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Recently, Lang suggested a quantum private comparison (QPC) without classical computation (Int J Theor Phys, 59(2020)2984). Lang claimed that this QPC protocol is secure against both the participant attack and the outside attack. It is pointed out in this paper that the third party (TP) can totally obtain the private binary sequences of two communicants by launching a special measurement attack; and moreover, an outside attacker can make this protocol fail by launching the disturbance attack. The corresponding methods are further put forward to overcome these drawbacks.

We propose a new scheme to strengthen the performance of the discrete-modulated continuous-variable measurement-device-independent quantum key distribution (DM-CV-MDI-QKD) protocol by introducing a quantum scissors (QS) operation to Bob’s side. According to the equivalent one-way scheme of the protocol, we further investigate the success probability of the QS operation, and analyze the security of the DM-CV-MDI-QKD equipped with this operation in the asymptotic case. Simulation results show that the QS operation can indeed effectively improve the performance of the existing protocol, and compared with the scheme without QS operation, our proposed scheme has a higher secret key rate and a longer secure transmission distance.

Entanglement-assisted quantum maximum distance separable (MDS) codes form a significant class of quantum codes. By using constacyclic codes, we construct some new classes of q-ary entanglement-assisted quantum error-correcting MDS codes. Most of these codes are new in the sense that their parameters are not covered by the codes available in the literature.

With entanglement-assisted (EA) formalism, arbitrary classical linear codes are allowed to transform into EAQECCs by using pre-shared entanglement between the sender and the receiver. In this paper, based on classical cyclic MDS codes by exploiting pre-shared maximally entangled states, we construct two families of $q$-ary entanglement-assisted quantum MDS codes $[[\frac{q^{2}+1}{a},\frac{q^{2}+1}{a}-2(d-1)+c,d;c]]$, where q is a prime power in the form of $am+l$, and $a=(l^2+1)$ or $a=\frac{(l^2+1)}{5}$. We show that all of $q$-ary EAQMDS have minimum distance upper limit much larger than the known quantum MDS (QMDS) codes of the same length. Most of these $q$-ary EAQMDS codes are new in the sense that their parameters are not covered by the codes available in the literature., arXiv admin note: substantial text overlap with arXiv:1803.04168, arXiv:1912.12031

Quantum correlations are physical resources for quantum information processing. The nonlocal advantage of quantum coherence (NAQC) is a kind of quantum correlation which is stronger than entanglement. We report here methods for enhancing thermal NAQC in the two-site, triangular, and tetrahedral lattices. It is found that for all the considered cases, the NAQC can be noticeably enhanced by introducing the Dzyaloshinsky-Moriya (DM) interaction to two spins and tune the anisotropy of the spin-spin coupling. Besides, the critical temperature below which the thermal NAQC exists can also be noticeably enhanced by introducing the DM interaction. Hence, our results provide a way to achieve NAQC for quantum tasks based on spin lattices.

Quantum secret sharing (QSS) protocols are designed to allow a secret message to be divided into several shadows, and the secret can be reconstructed cooperatively. Motivated by the eight quantum entangled (EQE) state, a tripartite verifiable QSS scheme is proposed. It involves three agents, in four phases, i.e., shadow distribution phase, eavesdropping detection phase, measurement and secret sharing phase, verification and secret recover phase. The protocol can not only share and recover the secret correctly, but also verify whether there are dishonest participants in communication. In addition, the protocol is extended to a multiparty quantum secret sharing scheme by utilizing the unitary operations. Security analysis shows that the proposed schemes achieve the fundamental security requirements against the external and internal attackers with the aid of the quantum decoy states. It is shown that the efficiency in classical and quantum transmission is higher than the other protocols.

In this paper, we construct a general Bell inequality for the graph state. Firstly, we show that the Bell inequality is maximally violated by graph state corresponding to some given graph. In addition, we obtain the classical bound and maximal quantum violation of Bell inequality are N + |n(i)|− 1 and $N+(\sqrt {2}-1)(|n(i)|+1)$ , respectively. Furthermore, the classical bound and maximal quantum violation of Bell inequality are dependent on the choice of the vertex for most graphs expect for complete graph.

A tripartite quantum operation sharing protocol is proposed by utilizing a five-qubit absolutely maximally entangled (AME) state presented by Helwig et al. (Phys. Rev. A 86, 052335 (2012). The security of the proposed protocol is analyzed and ensured. The essential role of the state in this quantum task is explained. The protocol determinacy and the sharer asymmetry are identified. The experimental feasibility of the proposed protocol is discussed and confirmed. Moreover, the protocol is compared with Peng’s tripartite protocol using a six-qubit AME state [Quantum Inf Process 14, 4255 (2015)] and its distinct advantages of consuming less quantum resources, degrading the intensity of necessary operations, and owning the higher intrinsic efficiency, are revealed.

We present a novel scheme for deterministically realizing remote preparation of three-dimensional quantum states in a controlled manner. In this scheme, to link the three legitimate parties, generalized Einstein-Podolsky-Rosen (EPR) states, generalized Greenberger-Horne-Zeilinger (GHZ) states or their combinations are employed to product the shared quantum resources. Then to complete the deterministic controlled remote state preparation (DCRSP) in a three-dimensional system, some suitable sets of mutually orthogonal quantum states are hired as the measuring bases. It is shown that, after performing projective measurements under the proper measuring bases, the remote preparation of two-qutrit equatorial states can be successfully realized under control of a third party with unit successful probability.

As an important topic of quantum cryptography, quantum voting has attracted more and more attention in recent years. In this paper, we propose a quantum voting scheme based on a new set of orthogonal product states. Since different particles in the same orthogonal product state are transmitted separately, the security of the vote message in the scheme can be protected. The availability and security analysis show that the scheme satisfies the basic properties of voting can resist known quantum attacks. Furthermore, our scheme solves the problem of difficult preparation of entangled states in actual situations and improves the practicability of voting scheme. We hoped that our research will provide new ideas for the further study of quantum voting.

We present a novel scheme of cyclic remote state preparation via a six-qubit entangled state as the quantum channel. By introducing three auxiliary particles and using feedforward measurement strategy, Alice can remotely prepare an arbitrary single-qubit quantum state for Bob, Bob can remotely prepare an arbitrary single-qubit quantum state on Charlie’s site and Charlie can also remotely prepare an arbitrary single-qubit quantum state for Alice. It is pointed out that the cyclic remote preparation in the opposite direction can be perfectly achieved by changing the quantum channel. Furthermore, we generalize the above scheme to systems having N observers, so that cyclic remote state preparation can be realized in quantum information networks with N observers in different directions by changing quantum channels.

We present a theoretical study on quantum breathers in a XXZ Heisenberg ferromagnet with the single-ion uniaxial anisotropy on a two-dimensional hexangular lattice. In our work, the full quantum and the semiclassical cases are considered, respectively. For the full quantum case, we find that some isolated two-magnon bands can exist below the free magnon band. Physically, each isolated two-magnon band correspond to a two-magnon bound state, which is the simplest quantum breather state. For the semiclassical case, the analytical form of the discrete breather solution with a line localized structure is obtained by adopting the Glauber’s coherent-state representation. Furthermore, the influence of the anisotropy on the properties of quantum breathers is discussed in detail.

Recently, Cui and Guo (Quantum Inform. Process. 18, 182, 2019) gave some quantum testing algorithms of multi-output Boolean functions, one of them was for resiliency testing. However, through the algorithm, we cannot get the probability distribution of a Boolean function. Improving the algorithm there, we present quantum algorithms for this problem. Under the condition of non-resiliency, we obtain not only the conclusion that the function F(x) is statistically dependent of which t variables but also the distance of the probability distribution from the uniform distribution.

In this work, we give an analytical derivation of the reduced density matrix between two qubits in a cavity field, which is described by the quantum Rabi model. Using the coherent state method and the generalized hypergeometric functions, we find a complete solution of the 4-by-4 reduced density matrix for each eigen energy by taking the partial trace over the cavity field states. Four kinds of measurements used to describe the quantum entanglement and quantum correlation between the two qubits, i.e., the concurrence, quantum discord, steerable weight, and robustness of coherence, are calculated for the ground state and excited states. For both the weak coupling ( $g\rightarrow 0$ ) and deep-strong coupling ( $g\rightarrow \infty $ ) regimes, quantum entanglement and quantum correlation between the two qubits are vanishing. An appropriate coupling in the deep strong coupling regime between the qubits and the cavity field is required if one wants to establish quantum entanglement between the qubits.

We provide a characterization of multipartite systems constraints in terms of quantum correlations. By using the Hamming weight of the binary vectors associated with the subsystems, we give the α th power of monogamy and β th power of polygamy inequalities for general quantum correlations. Using concurrence as an application, one gets tighter inequalities than the existing ones for some classes of quantum states. Detailed examples are presented.

In this paper, a multi-party quantum private comparison (MQPC) scheme is suggested based on entanglement swapping of Bell entangled states within d-level quantum system, which can accomplish the equality comparison of secret binary sequences from n users via one execution of scheme. Detailed security analysis shows that both the outside attack and the participant attack are ineffective. The suggested scheme needn't establish a private key among n users beforehand through the quantum key distribution (QKD) method to encrypt the secret binary sequences. Compared with previous MQPC scheme based on d-level Cat states and d-level Bell entangled states, the suggested scheme has distinct advantages on quantum resource, quantum measurement of third party (TP) and qubit efficiency., 8 pages, 1 figure, 1 table

Importance of quantum entanglement has been demonstrated in various applications. Usually, separability of a bipartite state is defined by its algebraic structure, i.e. a convex combination of product states. But it seems to be hard to check separability (equivalently, entanglement) of a state from its algebraic structure. In this note, we give some characterizations of separability of bipartite states based on POVM measurements. For bipartite pure states, we prove the separability, Bell locality, unsteerability and classical correlation are the same. As a consequence, every entangled pure bipartite state is always Bell nonlocal, steerable and quantum correlated.

Based on quantum renormalization group (QRG) method, we investigated quantum coherence and quantum phase transition (QPT) in XXZ chain and XY chain, respectively. The results show that both the geometric quantum coherence and entropic coherecne can accurately indicate the QPT at critical point after enough iteration steps. Moreover, the increasing anisotropy parameter destroys the coherence in the XXZ chain, while enhances it in the XY chain. In addition, focused on the XXZ chain we analyzed the nonanalytic phenomena and scaling behaviors with different theoretical exponents in detail.

The number of qubits involved in a quantum system increases as the quantum computation is being progressed. Restrictions in monolithic quantum computing systems capacity can be overcome by utilizing the distributed circuits. For the implementation of global gates (two-quibt gates whose control and target qubits belong to different partitions), it is required that one qubit be teleported to the other partition. Teleportation is a costly protocol (it requires sharing entanglement between two partitions), and the number of teleportations required for implement a given distributed circuit is called teleportation cost. It is desirable to distribute a quantum computation in such a way that the teleportation cost is reduced. A previous work has presented a way to optimize distributed quantum circuits in terms of teleportation cost for a predetermined partitioning. In this research, Shore circuit to factor number 15 synthesized in the single-qubit and CNOT gates is provided. After that, the circuit partitioning with the minimal cost of communication is presented.

In this paper, a quantum payment protocol based on a special set of local indistinguishable orthogonal product states (X-LIOP) is proposed. In the presented protocol, the purchase information is encoded as a sequence of X-LIOP states. With our security analysis, it can be seen that our protocol satisfies the requirements of blindness, unforgeability and undeniability. Specially, the blindness means the purchase information is only known to the buyer and the seller, while the others (including the bank) cannot obtain the purchase information by any means. Once the buyer and seller wants to forge or deny information, they will be found by a trusted third party. Furthermore, since the non-entangled states are applied in our protocol, the protocol can be easily implemented in practice.

Quantum state sharing (QSS) plays significant role in transmitting quantum secret information. However, in practical quantum communication situation, quantum information transmission is inevitably affected by the noisy environment. In this paper, we investigate the influence of correlated noise on QSS. We first present a QSS scheme and construct a noisy QSS. Subsequently, the fidelity of the scheme is discussed. It is found that there are different behaviors of fidelity in Markovian regime and non-Markovian regime. Furthermore, a method is proposed to steer the performance of the noisy QSS scheme with filtering operator.

A quantum secure multiparty summation protocol is constructed based on the phase shifting operation of d-level quantum system which utilizes the integer-by-integer technique to calculate the modulo d addition. The semi-honest third party prepares d-level two-particle entangled states and transmits the particle sequence composed by all second particles to n secrecy owners. n secrecy owners in turn encode their respective secrecy on this particle sequence through the phase shifting operation. Detailed security analysis turns out that both the outside attack and the participant attack are ineffective towards this protocol. Compared with the quantum secure summation protocols with bit-by-bit calculations, its calculation efficiency is higher; and compared with the protocols with smaller modulo, its applications are more extensive. Especailly, this protocol has extensive applications in the realm of quantum secure multiparty computation, such as quantum multiparty private comparison, quantum multiparty anonymous ranking, quantum multiparty anonymous voting, quantum multiparty key agreement, etc.

Quantum degenerate systems can be simulated by the classical resonant oscillators in the means of quantum-classical mapping theory. In this work, we show the classical version of shortcuts to adiabaticity-transitionless quantum driving (TQD) for the non-Abelian quantum systems by averaging the quantum version. The non-Abelian geometric angle corresponding to the quantum Wilczek-Zee phase is given and the non-Abelian angle gauge potential is just the opposite of the third term of TQD Hamiltonian or the averaging of Wilczek-Zee gauge potential. An example of Hamiltonian with two degenerate subspaces is employed to illustrate the classical non-Abelian dynamics, geometric angle and shortcuts to adiabaticity. This provides a promising platform to simulate the quantum shortcut or for quantum computation and quantum information processing.

A novel practical quantum secure direct communication (QSDC) protocol is constructed by utilizing the evolution law of atom via cavity QED. It transmits the atoms from one communicant to the other communicant in a two-step manner. It adopts two-atom product states as the initial quantum resource and the decoy atom technique to guarantee the security against the outside attack. It only needs single-atom measurements, and neither the quantum entanglement swapping nor the unitary operations.

Motivated by the existing circuit model of quantum convolutional neural network, a new quantum convolutional neural network circuit model is devised, which is combined with quantum chaotic map to construct a symmetric cryptosystem. Quantum chaotic map produces key stream for encryption and decryption. The cryptosystem simulates the basic process of communication. Theoretical analysis manifests that the cryptosystem is effective. Additionally, simulation experiments based on MNIST data set show that the cryptosystem is secure. Furthermore, the proposed cryptosystem can be applied not only for image data, but for text data. Therefore, the grid data can be encrypted by utilizing the cryptosystem.

We investigate the dynamical behaviors of quantum-memory-assisted entropic uncertainty relation (QMA-EUR) and quantum correlation (both quantum entanglement and quantum discord) for a two-qubit system coupled to a spin environment by a z–x-type interaction. Our purpose is to find out how the QMA-EUR and quantum correlations are affected by the pre-designed factors of the environment, including initial spin environmental states and the coupling constants. The numerical results show that the initial environmental state has significant effect on the dynamics of quantum correlations of the central spin system. We find that the environment should be prepared in a block entangled state with Bell state. This option is beneficial to reducing entropic uncertainty and inhibits the damping of quantum correlation. We also find that the high frequency particles in a spin bath can significantly enhance the robustness of quantum correlation of the system.

A comparative study of quantum properties associated with coherent correlations between the modes of light generated by a nondegenerate parametric down-conversion process is presented. Particularly, the degree of nonclassicality that can be quantified by logarithmic negativity and quantum discord is compared, and a striking similar tendency is observed. In the same manner, a comparison of the quadrature variance, the smallest eigenvalue of the symplectic matrix and Einstein-Podolsky-Rosen (EPR) steering is made whereby a significant similarity is witnessed. The highest degree of quantum features of the radiation is in general manifested near threshold, whereas the quantifying measure related to the smallest eigenvalue of the symplectic matrix is found to capture a better degree of quantumness. Since each criterion renders only sufficient condition, it is hoped that witnessing consistent outcome across different criteria enhances the chance for experimental verification and practical application.

In this paper, a linear generalized uncertainty principle (GUP), which suggests a minimum measurable length and a maximal measurable momentum, is used in analyzing COW experiment and Einstein-Bohr’s a photon box experiment. Based in these experiments a modified Schwarzschild metric was obtained in order to calculate a quantum corrections in Schwarzschild black hole thermodynamics and tunneling probability. It was found that GUP placed restrictions on the minimum mass, size and temperature of the black hole, indicating that there was a black hole remnant after the completion of the evaporation process. The resulting values of minimum mass and size of the black hole are identical to that values predicted by quadratic GUP, which points out that the two models are equivalence in Planck scale measurements.

We study the usefulness of the broken-line-type decoherence in quantum Hash functions based on discrete-time quantum walks on a cycle. We first observe that the time-evolution of probability distribution of quantum walks on a cycle is of high sensitivity to such broken-line-type decoherence, increasing with the number of steps in the walk. Based on this observation, we further propose a quantum Hash function based on the broken-line quantum walk on a cycle. Numerical simulation and performance analyses show that decoherence can be useful to improve the performances of quantum hash functions such as better diffusion and confusion, better collision resistance and more uniform distribution of hash values in the hash space. Moreover, our results promote the practical use of quantum-walk-based hash functions in realistic situations.

In this paper, we propose a mutual authenticated quantum key agreement scheme based on three-particle entangled states, which can achieve both completely secure and more efficient. In our scheme, the pre-shared keys are classical bit strings between the semi-honest server (SHS) and the client (Alice or Bob), so they are kept and use to authenticate each other easily. More important, by the SHS’s helping with three-particle entangled states, SHS and Alice/Bob can authenticate each other, and at the same time anyone else cannot get the session key between Alice and Bob even for SHS. The proposed scheme has the properties of completeness, information theoretic security, non-repudiation and unforgeability. Its information-theoretic security is ensured by quantum indistinguishability mechanics. Compared with the related works, our proposed scheme can increase efficiency factors η1 and η2 to 50% and 80% respectively in one communication round.

Quantum key agreement (QKA) and quantum search algorithm (QSA) are two important branches in quantum topic. The former asks all participants to negotiate the agreement key equally, and none of them can fully determine the agreement key. The latter is used to provide an acceleration in searching the marked item in an unsorted database. To date, several QKA schemes based on either BB84 or entangled states have been proposed, the QKA protocol based on QSA is rare, only exists one multi-party QKA (MQKA) protocol based on QSA. In this paper, on the basis of the properties of Grover’s QSA, the first two-party quantum key agreement protocol based on quantum search algorithm known as Grover’s algorithm is proposed. The participants transmit a two-particle quantum state sequence directly by inserting decoy photons randomly. The initial-prepared two-particle quantum states are easy to be prepared with current technology. Moreover, there is no swapping entanglement technology used in this protocol, it only needs unitary operations and single-particle measurements. Compared with the existing two-party QKA protocol, the proposed QKA protocol is more efficient. In addition, the security analysis shows that the proposed protocol is secure against both external attacks and internal ones. Finally, the proposed protocol is generated to MQKA protocol based on quantum search algorithm.

We investigate the dynamical behaviors of quantum-memory-assisted (QMA) entropic uncertainty for the central two-qubit system coupled to the N-site spin XY chain environment with z-component Dzyaloshinsky-Moriya (DM) interaction and external magnetic field, asymmetrically. The results show that the dynamics of QMA entropic uncertainty for a pair of Pauli observables are oscillatory and ascending gradually with evolution time, which is anti-correlated to the entanglement of the two-qubit system. We also find that QMA entropic uncertainty exhibits sudden change phenomena near the critical point of quantum phase transform both in the case of weak and strong coupling regimes, which can act as a new witness of the critical point of quantum phase transition. Meanwhile, the DM interactions of the spin chain environment have non-equivalent effects on the QMA entropic uncertainty when the external magnetic field strength is far from the critical point. Furthermore, the asymmetricallity of the qubit-environment couplings has slightly effects on QMA entropic uncertainty in the case of strong coupling regime of the two-qubit system. While, in the weak coupling regime of the two-qubit system, QMA entropic uncertainty is very sensitive to the asymmetricallity of qubit-environment couplings. Finally, the larger the number of spin sites of the environment, the more quickly the QMA entropic uncertainty increases to the maximal value both in the weak and strong coupling regimes of the two-qubit system.

Recently, Chen et al. [Int. J. Theor. Phys. 59, 1402–1412 (2020)] proposed a theoretical scheme for controlled quantum teleportation (CQT) of a Bell state by using seven-qubit entangled state as a quantum channel. In this comment, it is shown that the consumption of both the quantum and classical resources used by Chen et al. is excessively high because the actual task of CQT of a Bell state via seven-qubit entangled state can be reduced to the CQT of an arbitrary single-qubit state via three-qubit GHZ state. Hence, in this work, an improved scheme for CQT has been presented. We have also shown that the CQT of certain class of N-qubit entangled state can also be realized successfully by using a three-qubit GHZ state as the quantum channel. The intrinsic efficiency of the present communication scheme is very large as compared to that proposed by Chen et al.

We investigate the dynamics of quantum coherence of a system consisting of two interacting atoms coupling with a common cavity which is filled with a nonlinear Kerr-like medium, in the presence of intrinsic decoherence. It is shown that the stationary quantum coherence can arise in the system as the time approach to infinite. In particular, the amount of stationary quantum coherence can be enhanced by adjusting the Kerr interaction and dipole-dipole interaction. Furthermore, we also explore the influence of Kerr interaction and dipole-dipole interaction on the transfer of quantum information by a witness of the trace distance and find that the transferred information and stationary quantum information can be controlled by the Kerr interaction and dipole-dipole interaction.

Recently, Lang put forward for the first time a quantum gate-based quantum private comparison (QPC) protocol (Int J Theor Phys, 59(2020)833) which uses the quantum controlled-not gates to implement comparison instead of classical exclusive-or computations. It was claimed that this quantum gate-based QPC protocol is secure against both the outside attack and the participant attack. However, in this paper, it is pointed out that this protocol cannot resist a special measurement attack from the third party (TP) and the disturbance attack from an outside attacker. The corresponding improvements are further suggested to remedy these security loopholes.

Periodically driven non-Hermitian quantum systems have become the center of interest in recent years due to their rich physical phenomena. In this work, we consider a one-dimensional non-Hermitian lattice model induced by partially asymmetric coupling with time-periodic and spatially periodic modulations upon on-site potentials. Within Floquet theorem, we obtain the Floquet quasienergy spectrum of this one-dimensional non-Hermitian system. We show that the robust zero-energy modes exist in the band gap from the real parts of quasienergy spectrum. Compared with the case of no modulations, two pairs of the conjugate imaginary parts are added, which can be attributed to the combined modulations upon the on-site potentials. With the increase of non-Hermitian degree, the imaginary parts of the spectra are enlarged. We also observe the dynamical characteristics that, for different kinds of tunneling amplitudes between lattices, the amplitude of evolution gradually either decays to zero or eventually stabilizes at one particular value. Our protocol, possible to realize in photonic lattices, may facilitate the engineering of novel Floquet topological phases in non-Hermitian systems.

This paper proposes a novel quantum learning algorithm based on Bernstein and Vazirani’s quantum circuit to find the dependent variables of the 2-junta problem. Typically, for a given Boolean function f : {0, 1}n → {0, 1} that depends on only 2 out of n variables, the dependent variables are obtained by evaluating the function 4n times in the worst-case. However, the proposed quantum algorithm only requires O(log2n) function operations in the worst-case. Moreover, the algorithm requires an average of 5.3 function operations at the most when n ≥ 8.

We research the strong gravitational lensing for the quantum-modified Schwarzschild black hole which is derived from quantum Raychaudhuri equation. With the increase of quantum Raychaudhuri equation parameter η, we find that the distance between the black hole and the light passing by it becomes smaller; the deflection angle gets larger; the magnification of relativistic images is more similar; all of the relativistic images move towards the black hole while the images are farther to each other. These results, as we expect, will degenerate to the case of Schwarzschild black hole when $\eta \rightarrow 0$ .

The construction of maximum distance separable (MDS) linear complementary dual (LCD) codes and entanglement-assisted quantum MDS (EAQMDS) codes have been of a great interest. In this paper, for arbitrary prime power q, we construct two new families of MDS Hermitian LCD codes of length $n=\frac {{{q^{2}}+1}}{\lambda }$ and $n=\frac {q^{2}-1}{r},$ where rq + 1. By applying the obtained MDS Hermitian LCD codes to the EAQMDS codes, we derive new maximal entanglement EAQMDS codes of parameters ${\left [ \kern -0.30em\left [ {\frac {{{q^{2}}+1}}{\lambda },\frac {{{q^{2}}+1}}{\lambda }-l+1,l;l-1}\right ] \kern -0.30em\right ]_{q}}$ where $2\leq l\leq \left \lfloor \frac {{{q^{2}}+1+2\lambda }}{2\lambda }\right \rfloor $ and ${\left [ \kern -0.30em\left [ {\frac {{{q^{2}-}1}}{r},\frac {{{q^{2}-}1}}{r} -\gamma ,\gamma +1;\gamma }\right ] \kern -0.30em\right ]_{q}}$ where $1\leq \gamma \leq \frac {{{q^{2}}-1}}{2r}.$

A scheme is proposed for fast generation of entangled states in directly coupled bimodal-mode cavities based on shortcuts to adiabatic passage. The scheme can be realized by transitionless quantum driving with the help of quantum Zeno dynamics and non-resonant lasers. First, we simplify the system by the quantum Zeno dynamics. Then, under the large detuning condition, we get the effective Hamiltonian which is equivalent to the corresponding counter-diabatic driving Hamiltonian to speed up the evolution process. The effects of decoherence induced by atomic spontaneous emission, leakage of the cavity and operational imperfection are also taken into account. The numerical simulation result shows that this scheme is robust against these factors. During realizing the scheme, the laser pulses are not strongly limited and the auxiliary levels or multi-step operations are not needed. Moreover, for any quantum system whose Hamiltonian is possible to be simplified into the same form in the paper, the corresponding alternative physically feasible Hamiltonian can be built with present method, which provides a scalable way for the preparation of entangled states in theory.

Luo and Hwang [Quantum Inf. Process (2016) 15:947–958] proposed the authenticated semi-quantum direct communication protocols for a quantum participant to be able to transmit secret messages to a classical participant without employing an authenticated classical channel. However, this study indicates that there is an information leakage problem in Luo and Hwang’s measure-resend protocol. The information leakage problem might allow an attacker to use an intercept-resend attack to obtain partial secret messages. Finally, an improved method is proposed to overcome the information leakage problem.

In this paper we design a deterministic controllable quantum communication protocol for remotely preparing three-qubit GHZ-type and four-qubit W-type entangled states at two different locations at the same time. Two parties (the preparers) along with a third party (the controller) are connected through a proper multipartite entangled resource. The states to be prepared are not physically available, only the classical information of each state is known by a party who intends to remotely prepare it at the end of the other party under the same control of a third party. Concretely, it is a multi-tasking protocol in which remote preparations of the two inequivalent states are accomplished not only simultaneously but also controllably through execution of a single protocol by utilizing an eleven-qubit entangled state as shared quantum resource. We also propose a generation process of the multipartite quantum resource used.

Our aim is to compare the fundamental notions of quantum physics - contextuality vs. incompatibility. One has to distinguish two different notions of contextuality, Bohr-contextuality and Bell-contextuality. The latter is defined operationally via violation of noncontextuality (Bell type) inequalities. This sort of contextuality will be compared with incompatibility. It is easy to show that, for quantum observables, there is no contextuality without incompatibility. The natural question arises: What is contextuality without incompatibility? (What is “dry-residue”?) Generally this is the very complex question. We concentrated on contextuality for four quantum observables. We shown that, for “natural quantum observables” , contextuality is reduced to incompatibility. But, generally contextuality without incompatibility may have some physical content. We found a mathematical constraint extracting the contextuality component from incompatibility. However, the physical meaning of this constraint is not clear. In Appendix 1, we briefly discuss another sort of contextuality based on Bohr’s contextuality-incompatibility principle. Bohr-contextuality plays the crucial role in quantum foundations. Incompatibility is, in fact, a consequence of Bohr-contextuality. Finally, we remark that outside of physics, e.g., in cognitive psychology and decision making Bell-contextuality distilled of incompatibility can play the important role.

Quantum computing is proving to be very beneficial for solving complex machine learning problems. Quantum computers are inherently excellent in handling and manipulating vectors and matrix operations. The ever increasing size of data has started creating bottlenecks for classical machine learning systems. Quantum computers are emerging as potential solutions to tackle big data related problems. This paper presents a quantum machine learning model based on quantum support vector machine (QSVM) algorithm to solve a classification problem. The quantum machine learning model is practically implemented on quantum simulators and real-time superconducting quantum processors. The performance of quantum machine learning model is computed in terms of processing speed and accuracy and compared against its classical counterpart. The breast cancer dataset is used for the classification problem. The results are indicative that quantum computers offer quantum speed-up.

Photonic hyperentanglement, which involves photons simultaneously entangled in more than one degree of freedom (DOF), has many important applications in quantum information processing, especially in high-capacity quantum communications. Interestingly, single-photon qubits encoded in the time-bin DOF are robust for long-distance transmissions in noisy channels. In this paper, we present a hyperentangled-Bell-state generation (HBSG) scheme for preparing two-photon six-qubit states which are simultaneously entangled in the polarization, spatial-mode, and time-bin DOFs. Compared with previous HBSG schemes, we construct an error-detected circuit unit with a quantum-dot (QD) spin in a double-sided optical microcavity, with which errors due to imperfect interactions between photons and QD systems can be easily detected, so that the error-detected circuit unit can relax the experimental requirement and improve the fidelity of our scheme largely. Meanwhile, our scheme is used to prepare two-photon hyperentangled states in polarization-spatial-time three DOFs, which is significant for faithful entanglement distribution and quantum repeater. These features make our scheme more feasible and useful in high-capacity and long-distance quantum communications with hyperentanglement.

The conformal cyclic cosmological evolution of the universe is discussed with the principles of loop quantum gravity. The application of quantum mechanical aspects enables connecting surface between two cyclic aeons. From existing models entropy of conformal evolution is found to be modified in the light of this discussion. Infinite volume problem in conformal cyclic cosmology model is resolved with these loop quantum gravitational solutions. Various bouncing scale factors are compared. Conformal cyclic cosmological evolution does have a connection with the loop quantum cosmological scenario with this idea bridged. This work briefs the possible initial and final stages of the universe from the CCC and LQG scenario. In the connecting point between two aeons, the existence of curvature duality is also obtained and presented.

The skew information has important applications in quantum theory. In this paper, a measure for correlations in terms of the skew information is introduced and discussed. Its fundamental properties are obtained, which include the measure is locally unitary invariant and convex on the set of states with the fixed marginal state, moreover, it decreases under local random unitary operation. Lastly, we propose an entanglement criterion in terms of the quantum skew information and illustrate the significance of this criterion by some examples.

Descrying all aspects of the quantum entanglement of multipartite quantum systems is an essential part when researching the quantum entanglement. Maximally multi-qubit entangled state is one of the research objects. Recently, attracted by a criterion for maximally entangled nine-qubit state and construct a nine-qubit maximally entangled state, we construct a new genuine maximally nine-qubit entangled state via the recurrence relation. Further, nine-qubit entangled state is found which can be seen as a new form maximally nine-qubit entangled state. There are 108 of purity equal to 1/16, 18 of purity equal to 1/8 in observation. We believe the result could provide a new idea for constructing more new maximally multi-qubit states.

The purpose of this paper is to develop a (N − k) threshold quantum secret sharing (QSS) scheme by using entangled multi-qudit states shared between N qudits such that (k ≤ N − k). We introduce first multi-qudit separable states of a Hilbert space associated with a disconnected multi-qudit system. The entangled multi-qudit states are obtained from disconnected states by means of a unitary interaction operator governing the evolution of the multi-qudit system, where the pairwise interaction establishes links between qudits. The generated entangled states are chosen to be maximally entangled with respect to a specific bi-partition ( $A_{2} \bigcup A_{1} $ ) with k = |A2|≤|A1| = (N − k) of the whole system such that the von Neumann entropy $S(\rho _{A_{2}})$ is maximal. The maximally entanglement property with respect to the splitting ( $A_{2} \bigcup A_{1} $ ) of this N-qudit entangled states will be used by a dealer (D) to share an encoded quantum secret with (N − 1) other players, such that at least the (N − k) specified players belonging to A1 have to cooperate jointly to get the complete information about the secret.

We study the coherence of qubit states with respect to any set of mutually unbiased bases (MUBs), in terms of the l1 norm of coherence, the modified trace norm of coherence and the geometry measure of coherence. We present the arbitrary expressions of a complete set of MUBs in C2 and the forms of any qubit states under these complete sets of MUBs. Then we calculate coherence of qubit states with respect to any complete sets of MUBs based on different coherence measures. It is shown that the sum of the coherence or the squared coherence is upper or lower bounded. We derive analytically these bounds and establish tight relations between quantum coherence and mutually unbiased bases.