Exact Calculations of Coherent Information for Toric Codes under Decoherence: Identifying the Fundamental Error Threshold

The toric code is a canonical example of a topological error-correcting code. Two logical qubits stored within the toric code are robust against local decoherence, ensuring that these qubits can be faithfully retrieved as long as the error rate remains below a certain threshold. Recent studies have explored such a threshold behavior as an intrinsic information-theoretic transition, independent of the decoding protocol. These studies have shown that information-theoretic metrics, calculated using the Renyi (replica) approximation, demonstrate sharp transitions at a specific error rate. However, an exact analytic expression that avoids using the replica trick has not been shown, and the connection between the transition in information-theoretic capacity and the random bond Ising model (RBIM) has only been indirectly established. In this work, we present the first analytic expression for the coherent information of a decohered toric code, thereby establishing a rigorous connection between the fundamental error threshold and the criticality of the RBIM.Comment: 5 + 2 pages, 3 figure

Signatures of a Deconfined Phase Transition on the Shastry-Sutherland Lattice: Applications to Quantum Critical SrCu2_2(BO3_3)2_2

We study a possible deconfined quantum phase transition in a realistic model of a two-dimensional Shastry-Sutherland quantum magnet, using both numerical and field theoretic techniques. Using the infinite density matrix renormalization group (iDMRG) method, we verify the existence of an intermediate plaquette valence bond solid (pVBS) order, with two fold degeneracy, between the dimer and N\'eel ordered phases. We argue that the quantum phase transition between the N\'eel and pVBS orders may be described by a deconfined quantum critical point (DQCP) with an emergent O(4) symmetry. By analyzing the correlation length spectrum obtained from iDMRG, we provide evidence for the DQCP and emergent O(4) symmetry in the lattice model. Such a phase transition has been reported in the recent pressure tuned experiments in the Shastry-Sutherland lattice material $\mathrm{SrCu_2 (BO_3)_2}$. The non-symmorphic lattice structure of the Shastry-Sutherland compound leads to extinction points in the scattering, where we predict sharp signatures of a DQCP in both the phonon and magnon spectra associated with the spinon continuum. The effect of weak interlayer couplings present in the three dimensional material is also discussed. Our results should help guide the experimental study of DQCP in quantum magnets.Comment: 22 pages, 6 tables, 15 figures; in v2 numerical details added in appendi

A study on postpartum symptoms and their related factors in Korea

AbstractObjectiveThis study was aimed to identify the physical and mental state of women after delivery, to investigate the factors that influence those, and to examine the effects of postpartum care performance, which is traditionally believed to be appropriate care in Korea, on women's physical and mental status.Materials and MethodsA total of 148 women who visited our hospital for postpartum check-up on the 2nd week or 6th week after delivery were selected. We researched postpartum care methods using a questionnaire and had the women self-evaluate their postpartum symptoms. Depression was evaluated using the Beck Depression Inventory.ResultsThe average points of the 27 postpartum symptoms was 2.70 points (from 1 = very good to 5 = very bad). Seventy-two women had depression. Factors related to postpartum symptoms and depression were smoking before pregnancy, low marital satisfaction, bad mood during and after pregnancy, lack of support from husbands, and bad quality of sleep during puerperium. Treating the joints of hands carefully when milking breasts, and avoiding squatting down, demonstrated a negative correlation with the average points of postpartum symptoms. Multivariate linear regression analysis showed that mood during puerperium and Beck Depression Inventory points were significant factors related to the average points of postpartum symptoms and that the degree of support from husbands and mood during pregnancy were statistically related with depression.ConclusionMany women complained of postpartum discomfort. Although, while some postpartum care methods which are traditionally believed to be appropriate care in Korea can be helpful to women's recovery, most of them are not. We confirmed that physical symptoms and depression are closely related to each other

Practical variational tomography for critical 1D systems

We improve upon a recently introduced efficient quantum state reconstruction procedure targeted to states well-approximated by the multi-scale entanglement renormalization ansatz (MERA), e.g., ground states of critical models. We show how to numerically select a subset of experimentally accessible measurements which maximizes information extraction about renormalized particles, thus dramatically reducing the required number of physical measurements. We numerically estimate the number of measurements required to characterize the ground state of the critical 1D Ising (resp. XX) model and find that MERA tomography on 16-qubit (resp. 24-qubit) systems requires the same experimental effort than brute-force tomography on 8 qubits. We derive a bound computable from experimental data which certifies the distance between the experimental and reconstructed states

Spontaneous breaking of U(1) symmetry at zero temperature in one dimension

The Hohenberg--Mermin--Wagner theorem states that there is no spontaneous breaking of continuous symmetries in spatial dimensions $d\leq2$ at finite temperature. At zero temperature, the classical/quantum mapping further implies the absence of continuous symmetry breaking in one dimension, which is also known as Coleman's theorem in the context of relativistic quantum field theories. Except for the classic example of the Heisenberg ferromagnet and its variations, there has been no known counterexample to the theorem. In this Letter, we discuss new examples that display spontaneous breaking of a U(1) symmetry at zero temperature, although the order parameter does not commute with the Hamiltonian unlike the Heisenberg ferromagnet. We argue that a more general condition for this behavior is that the Hamiltonian is frustration-free.Comment: 5 pages, 1 figure + Supplementary Material (16 pages and 3 figures

k-Space Deep Learning for Reference-free EPI Ghost Correction

Nyquist ghost artifacts in EPI are originated from phase mismatch between the even and odd echoes. However, conventional correction methods using reference scans often produce erroneous results especially in high-field MRI due to the non-linear and time-varying local magnetic field changes. Recently, it was shown that the problem of ghost correction can be reformulated as k-space interpolation problem that can be solved using structured low-rank Hankel matrix approaches. Another recent work showed that data driven Hankel matrix decomposition can be reformulated to exhibit similar structures as deep convolutional neural network. By synergistically combining these findings, we propose a k-space deep learning approach that immediately corrects the phase mismatch without a reference scan in both accelerated and non-accelerated EPI acquisitions. To take advantage of the even and odd-phase directional redundancy, the k-space data is divided into two channels configured with even and odd phase encodings. The redundancies between coils are also exploited by stacking the multi-coil k-space data into additional input channels. Then, our k-space ghost correction network is trained to learn the interpolation kernel to estimate the missing virtual k-space data. For the accelerated EPI data, the same neural network is trained to directly estimate the interpolation kernels for missing k-space data from both ghost and subsampling. Reconstruction results using 3T and 7T in-vivo data showed that the proposed method outperformed the image quality compared to the existing methods, and the computing time is much faster.The proposed k-space deep learning for EPI ghost correction is highly robust and fast, and can be combined with acceleration, so that it can be used as a promising correction tool for high-field MRI without changing the current acquisition protocol.Comment: To appear in Magnetic Resonance in Medicin

A KINEMATICAL ANALYSIS OF THE TAEKWONDO APCHAGI

The purpose of this study was to investigate the kinematical characteristics of Apchagi in Taekwondo kicking motion using the techniques of three dimensional cinematographic techniques. Four college athletes were selected as subjects. After analyzing Apchgi motion, it is concluded the followings. In performing Apchagi, the average time was 0.61 ± 0.02 seconds and the center of body moved right-left (X-axis) 3.7 ± 0.8 cm, forward-back (Y-axis) 46.1 ± 4.5 cm, up-down (Z-axis) 14.4 ± 2.4 cm. Y-axis movement showed the biggest scale among these three direction variances because it need to move the body forward to kick the target. In preparing the motion, pelvic angle showed 150.9 ± 1.05° and in kicking motion 118.5 ± 1.28°. Knee's angle was 71.0 ± 1.33° in f1exion motion. On the other hand, Ankle angle was 113.2 ± 1.73° for preparing the motion and 136.1 ± 4.16° for taking off motion. For flexion phase it increased up to 162.1 ± 5.85° and decreased to 150.9 ± 3.50° in kicking motion