International Journal of Quantum Information

Steering, a quantum property existing in some bipartite entangled systems, causes the local measurements on one part to change the state of the other part at any distance. In this paper, the dynamics of steering between two uncoupled oscillators in squeezed thermal, thermal and vacuum environments are compared. Assuming that the two oscillators are coupled to a common environment or two similar environments, the evolution of steering is obtained using Linblad equation in Born–Markov approximation. It is observed that when the two oscillators are initially in uni-modal squeezed states, the interaction with a common squeezed thermal environment induces steering between them after a short time. However, in other common and the two similar environments, steering does not appear. In addition, when two oscillators are initially in a squeezed thermal state, it is observed that steering decreases monotonically and disappears in a short time in common thermal, common vacuum and the two similar environments. Moreover, steering survives the most in a common squeezed thermal environment.

Randomized benchmarking (RB) is a popular procedure used to gauge the performance of a set of gates useful for quantum information processing (QIP). Recently, Proctor et al. [Phys. Rev. Lett. 119 (2017) 130502] demonstrated a practically relevant example where the RB measurements give a number $r$, very different from the actual average gate-set infidelity $ϵ$, despite past theoretical assurances that the two should be equal. Here, we derive formulas for $ϵ$, and for $r$ from the RB protocol, in a manner permitting easy comparison of the two. We show in general that, indeed, $r\ne ϵ$, i.e. RB does not measure average infidelity, and, in fact, neither one bounds the other. We give several examples, all plausible in real experiments, to illustrate the differences in $ϵ$ and $r$. Many recent papers on experimental implementations of QIP have claimed the ability to perform high-fidelity gates because they demonstrated small $r$ values using RB. Our analysis shows that such a statement from RB alone has to be interpreted with caution.

Protecting the accelerated information coherence and suppressing of its decay due to the acceleration is achieved by using different noisy channels. The behavior of three different types of information; Fisher, nonlocal and local information of qubit–qutrit system is discussed. It is shown that, the estimation rate of the acceleration parameter is maximized if both subsystems are accelerated and interacted locally with their noise channels. However, if the largest subsystem is accelerated, then the estimation rate is minimized. The rate of change of the nonlocal information depends on which subsystem is accelerated. The results display that the local information is almost unaltered during the acceleration process, that is, the information is frozen. We show that the phase-flip channel represents the weak channel, where its suppressing of the decay due to the acceleration is smaller than the dephasing and depolarize of channels.

Based on the novel enhanced quantum representation for quantum image (NEQR), a new blind quantum steganography scheme is proposed. In this scheme, an improved quantum representation of text utilizing American Standard Code for Information Interchange (ASCII) is provided that uses two qubit sequences to store the same quantum text message. The general embedding process of the scheme is as follows: First, the cover image of size $2^n\times 2^n$ will be divided into eight blocks of size $2^{n-2}\times 2^{n-1}$ and the secret quantum text of size $2^{n-2}\times 2^{n-1}$ is scrambled by Gray code transform method. Then, the disorder quantum text is embedded into the eight blocks of cover image employing the Gray code as a judgment condition. Meanwhile, the corresponding quantum circuits are drawn. Through the analysis of all quantum circuits, it can be concluded that the scheme has a lower complexity that is $\mathrm{\text{O}}(n)$. And the performance of the proposed scheme is analyzed in terms of simulation results of three items: visual quality, capacity and robustness.

A kind of new geometric measure of quantum correlations is formulated. The proposed formulation is in terms of the quantum Tsallis relative entropy and can naturally be viewed as a one-parameter extension quantum discordlike measure that satisfies all requirements of a good measure of quantum correlations. It is of an elegant analytic expression and contains several existing good quantum correlation measures as special cases. The partial coherence measure is also investigated.

We propose a measure of nonclassical correlation $N_{{ℱ}}^{{𝒢}}$ in terms of local Gaussian unitary operations based on square of the fidelity ${ℱ}$ for bipartite continuous-variable systems. This quantity is easier to be calculated or estimated and is a remedy for the local ancilla problem associated with the geometric measurement-induced nonlocality. A simple computation formula of $N_{{ℱ}}^{{𝒢}}$ for any $(1+1)$-mode Gaussian states is presented and an estimation of $N_{{ℱ}}^{{𝒢}}$ for any $(n+m)$-mode Gaussian states is given. For any $(1+1)$-mode Gaussian states, $N_{{ℱ}}^{{𝒢}}$ does not increase after performing a local Gaussian channel on the unmeasured subsystem. Comparing $N_{{ℱ}}^{{𝒢}}({\rho }_{AB})$ in scale with other quantum correlations such as Gaussian geometric discord for two-mode symmetric squeezed thermal states reveals that $N_{{ℱ}}^{{𝒢}}$ is much better in detecting quantum correlations of Gaussian states.

Originating from the superposition principle in quantum mechanics, coherence has been extensively studied as a kind of important resource in quantum information processing. We investigate the distinguishability of coherence-breaking channels with the help of quantum entanglement. By explicitly computing the minimal error probability of channel discrimination, it is shown that entanglement can enhance the capacity of coherence-breaking channel distinguishability with same types for some cases while it cannot be enhanced for some other cases. For coherence-breaking channels with different types, the channel distinguishability cannot be enhanced via entanglement.

A discussion of fundamental aspects of quantum theory is presented, stressing the essential role of “events.”

In order to improve the security of watermark image, a scheme of quantum watermarking algorithm which is based on chaotic affine scrambling is proposed and it includes scrambling, embedding and extracting procedures. In the embedding process, the position and the color of the watermark image are scrambled by chaotic affine and the size of the scrambled watermark image is extended from $2^{n-1}\times 2^{n-1}$ to $2^n\times 2^n$. Meanwhile, the color value of the pixel is changed from 24-bits to 3-(1-bit per channel) bits. The extended watermark image is embedded into the carrier image through a two-bit embedding strategy, and the extraction process is the inverse one of the embedding process. The simulation results show that the proposed scheme is superior to the comparison scheme in terms of visual quality, peak signal-to-noise ratio (PSNR).

In terms of quantum probability statistics, the Bell inequality (BI) and its violation are extended to spin-$s$ entangled Schrödinger cat state (called the Bell cat state) with both parallel and antiparallel spin-polarizations. Except the spin-1/2, the BI is never ever violated by the Bell cat states with the measuring outcomes including entire Hilbert space. If, on the other hand, measuring outcomes are restricted in the subspace of spin coherent state (SCS), a universal Bell-type inequality (UBI), $p_s^{lc}\le 0$, is formulated in terms of the local realistic model. We observe a spin parity effect that the UBI can be violated only by the Bell cat states of half-integer but not the integer spins. The violation of UBI is seen to be a direct result of nontrivial Berry phase between the SCSs of south- and north-pole gauges for half-integer spin, while the geometric phase is trivial for the integer spins. A maximum violation bound of UBI is found as $p_s^{max}=1$, which is valid for arbitrary half-integer spin-$s$ states.