Fault tolerant deterministic secure quantum communication using logical Bell states against collective noise

This study proposes two novel fault tolerant deterministic secure quantum communication （DSQC） schemes resistant to collective noise using logical Bell states. Either DSQC scheme is constructed based on a new coding function, which is designed by exploiting the property of the corresponding logical Bell states immune to collective-dephasing noise and collective-rotation noise, respectively. The secret message can be encoded by two simple unitary operations and decoded by merely performing Bell measurements, which can make the proposed scheme more convenient in practical applications. Moreover, the strategy of one-step quanta transmission, together with the technique of decoy logical qubits checking not only reduces the influence of other noise existing in a quantum channel, but also guarantees the security of the communication between two legitimate users. The final analysis shows that the proposed schemes are feasible and robust against various well-known attacks over the collective noise channel.

On Algebraic Immunity of Trace Inverse Functions on Finite Fields of Characteristic Two

The trace inverse functions Tr(λx^(-1)) over the finite field F_(2~n) are a class of very important Boolean functions and are used in many stream ciphers such as SFINKS,RAKAPOSHI,the simple counter stream cipher(SCSC) presented by Si W and Ding C(2012),etc.In order to evaluate the security of those ciphers in resistance to(fast) algebraic attacks,the authors need to characterize algebraic properties of Tr(λx^(-1)).However,currently only some bounds on algebraic immunity of Tr(λx^(-1)) are given in the public literature,for example,the NGG upper bound and the Bayev lower bound,etc.This paper gives the exact value of the algebraic immunity of Tr(λx^(-1)) over F_(2~n),that is,AI(Tr(λx^(-1))) =[2n^(1/2)]- 2,where n ≥ 2,A ∈ F_(2~n) and λ≠ 0,which shows that Dalai's conjecture on the algebraic immunity of Tr(λx^(-1)) is correct.What is more,the authors demonstrate some weak properties of Tr(λx^(-1)) against fast algebraic attacks.

A blind quantum signature protocol using the GHZ states

Recently,some blind quantum signature(BQS) protocols have been proposed.But the previous schemes have security and efficiency problems.Based on the entangled Greenberger-Horne-Zeilinger(GHZ) states,a new weak BQS protocol is proposed.Compared with some existing schemes,our protocol has 100% efficiency.Besides,the protocol is simple and easy to implement.The security of the protocol is guaranteed by the correlation of the GHZ particles held by each participant.In our protocol,the signatory is kept blind from the content of the message.According to the security analysis,the signatory cannot disavowal his/her signature while the signature cannot be forged by others.

Self-Dual Hadamard Bent Sequences

A new notion of bent sequence related to Hadamard matrices was introduced recently,motivated by a security application(Solé,et al.,2021).The authors study the self-dual class in length at most 196.The authors use three competing methods of generation:Exhaustion,Linear Algebra and Gr?bner bases.Regular Hadamard matrices and Bush-type Hadamard matrices provide many examples.The authors conjecture that if v is an even perfect square,a self-dual bent sequence of length v always exists.The authors introduce the strong automorphism group of Hadamard matrices,which acts on their associated self-dual bent sequences.The authors give an efficient algorithm to compute that group.

A Novel Quantum Covert Channel Protocol Based on Any Quantum Secure Direct Communication Scheme

By analyzing the basic properties of unitary transformations used in a quantum secure direct communication (QSDC) protocol, we show the main idea why a covert channel can be established within any QSDC channel which employs unitary transformations to encode information. On the basis of the fact that the unitary transformations used in a QSDC protocol are secret and independent, a novel quantum covert channel protocol is proposed to transfer secret messages with unconditional security. The performance, including the imperceptibility, capacity and security of the proposed protocol are analyzed in detail.

Universal quantum computation with qudits

Quantum circuit model has been widely explored for various quantum applications such as Shors algorithm and Grovers searching algorithm.Most of previous algorithms are based on the qubit systems.Herein a proposal for a universal circuit is given based on the qudit system,which is larger and can store more information.In order to prove its universality for quantum applications,an explicit set of one-qudit and two-qudit gates is provided for the universal qudit computation.The one-qudit gates are general rotation for each two-dimensional subspace while the two-qudit gates are their controlled extensions.In comparison to previous quantum qudit logical gates,each primitive qudit gate is only dependent on two free parameters and may be easily implemented.In experimental implementation,multilevel ions with the linear ion trap model are used to build the qudit systems and use the coupling of neighbored levels for qudit gates.The controlled qudit gates may be realized with the interactions of internal and external coordinates of the ion.

A Spatial Domain Quantum Watermarking Scheme

This paper presents a spatial domain quantum watermarking scheme. For a quantum watermarking scheme,a feasible quantum circuit is a key to achieve it. This paper gives a feasible quantum circuit for the presented scheme. In order to give the quantum circuit, a new quantum multi-control rotation gate, which can be achieved with quantum basic gates, is designed. With this quantum circuit, our scheme can arbitrarily control the embedding position of watermark images on carrier images with the aid of auxiliary qubits. Besides reversely acting the given quantum circuit, the paper gives another watermark extracting algorithm based on quantum measurements. Moreover, this paper also gives a new quantum image scrambling method and its quantum circuit. Differ from other quantum watermarking schemes, all given quantum circuits can be implemented with basic quantum gates. Moreover, the scheme is a spatial domain watermarking scheme, and is not based on any transform algorithm on quantum images. Meanwhile, it can make sure the watermark be secure even though the watermark has been found. With the given quantum circuit, this paper implements simulation experiments for the presented scheme. The experimental result shows that the scheme does well in the visual quality and the embedding capacity.