Upper Bounds on the Size of Quantum Codes

基于完全解耦置信传播的蒙特卡洛方法确定量子稳定子码码距上界

Determining the upper bound of code distance of quantum stabilizer codes through Monte Carlo method based on fully decoupled belief propagation

本文提出基于完全解耦置信传播的蒙特卡洛算法，高效确定量子稳定子码码距上界，验证其精度并支持XYZ乘积码码距达$O(N^{2/3})$的猜想。

Upper bounds of eavesdropper's performances in finite-length code with decoy method

Security formulas of quantum key distribution (QKD) with imperfect resources are obtained for finite-length code when the decoy method is applied. This analysis is useful for guaranteeing the security of implemented QKD systems. Our formulas take into account the effect of the vacuum state and dark counts in the detector. We compare the asymptotic key generation rate in presence of dark counts with that without.

Quantum Error Detection II: Bounds

In Part II we show that there exist quantum codes whose probability of undetected error falls exponentially with the length of the code and derive bounds on this exponent.The lower (existence) bound for stabilizer codes is proved by a counting argument for classical self-orthogonal quaternary codes. Upper bounds for any quantum codes are proved by linear programming. We present two general solutions of the LP problem. Together they give an upper bound on the exponent of undetected error. The upper and lower asymptotic bounds coincide for a certain interval of code rates close to 1.

A semidefinite programming upper bound of quantum capacity

Recently the power of positive partial transpose preserving (PPTp) and no-signalling (NS) codes in quantum communication has been studied. We continue with this line of research and show that the NS/PPTp/NS$\cap$PPTp codes assisted zero-error quantum capacity depends only on the non-commutative bipartite graph of the channel and the one-shot case can be computed efficiently by semidefinite programming (SDP). As an example, the activated PPTp codes assisted zero-error quantum capacity is carefully studied. We then present a general SDP upper bound $Q_Γ$ of quantum capacity and show it is always…

Upper Bounds on the Rate of Low Density Stabilizer Codes for the Quantum Erasure Channel

Using combinatorial arguments, we determine an upper bound on achievable rates of stabilizer codes used over the quantum erasure channel. This allows us to recover the no-cloning bound on the capacity of the quantum erasure channel, R is below 1-2p, for stabilizer codes: we also derive an improved upper bound of the form : R is below 1-2p-D(p) with a function D(p) that stays positive for 0 < p < 1/2 and for any family of stabilizer codes whose generators have weights bounded from above by a constant - low density stabilizer codes. We obtain an application to percolation theory for a family of …

启发式搜索用于量子APM-LDPC码最小距离上界见证

Heuristic Search for Minimum-Distance Upper-Bound Witnesses in Quantum APM-LDPC Codes

本文研究了通过构造低权非稳定逻辑代表来确定量子APM-LDPC码最小距离上界的方法，利用统一框架和特定结构生成候选，通过排除测试后获得精确上界。