相关论文: Optimal measurements for the dihedral hidden subgr…

The problem of Group Testing is to identify defective items out of a set of objects by means of pool queries of the form "Does the pool contain at least a defective?". The aim is of course to perform detection with the fewest possible…

It is known that any quantum algorithm for Graph Isomorphism that works within the framework of the hidden subgroup problem (HSP) must perform highly entangled measurements across \Omega(n \log n) coset states. One of the only known models…

Quantum detectors provide information about quantum systems by establishing correlations between certain properties of those systems and a set of macroscopically distinct states of the corresponding measurement devices. A natural question…

We show that several problems that figure prominently in quantum computing, including Hidden Coset, Hidden Shift, and Orbit Coset, are equivalent or reducible to Hidden Subgroup for a large variety of groups. We also show that, over…

We prove the expected disturbance caused to a quantum system by a sequence of randomly ordered two-outcome projective measurements is upper bounded by the square root of the probability that at least one measurement in the sequence accepts.…

The discrete logarithm problem in a finite group is the basis for many protocols in cryptography. The best general algorithms which solve this problem have time complexity of $\mathcal{O}(\sqrt{N}\log N)$, and a space complexity of…

Quantum sensing is commonly described as a constrained optimization problem: maximize the information gained about an unknown quantity using a limited number of particles. Important sensors including gravitational-wave interferometers and…

Many quantum algorithms, including Shor's celebrated factoring and discrete log algorithms, proceed by reduction to a hidden subgroup problem, in which a subgroup H of a group G must be determined from a quantum state y uniformly supported…

To address the issue of excessive quantum resource requirements in Kuperberg's algorithm for the dihedral hidden subgroup problem, this paper proposes a distributed algorithm based on the function decomposition. By splitting the original…

Recently, a technique known as quantum symmetry test has gained increasing attention for detecting bipartite entanglement in pure quantum states. In this work we show that, beyond qualitative detection, a family of well-defined measures of…

We study an optimized measurement which discriminates N mixed quantum states occurring with given prior robabilities. The measurement yields the maximum achievable confidence for each of the N conclusive outcomes, thereby keeping the…

We study the hardness of the dihedral hidden subgroup problem. It is known that lattice problems reduce to it, and that it reduces to random subset sum with density $> 1$ and also to quantum sampling subset sum solutions. We examine a…

We analyze the fundamental resolution of incoherent optical point sources from the perspective of a quantum detection problem: deciding whether the optical field on the image plane is generated by one source or two weaker sources with…

Entanglement is a fundamental feature of quantum mechanics and holds great promise for enhancing metrology and communications. Much of the focus of quantum metrology so far has been on generating highly entangled quantum states that offer…

We study an optimized measurement that discriminates two mixed quantum states with maximum confidence for each conclusive result, thereby keeping the overall probability of inconclusive results as small as possible. When the rank of the…

The study of Dense-$3$-Subhypergraph problem was initiated in Chlamt{\'{a}}c et al. [Approx'16]. The input is a universe $U$ and collection ${\cal S}$ of subsets of $U$, each of size $3$, and a number $k$. The goal is to choose a set $W$ of…

Experimental characterizations of a quantum system involve the measurement of expectation values of observables for a preparable state |psi> of the quantum system. Such expectation values can be measured by repeatedly preparing |psi> and…

As the connection between classical and quantum worlds, quantum measurements play a unique role in the era of quantum information processing. Given an arbitrary function of quantum measurements, how to obtain its optimal value is often…

We advocate a new approach of addressing hidden structure problems and finding efficient quantum algorithms. We introduce and investigate the Hidden Symmetry Subgroup Problem (HSSP), which is a generalization of the well-studied Hidden…

The group testing problem consists of determining a sparse subset of defective items from within a larger set of items via a series of tests, where each test outcome indicates whether at least one defective item is included in the test. We…