Jae-Weon Lee, DoYong Kwon, Jaewan Kim
From the NP-hardness of the quantum separability problem and the relation between bipartite entanglement and the secret key correlations, it is shown that the problem deciding whether a given quantum state has secret correlations in it or not is in NP-complete.
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We study the probability of making an error if, by querying an oracle a fixed number of times, we declare constant a randomly chosen n-bit Boolean function. We compare the classical and the quantum case, and we determine for how many oracle-queries k and for how many bits n one querying procedure is more efficient than the other.
Deciding Whether a C-Q Channel Preserves a Bit is QCMA-Complete
本文证明判定C-Q信道能否精确保持单个经典比特是QCMA完全的，通过矩阵分析刻画最优见证，为比特保持及正交性约束优化问题提供了简明的QCMA完全性证明。
To decide whether a quantum channel is degradable is relatively easy: one has to find at least one example of a degrading quantum channel. But in general, no conclusive criterion exists to show the opposite. Using elementary methods we derive a necessary and sufficient condition to decide under what circumstances the conclusion is unambiguous. The findings lead to an extension of the antidegradability region for qubit and qutrit transpose depolarizing channels. In the qubit case we reproduce the known results for the class of qubit depolarizing channels (due to their equivalence). One of the c…
Advance sharing for stabilizer-based quantum secret sharing schemes
针对基于稳定子的量子秘密共享中禁止集是否均可提前共享的未知问题，通过反例指出现有方案的局限，并提出新方案实现所有禁止集的提前共享。
Quantum key distribution performs the trick of growing a secret key in two distant places connected by a quantum channel. The main reason is that the legitimate users can bound the information gathered by the eavesdropper. In practical systems, whether because of finite resources or external conditions, the quantum channel is subject to fluctuations. A rate adaptive information reconciliation protocol, that adapts to the changes in the communication channel, is then required to minimize the leakage of information in the classical postprocessing. We consider here the leakage of a rate-adaptive …
Advance sharing of quantum shares for quantum secrets
针对量子秘密共享中其他访问结构能否提前分发份额的问题，提出一种支持在秘密确定前分发份额的量子秘密共享方案。
We study space and time efficient quantum algorithms for two graph problems -- deciding whether an $n$-vertex graph is a forest, and whether it is bipartite. Via a reduction to the s-t connectivity problem, we describe quantum algorithms for deciding both properties in $\tilde{O}(n^{3/2})$ time and using $O(\log n)$ classical and quantum bits of storage in the adjacency matrix model. We then present quantum algorithms for deciding the two properties in the adjacency array model, which run in time $\tilde{O}(n\sqrt{d_m})$ and also require $O(\log n)$ space, where $d_m$ is the maximum degree of …
In this brief report, we consider the equivalence between two sets of $m+1$ bipartite quantum states under local unitary transformations. For pure states, this problem corresponds to the matrix algebra question of whether two degree $m$ matrix polynomials are unitarily equivalent; i.e. $UA_iV^\dagger=B_i$ for $0\leq i\leq m$ where $U$ and $V$ are unitary and $(A_i, B_i)$ are arbitrary pairs of rectangular matrices. We present a randomized polynomial-time algorithm that solves this problem with an arbitrarily high success probability and outputs transforming matrices $U$ and $V$.
Advance Sharing with Ogawa et al.'s Ramp Quantum Secret Sharing Scheme
针对Ogawa等人的斜坡量子秘密共享方案，提出在秘密给出前分发部分份额的方法，并确定了可提前分发份额集合的充分必要条件。
In this paper we investigate the use of quantum information to share classical secrets. While every quantum secret sharing scheme is a quantum error correcting code, the converse is not true. Motivated by this we sought to find quantum codes which can be converted to secret sharing schemes. If we are interested in sharing classical secrets using quantum information, then we show that a class of pure $[[n,1,d]]_q$ CSS codes can be converted to perfect secret sharing schemes. These secret sharing schemes are perfect in the sense the unauthorized parties do not learn anything about the secret. Go…
A weak odd dominated (WOD) set in a graph is a subset B of vertices for which there exists a distinct set of vertices C such that every vertex in B has an odd number of neighbors in C. We point out the connections of weak odd domination with odd domination, [sigma,rho]-domination, and perfect codes. We introduce bounds on κ(G), the maximum size of WOD sets of a graph G, and on κ'(G), the minimum size of non WOD sets of G. Moreover, we prove that the corresponding decision problems are NP-complete. The study of weak odd domination is mainly motivated by the design of graph-based quantum secret …
Composable, unconditional security without a Quantum secret key: public broadcast channels and their conceptualizations, adaptive bit transmission rates, fidelity pruning under wiretaps
研究提出在无条件安全条件下，通过公开广播信道及其概念化实现无需密钥的量子通信协议，并探讨了保密性和认证性的实现条件。
Complexity of Fermionic 2-SAT
本文引入费米子可满足性问题，证明Fermionic 2-SAT及其固定粒子数宇称判定可经典高效求解，而粒子数守恒版本为NP完全，Fermionic 9-SAT为QMA1-hard。
First, we consider the problem of deciding whether a nonlocal game admits a perfect entangled strategy that uses projective measurements on a maximally entangled shared state. Via a polynomial-time Karp reduction, we show that independent set games are the hardest instances of this problem. Secondly, we show that if every independent set game whose entangled value is equal to one admits a perfect entangled strategy, then the same holds for all symmetric synchronous games. Finally, we identify combinatorial lower bounds on the classical and entangled values of synchronous games in terms of vari…
The unbearable hardness of deciding about magic
该研究证明了确定魔法状态的计算难度为超级指数级，揭示了经典模拟和量子资源利用的内在限制。
Advance Sharing Procedures for the Ramp Quantum Secret Sharing Schemes With the Highest Coding Rate
本文针对具有最高编码率的斜坡量子秘密共享方案，提出在秘密给定之前提前分发部分份额的程序，并证明新编码程序不改变量子秘密与份额的对应关系，从而保留原方案的最高编码率。
QMA and QCMA are possible quantum analogues of the complexity class NP. In QCMA the verifier is a quantum program and the proof is classical. In contrast, in QMA the proof is also a quantum state. We show that two known QMA-complete problems can be modified to QCMA-complete problems in a natural way: (1) Deciding whether a 3-local Hamiltonian has low energy states (with energy smaller than a given value) that can be prepared with at most k elementary gates is QCMA-complete, whereas it is QMA-complete when the restriction on the complexity of preparation is dropped. (2) Deciding whether a (clas…
Non-additivity is one of the distinctive traits of Quantum Information Theory: the combined use of quantum objects may be more advantageous than the sum of their individual uses. Non-additivity effects have been proven, for example, for quantum channel capacities, entanglement distillation or state estimation. In this work, we consider whether non-additivity effects can be found in Classical Information Theory. We work in the secret-key agreement scenario in which two honest parties, having access to correlated classical data that are also correlated to an eavesdropper, aim at distilling a sec…
In this paper, we consider the secret-string-learning problem in the teacher-student setting: the teacher has a secret string $s\in {\{0,1\}^{n}}$, and the student wants to learn the secret $s$ by question-answer interactions with the teacher, where at each time, the student can ask the teacher with a pair $(x, q) \in {\{0,1\}^{n}}\times\{0,1,\cdots, n-1\}$ and the teacher returns a bit given by the oracle $f_{s}(x,q)$ that indicates whether the length of the longest common prefix of $s$ and $x$ is greater than $q$ or not. Our contributions are as follows. (i) We prove that any classical deter…
In this paper, a novel multi-party quantum private comparison (MQPC) protocol with a semi-honest third party (TP) is proposed based on the entanglement swapping of d-level cat states and d-level Bell states. Here, TP is allowed to misbehave on his own but will not conspire with any party. In our protocol, n parties employ unitary operations to encode their private secrets and can compare the equality of their private secrets within one time execution of the protocol. Our protocol can withstand both the outside attacks and the participant attacks on the condition that none of the QKD methods is…
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