相关论文: Optimal measurements for the dihedral hidden subgr…
We find the optimal measurement for distinguishing between symmetric multi-mode phase-randomized coherent states. A motivation for this is that phase-randomized coherent states can be used for quantum communication, including quantum…
Entanglement is one of the key resources of quantum information science which makes identification of entangled states essential to a wide range of quantum technologies and phenomena. This problem is however both computationally and…
Given $n$ linearly independent pure states and their prior probabilities, we study the problem of optimum unambiguous discrimination of these states. We derive the properties of the optimum solution and the equations that must be satisfied…
We consider the group isomorphism problem: given two finite groups G and H specified by their multiplication tables, decide if G and H are isomorphic. The n^(log n) barrier for group isomorphism has withstood all attacks --- even for the…
We prove a tight and close-to-optimal lower bound on the effectiveness of local quantum measurements (without classical communication) at discriminating any two bipartite quantum states. Our result implies, for example, that any two…
The log-density method is a powerful algorithmic framework which in recent years has given rise to the best-known approximations for a variety of problems, including Densest-$k$-Subgraph and Bipartite Small Set Vertex Expansion. These…
Von Neumann projections are the main operations by which information can be extracted from the quantum to the classical realm. They are however static processes that do not adapt to the states they measure. Advances in the field of adaptive…
We consider the problem of discriminating qubit states that are sent over a quantum channel and derive a necessary and sufficient condition for an optimal measurement to be preserved by the channel. We apply the result to the…
This paper presents a method for the robust selection of measurements in a simultaneous localization and mapping (SLAM) framework. Existing methods check consistency or compatibility on a pairwise basis, however many measurement types are…
The basic goal in combinatorial group testing is to identify a set of up to $d$ defective items within a large population of size $n \gg d$ using a pooling strategy. Namely, the items can be grouped together in pools, and a single…
The quantum hidden subgroup approach is an actively studied approach to solve combinatorial problems in quantum complexity theory. With the success of the Shor's algorithm, it was hoped that similar approach may be useful to solve the other…
In the King's Problem, a physicist is asked to prepare a d-state quantum system in any state of her choosing and give it to a king who measures one of (d+1) sets of mutually unbiased observables on it. The physicist is then allowed to make…
Uncertainty principle is an inherent nature of quantum system that undermines the precise measurement of incompatible observables and hence the applications of quantum theory. Entanglement, another unique feature of quantum physics, was…
Every sufficiently rich set of measurements on a fixed quantum system defines a statistical norm on the states of that system via the optimal bias that can be achieved in distinguishing the states using measurements from that set (assuming…
In this paper we show that certain special cases of the hidden subgroup problem can be solved in polynomial time by a quantum algorithm. These special cases involve finding hidden normal subgroups of solvable groups and permutation groups,…
The subset sum problem is known to be an NP-hard problem in the field of computer science with the fastest known approach having a run-time complexity of $O(2^{0.3113n})$. A modified version of this problem is known as the perfect sum…
The distinct elements problem is one of the fundamental problems in streaming algorithms --- given a stream of integers in the range $\{1,\ldots,n\}$, we wish to provide a $(1+\varepsilon)$ approximation to the number of distinct elements…
Quantum state tomography is a fundamental problem in quantum computing. Given $n$ copies of an unknown $N$-qubit state $\rho \in \mathbb{C}^{d \times d},d=2^N$, the goal is to learn the state up to an accuracy $\epsilon$ in trace distance,…
We present optimal schemes, based on photon number measurements, for Gaussian state tomography and for Gaussian process tomography. An $n$-mode Gaussian state is completely specified by $2 n^2+3n$ parameters. Our scheme requires exactly $2…
We investigate the tradeoff between the quality of an approximate version of a given measurement and the disturbance it induces in the measured quantum system. We prove that if the target measurement is a non-degenerate von Neumann…