Related papers: Constructing a qubit POVM from quantum data

Constructing a qubit POVM from quantum data

URL: http://arxiv.org/abs/2011.01987v1
Date: Tue, 3 Nov 2020 20:07:24 GMT
Title: Constructing a qubit POVM from quantum data
Authors: Mark Hillery
Abstract summary: We find a POVM that will discriminate between the two states by measuring the qubits. We do not know the states, and for any given qubit, we do not know which of the two states it is in. The POVM can be used to separate the remaining qubits into two groups, corresponding to the two states present in the ensemble.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: Given an ensemble of qubits, which we are told consists of a mixture of two pure states, one with probability $\eta_{0}$ and one with probability $\eta_{1}$, we want to find a POVM that will discriminate between the two states by measuring the qubits. We do not know the states, and for any given qubit, we do not know which of the two states it is in. This can be viewed as learning a POVM from quantum data. Once found, the POVM can be used to separate the remaining qubits in the ensemble into two groups, corresponding to the two states present in the ensemble. In order to find the POVM, we need more information about the possible states. We examine several cases. First, we suppose that we know that the Bloch vectors of the states lie in the x-z plane and their \emph{a priori} probabilities are equal. We next keep the restriction to the x-z plane, but allow the \emph{a priori} probabilities to be different. Finally, we consider the case in which the Bloch vectors of the states have the same z component.

Related papers

Unsupervised state learning from pairs of states [0.0]
We show that if an additional copy of each qubit is supplied, that is, one receives pairs of qubits, both in the same state, rather than single qubits. We then simulate numerically the measurement of a sequence of qubit pairs and show that the unknown states and their respective probabilities of occurrence can be found with high accuracy.
arXiv Detail & Related papers (2024-09-17T12:19:56Z)
Pseudorandom and Pseudoentangled States from Subset States [49.74460522523316]
A subset state with respect to $S$, a subset of the computational basis, is [ frac1sqrt|S|sum_iin S |irangle. We show that for any fixed subset size $|S|=s$ such that $s = 2n/omega(mathrmpoly(n))$ and $s=omega(mathrmpoly(n))$, a random subset state is information-theoretically indistinguishable from a Haar random state even provided
arXiv Detail & Related papers (2023-12-23T15:52:46Z)
Nonlocality under Computational Assumptions [51.020610614131186]
A set of correlations is said to be nonlocal if it cannot be reproduced by spacelike-separated parties sharing randomness and performing local operations. We show that there exist (efficient) local producing measurements that cannot be reproduced through randomness and quantum-time computation.
arXiv Detail & Related papers (2023-03-03T16:53:30Z)
Correspondence between entangled states and entangled bases under local transformations [0.0]
We prove that for bipartite states with a local dimension that is either $2, 4$ or $8$, every state corresponds to a basis. For some states of four qubits we are unable to find a basis, leading us to conjecture that not all quantum states admit a corresponding measurement.
arXiv Detail & Related papers (2023-01-30T20:53:12Z)
Subsystem Trace-Distances of Two Random States [0.0]
We study two-state discrimination in chaotic quantum systems. We analytically calculate the corresponding crossover for finite numbers $N$ of qubits. We test our predictions against exact diagonalization of models for many-body chaos.
arXiv Detail & Related papers (2022-10-06T21:16:10Z)
Maximal gap between local and global distinguishability of bipartite quantum states [7.605814048051737]
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.
arXiv Detail & Related papers (2021-10-08T21:40:02Z)
Machine-Learning-Derived Entanglement Witnesses [55.76279816849472]
We show a correspondence between linear support vector machines (SVMs) and entanglement witnesses. We use this correspondence to generate entanglement witnesses for bipartite and tripartite qubit (and qudit) target entangled states.
arXiv Detail & Related papers (2021-07-05T22:28:02Z)
Partitioning dysprosium's electronic spin to reveal entanglement in non-classical states [55.41644538483948]
We report on an experimental study of entanglement in dysprosium's electronic spin. Our findings open up the possibility to engineer novel types of entangled atomic ensembles.
arXiv Detail & Related papers (2021-04-29T15:02:22Z)
Stochastic behavior of outcome of Schur-Weyl duality measurement [45.41082277680607]
We focus on the measurement defined by the decomposition based on Schur-Weyl duality on $n$ qubits. We derive various types of distribution including a kind of central limit when $n$ goes to infinity.
arXiv Detail & Related papers (2021-04-26T15:03:08Z)
Analysis of KNN Density Estimation [56.29748742084386]
kNN density estimation is minimax optimal under both $ell_infty$ and $ell_infty$ criteria, if the support set is known. The $ell_infty$ error does not reach the minimax lower bound, but is better than kernel density estimation.
arXiv Detail & Related papers (2020-09-30T03:33:17Z)
Constructing a ball of separable and absolutely separable states for $2\otimes d$ quantum system [0.0]
We find that the absolute separable states are useful in quantum computation even if it contains infinitesimal quantum correlation in it. In particular, for qubit-qudit system, we show that the newly constructed ball contain larger class of absolute separable states.
arXiv Detail & Related papers (2020-07-02T05:34:57Z)

This list is automatically generated from the titles and abstracts of the papers in this site.