The Parity Bit in Quantum Cryptography

An $n$-bit string is encoded as a sequence of non-orthogonal quantum states. The parity bit of that $n$-bit string is described by one of two density matrices, $\rho_0^{(n)}$ and $\rho_1^{(n)}$, both in a Hilbert space of dimension $2^n$. In order to derive the parity bit the receiver must distinguish between the two density matrices, e.g., in terms of optimal mutual information. In this paper we find the measurement which provides the optimal mutual information about the parity bit and calculate that information. We prove that this information decreases exponentially with the length of the string in the case where the single bit states are almost fully overlapping. We believe this result will be useful in proving the ultimate security of quantum crytography in the presence of noise.Comment: 19 pages, RevTe

Satisfaction with care after total hip or knee replacement predicts self-perceived health status after surgery

<p>Abstract</p> <p>Background</p> <p>Inpatient satisfaction with care is a standard indicator of the quality of care delivered during hospitalization. Total hip and knee replacement (THR/TKR) for osteoarthritis (OA) are among the most successful orthopaedic interventions having a positive impact on health-related quality of life (HRQoL). The aim was to evaluate the effect of satisfaction shortly after hospital discharge on 1-month, 6-month and 1-year Medical Outcomes Study 36-item Short Form (SF-36) scores for OA patients after THR and TKR, controlling for patient characteristics, clinical presentation and preoperative SF-36 scores.</p> <p>Methods</p> <p>A multicenter prospective cohort study recruited 231 patients with OA scheduled to receive THR or TKR. Satisfaction was assessed by the Patients Judgment of Hospital Quality (PJHQ) questionnaire and HRQoL by the SF-36 questionnaire. Linear models for repeated measures assessed the relation between satisfaction (scores were dichotomized) and postoperative SF-36 scores.</p> <p>Results</p> <p>Of 231 participants, 189 were followed up 12 months after discharge (mean age 69 SD = 8; 42.6% male). The mean length of hospital stay was 13.5 (SD = 4) days. After adjustment for preoperative SF-36 scores, sociodemographic and clinical patient characteristics, satisfied patients (PJHQ score > 70) had higher SF-36 scores 1 year after surgery than did less-satisfied patients. Admission, medical care, and nursing and daily care scores mainly predicted bodily pain, mental health, social functioning, vitality and general health scores of the SF-36.</p> <p>Conclusion</p> <p>Besides being a quality-of-care indicator, immediate postoperative patient satisfaction with care may bring a new insight into clinical practice, as a predictor of self-perceived health status after surgery.</p

A review of symptomatic leg length inequality following total hip arthroplasty

Leg length inequality (LLI) following total hip replacement is a complication which features increasingly in the recent literature. The definition of LLI is complicated by lack of consensus regarding radiological measurement, clinical measurement and the incomplete relationship between LLI and associated symptoms. This paper reviews 79 reports relating to LLI post hip replacement, detailing definitions and classification and highlighting patient populations prone to symptomatic LLI. While there is no universal definition of LLI, there is a broad consensus that less than 10 mm of difference on AP view plain radiographs is clinically acceptable. There are few techniques described that consistently produce a postoperative LLI of less than this magnitude. Where postoperative LLI exists, lengthening appears to cause more problems than shortening. In cases of mild LLI, non-surgical management produces adequate outcomes in the majority of cases, with functional LLI cases doing better than those with true LLI. Operative correction is effective in half of cases, even where nerve palsy is present, and remains an important option of last resort. Poor outcomes in patients with LLI may be minimised if individuals at risk are identified and counselled appropriately