic spontaneous emission is also discussed by numerical calculation. The advantages of the scheme are that the initial input states of atoms are not entangled and the fidelity is insensitive to cavity decay and atomic spontaneous emission due to no exciting the cavity fields during the whole evolution and the large detuning condition. [ABSTRACT FROM AUTHOR]

We propose a scheme for fast synthesizing the Fredkin gate with rf SQUID qubits. This scheme utilizes the quantum Zeno dynamics induced by continuous couplings and the non-identical couplings between SQUIDs and superconducting cavity. The effects of decoherence on the performance for the gate are analyzed in virtue of master equation and non-unitary evolution with full Hamiltonian. The strictly numerical simulation shows that the fidelity of this Fredkin gate is relatively high corresponding to current typical experimental parameters. Furthermore, an equivalent physical model is also constructed in an array of coupled cavities. [ABSTRACT FROM AUTHOR]

The dynamics of classical and quantum correlations under nondissipative and dissipative decoherences are analytically and numerically investigated with both one-side measures and two-side measures. Specifically, two qubits under local amplitude damping decoherence and depolarizing decoherence channels are considered. We show that, under the action of amplitude damping decoherence, both the entanglement and correlations of the different types of initial states with same initial values, suffer different types of dynamics. Moreover, the transfers of the entanglement and correlations between the system and the environment for different types of initial states are also shown to be different. While for the action of depolarizing decoherence, there does not exist sudden change in the decay rates of both the classical and quantum correlations, which is different from some other nondissipative channels. Furthermore, the quantum dissonance can be found to keep unchanged under the action of depolarizing decoherence. Such different dynamic behaviors of different noisy quantum decoherence channels reveal distinct transmission performance of classical and quantum information. [ABSTRACT FROM AUTHOR]

diabatic quantum computation (AQC) is a universal model for quantum computation which seeks to transform the initial ground state of a quantum system into a final ground state encoding the answer to a computational problem. AQC initial Hamiltonians conventionally have a uniform superposition as ground state. We diverge from this practice by introducing a simple form of heuristics: the ability to start the quantum evolution with a state which is a guess to the solution of the problem. With this goal in mind, we explain the viability of this approach and the needed modifications to the conventional AQC (CAQC) algorithm. By performing a numerical study on hard-to-satisfy 6 and 7 bit random instances of the satisfiability problem (3-SAT), we show how this heuristic approach is possible and we identify that the performance of the particular algorithm proposed is largely determined by the Hamming distance of the chosen initial guess state with respect to the solution. Besides the possibility of introducing educated guesses as initial states, the new strategy allows for the possibility of restarting a failed adiabatic process from the measured excited state as opposed to restarting from the full superposition of states as in CAQC. The outcome of the measurement can be used as a more refined guess state to restart the adiabatic evolution. This concatenated restart process is another heuristic that the CAQC strategy cannot capture. [ABSTRACT FROM AUTHOR]

We analyze continuous-time quantum and classical random walk on spidernet lattices. In the framework of Stieltjes transform, we obtain density of states, which is an efficiency measure for the performance of classical and quantum mechanical transport processes on graphs, and calculate the spacetime transition probabilities between two vertices of the lattice. Then we analytically show that there are two power law decays ∼ t−3 and ∼ t−1.5 at the beginning of the transport for transition probability in the continuous-time quantum and classical random walk, respectively. This results illustrate the decay of quantum mechanical transport processes is quicker than that of the classical one. Due to the result, the characteristic time t c, which is the time when the first maximum of the probabilities occur on an infinite graph, for the quantum walk is shorter than that of the classical walk. Therefore, we can interpret that the quantum transport speed on spidernet is faster than that of the classical one. In the end, we investigate the results by numerical analysis for two examples. [ABSTRACT FROM AUTHOR]

Simple schemes are proposed for implementing deterministic teleportation, superdense coding, and quantum information splitting with W-type entangled states. The physical realization of these schemes should be much simpler than previous ones due to the assistance of an auxiliary particle. We illustrate the ideas in cavity quantum electrodynamics. The important features of our schemes can also be demonstrated in other systems. [ABSTRACT FROM AUTHOR]

We consider discrete-time nearest-neighbor quantum walks on random environments in one dimension. Using the method based on a path counting, we present both quenched and annealed weak limit theorems for the quantum walk. [ABSTRACT FROM AUTHOR]

A M-matrix which satisfies the Hecke algebraic relations is presented. Via the Yang–Baxterization approach, we obtain a unitary solution $${\breve{R}(\theta,\varphi_{1},\varphi_{2})}$$ of Yang–Baxter equation. It is shown that any pure two-qutrit entangled states can be generated via the universal $${\breve{R}}$$-matrix assisted by local unitary transformations. A Hamiltonian is constructed from the $${\breve{R}}$$-matrix, and Berry phase of the Yang–Baxter system is investigated. Specifically, for $${\varphi_{1}\,{=}\,\varphi_{2}}$$, the Hamiltonian can be represented based on three sets of SU(2) operators, and three oscillator Hamiltonians can be obtained. Under this framework, the Berry phase can be interpreted. [ABSTRACT FROM AUTHOR]

With the purpose to reveal consistency between multiple quantum (MQ) coherences and entanglement, we investigate numerically the dynamics of these phenomena in one-dimensional linear chains and ring of nuclear spins 1/2 coupled by dipole–dipole interactions. As opposed to the calculation of the MQ coherence intensity based on the density matrix describing the spin system as a whole, we consider the “differentiated” intensity related only to the chosen spin pair based on the reduced density matrix. It is shown that the entanglement and the MQ coherence have similar dynamics only for nearest neighbors while we did not obtained any consistency for remote spins. [ABSTRACT FROM AUTHOR]

We analyze quantum two prover one round interactive proof systems, in which noninteracting provers can share unlimited entanglement. The maximum acceptance probability is characterized as a superoperator norm. We get some partial results and in particular we analyze the “rank one” case. [ABSTRACT FROM AUTHOR]

We describe a model for the interaction of the internal (spin) degree of freedom of a quantum lattice-gas particle with an environmental bath. We impose the constraints that the particle-bath interaction be fixed, while the state of the bath is random, and that the effect of the particle-bath interaction be parity invariant. The condition of parity invariance defines a subgroup of the unitary group of actions on the spin degree of freedom and the bath. We derive a general constraint on the Lie algebra of the unitary group which defines this subgroup, and hence guarantees parity invariance of the particle-bath interaction. We show that generalizing the quantum lattice gas in this way produces a model having both classical and quantum discrete random walks as different limits. We present preliminary simulation results illustrating the intermediate behavior in the presence of weak quantum noise [ABSTRACT FROM AUTHOR]

We employ a quasirandom methodology, recently developed by Martin Roberts, to estimate the separability probabilities, with respect to the Bures (minimal monotone/statistical distinguishability) measure, of generic two-qubit and two-rebit states. This procedure, based on generalized properties of the golden ratio, yielded, in the course of almost seventeen billion iterations (recorded at intervals of five million), two-qubit estimates repeatedly close to nine decimal places to 25 341 = 5 2 11 · 31 ≈ 0.073313783 . However, despite the use of over twenty-three billion iterations, we do not presently perceive an exact value (rational or otherwise) for an estimate of 0.15709623 for the Bures two-rebit separability probability. The Bures qubit–qutrit case—for which Khvedelidze and Rogojin gave an estimate of 0.0014—is analyzed too. The value of 1 715 = 1 5 · 11 · 13 ≈ 0.00139860 is a well-fitting value to an estimate of 0.00139884. Interesting values (16 12375 = 4 2 3 2 · 5 3 · 11 and 625 109531136 = 5 4 2 12 · 11 2 · 13 · 17 ) are conjectured for the Hilbert–Schmidt (HS) and Bures qubit–qudit ( 2 × 4 ) positive-partial-transpose (PPT)-probabilities. We re-examine, strongly supporting, conjectures that the HS qubit–qutrit and rebit–retrit separability probabilities are 27 1000 = 3 3 2 3 · 5 3 and 860 6561 = 2 2 · 5 · 43 3 8 , respectively. Prior studies have demonstrated that the HS two-rebit separability probability is 29 64 and strongly pointed to the HS two-qubit counterpart being 8 33 and a certain operator monotone one (other than the Bures) being 1 - 256 27 π 2 . [ABSTRACT FROM AUTHOR]

A topic about synthesis of quantum images is proposed, and a specific phase rotation transform constructed is adopted to theoretically realize the synthesis of two quantum images. The synthesis strategy of quantum images comprises three steps, which include: (1) in the stage of phase extraction, we obtain the phases of the state of the quantum image by transforming the state of the quantum image to prepare the conditions for multiple phases extraction. (2) In the stage of rotation operator construction, the phases obtained in the first stage are used to construct the rotation operator where a mechanism is introduced into it to reduce the phase overflow. (3) In the stage of application of the rotation operator, we apply the operator constructed in the second stage on the state of quantum image to get a goal state. Additionally, numerical analysis gives the joint uncertainty relation of the pixel of the synthesized quantum image. The analysis result about the compression ratio indicates that the phase rotation transform and the overflow control mechanism are effective. [ABSTRACT FROM AUTHOR]

We consider the optimal approximation of arbitrary qubit states with respect to an available states consisting the eigenstates of two of three Pauli matrices, the B2-distance of an arbitrary target state. Both the analytical formulae of the B2-distance and the corresponding complete optimal decompositions are obtained. The trade-off relations for both the sum and the squared sum of the B2-distances have been analytically and numerically investigated. [ABSTRACT FROM AUTHOR]