In this paper, we introduce a criterion for detecting entanglement based on the uncertainty relation. Our focus is on the generalized Landau-Pollak uncertainty relation and the generalized quantum measurements$(N, M)$-POVMs for quantum state tomography. We introduce a generalized Landau-Pollak uncertainty relation for$(N, M)$-POVMs, which is tighter than other inequalities of its kind. Using this relation, we introduce the criterion for detecting entanglement. In this criterion, a relation between the certainty of a bipartite system and the certainty of the subsystem plays the important role. We also demonstrate the ability to detect both the maximally entangled state and the isortopic state under certain parameters.

In this paper, we introduce the extended mean king's problem and its solutions. Also, we show a quantum key distribution (QKD) using the extended mean king's problem. By using the quantum key distribution, a sender can share a secret key with each of receivers. Besides, we consider the tolerance to an eavesdropper who makes intercept-resend attacks. As a result, in the case of two receivers, we indicate that the quantum key distribution is robust against the intercept-resend attacks by showing that the error occurs between the secret keys of a sender and receivers.

The frame error rate (FER) of spatially-coupled irregular low-density parity-check (SC-iLDPC) code ensemble in error floor region is estimated. First, the number of codewords of each weight is calculated by the permutations of all the sub-codewords at their coupling positions. Second, the FER is estimated by these numbers of the codewords of each weight. Numerical results show that the FER performances in the error floor regions of the SC-iLDPC code ensembles are superior to the conventional irregular LDPC code ensembles at almost identical belief-propagation (BP) thresholds.

A K-user nonbinary parallel concatenated code (PCC) is proposed for a Gaussian MAC with symbol synchronization, equal-power, and equal-rate users. In a K-user q-ary PCC over finite field GF(q), each user employs a parallel concatenated code, with a rate-(1/r) q-ary repetition component code and M rate-1 q-ary accumulation component codes. Employing q-ary repetition code is to overcome the multi-user interference and also provide coding gain. The K-user q-ary PCC is not only rate compatible, but also with very low encoding and decoding complexities due to employing such simple component codes. An EXIT chart analysis is given to estimate the decoding threshold of the K-user q-ary PCC. Numerical results show that the decoding threshold of K-user q-ary PCC improves as the field order q increases. The 10-user 64-ary PCC improves the decoding threshold by 1.88 dB over the binary case. The decoding threshold of 15-user 64-ary PCC at sum rate 3/4 is only 0.75 dB away from the Shannon bound. Bit-error-rate simulations are provided to verify the analysis.

It is anticipated that quantum key distribution enable us to share a secret key while guaranteeing unconditionally security. In this paper, we discuss the quantum key distribution using the Mean King Problem which was proposed by J. Bub in 2001. While this two-way quantum protocol is essentially different from the other one-way protocols like the BB84, it has been shown that Eve cannot gain any information without being detected even in this protocol. Assuming two attack scenarios in this protocol, we derive two trade-off inequalities showing that the larger Eve's information gain is, the higher the detectability becomes. These quantitative inequalities enables the legitimate users to estimate Eve's information gain.