On the Measurement attaining the Quantum Guesswork
- URL: http://arxiv.org/abs/2302.06783v2
- Date: Thu, 21 Mar 2024 01:18:03 GMT
- Title: On the Measurement attaining the Quantum Guesswork
- Authors: Michele Dall'Arno,
- Abstract summary: The guesswork quantifies the minimum cost incurred in guessing the state of an ensemble, when only one state can be queried at a time.
In the classical case, the optimal strategy trivially consists of querying the states in their non-increasing order of posterior probability.
In the quantum case, the most general strategy to obtain the optimal ordering in which to perform the queries consist of a quantum measurement.
- Score: 2.900810893770134
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: The guesswork quantifies the minimum cost incurred in guessing the state of an ensemble, when only one state can be queried at a time. In the classical case, it is well known that the optimal strategy trivially consists of querying the states in their non-increasing order of posterior probability. In the quantum case, on the other hand, the most general strategy to obtain the optimal ordering in which to perform the queries consist of a quantum measurement. Here, we solve such an optimization problem by deriving the quantum measurement attaining the guesswork for a broad class of ensembles and cost functions.
Related papers
- Data Processing Inequality for The Quantum Guesswork [4.956709222278243]
Non-orthogonal quantum states cannot be distinguished with absolute certainty.
Quantum guesswork has emerged as a crucial measure in assessing the distinguishability of non-orthogonal quantum states.
arXiv Detail & Related papers (2024-07-22T19:42:16Z) - Sparse random Hamiltonians are quantumly easy [105.6788971265845]
A candidate application for quantum computers is to simulate the low-temperature properties of quantum systems.
This paper shows that, for most random Hamiltonians, the maximally mixed state is a sufficiently good trial state.
Phase estimation efficiently prepares states with energy arbitrarily close to the ground energy.
arXiv Detail & Related papers (2023-02-07T10:57:36Z) - Anticipative measurements in hybrid quantum-classical computation [68.8204255655161]
We present an approach where the quantum computation is supplemented by a classical result.
Taking advantage of its anticipation also leads to a new type of quantum measurements, which we call anticipative.
In an anticipative quantum measurement the combination of the results from classical and quantum computations happens only in the end.
arXiv Detail & Related papers (2022-09-12T15:47:44Z) - Variational Approach to Quantum State Tomography based on Maximal
Entropy Formalism [3.6344381605841187]
We employ the maximal entropy formalism to construct the least biased mixed quantum state that is consistent with the given set of expectation values.
We employ a parameterized quantum circuit and a hybrid quantum-classical variational algorithm to obtain such a target state making our recipe easily implementable on a near-term quantum device.
arXiv Detail & Related papers (2022-06-06T01:16:22Z) - Entanglement and coherence in Bernstein-Vazirani algorithm [58.720142291102135]
Bernstein-Vazirani algorithm allows one to determine a bit string encoded into an oracle.
We analyze in detail the quantum resources in the Bernstein-Vazirani algorithm.
We show that in the absence of entanglement, the performance of the algorithm is directly related to the amount of quantum coherence in the initial state.
arXiv Detail & Related papers (2022-05-26T20:32:36Z) - Improved Quantum Algorithms for Fidelity Estimation [77.34726150561087]
We develop new and efficient quantum algorithms for fidelity estimation with provable performance guarantees.
Our algorithms use advanced quantum linear algebra techniques, such as the quantum singular value transformation.
We prove that fidelity estimation to any non-trivial constant additive accuracy is hard in general.
arXiv Detail & Related papers (2022-03-30T02:02:16Z) - A Quantum Optimal Control Problem with State Constrained Preserving
Coherence [68.8204255655161]
We consider a three-level $Lambda$-type atom subjected to Markovian decoherence characterized by non-unital decoherence channels.
We formulate the quantum optimal control problem with state constraints where the decoherence level remains within a pre-defined bound.
arXiv Detail & Related papers (2022-03-24T21:31:34Z) - Quantum mean value approximator for hard integer value problems [19.4417702222583]
We show that an optimization can be improved substantially by using an approximation rather than the exact expectation.
Together with efficient classical sampling algorithms, a quantum algorithm with minimal gate count can thus improve the efficiency of general integer-value problems.
arXiv Detail & Related papers (2021-05-27T13:03:52Z) - One-shot quantum state redistribution and quantum Markov chains [15.66921140731163]
We revisit the task of quantum state redistribution in the one-shot setting.
We design a protocol for this task with communication cost in terms of a measure of distance from quantum Markov chains.
Our result is the first to operationally connect quantum state redistribution and quantum chains.
arXiv Detail & Related papers (2021-04-18T07:34:22Z) - Guesswork of a quantum ensemble [3.867363075280544]
We derive analytical solutions of the guesswork problem subject to a finite set of conditions.
As explicit examples, we compute the guesswork for any qubit regular polygonal and polyhedral ensemble.
arXiv Detail & Related papers (2020-12-17T01:47:18Z) - Quantum Gram-Schmidt Processes and Their Application to Efficient State
Read-out for Quantum Algorithms [87.04438831673063]
We present an efficient read-out protocol that yields the classical vector form of the generated state.
Our protocol suits the case that the output state lies in the row space of the input matrix.
One of our technical tools is an efficient quantum algorithm for performing the Gram-Schmidt orthonormal procedure.
arXiv Detail & Related papers (2020-04-14T11:05:26Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.