Attainability of quantum state discrimination bounds with collective measurements on finite copies

• URL: http://arxiv.org/abs/2408.06678v2
• Date: Tue, 01 Apr 2025 11:06:05 GMT
• Title: Attainability of quantum state discrimination bounds with collective measurements on finite copies
• Authors: Lorcan Conlon, Jin Ming Koh, Biveen Shajilal, Jasminder Sidhu, Ping Koy Lam, Syed M. Assad,
• Abstract summary: We find analytic expressions for the Helstrom bound for arbitrarily many copies of the unknown state in several simple qubit examples.<n>We also investigate the necessary conditions to saturate the M-copy Helstrom bound.
• Score: 0.21111026813272177
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: One of the fundamental tenets of quantum mechanics is that non-orthogonal states cannot be distinguished perfectly. When distinguishing multiple copies of a mixed quantum state, a collective measurement, which generates entanglement between the different copies of the unknown state, can achieve a lower error probability than non-entangling measurements. The error probability that can be attained using a collective measurement on a finite number of copies of the unknown state is given by the Helstrom bound. In the limit where we can perform a collective measurement on asymptotically many copies of the quantum state, the quantum Chernoff bound gives the attainable error probability. It is natural to ask at what rate does the error tend to this asymptotic limit, and whether the asymptotic limit can be attained for any finite number of copies. In this paper we address these questions. We find analytic expressions for the Helstrom bound for arbitrarily many copies of the unknown state in several simple qubit examples. Using these analytic expressions, we investigate how the attainable error rate changes as we allow collective measurements on finite numbers of copies of the quantum state. We also investigate the necessary conditions to saturate the M-copy Helstrom bound. It is known that a collective measurement on all M-copies of the unknown state is always sufficient to saturate the M-copy Helstrom bound. However, general conditions for when such a measurement is necessary to saturate the Helstrom bound remain unknown. We investigate specific measurement strategies which involve entangling operations on fewer than all M-copies of the unknown state. For many regimes we find that a collective measurement on all M-copies of the unknown state is necessary to saturate the M-copy Helstrom bound.

Related papers

• Quantum state exclusion with many copies [18.6184930294792]
  We show that for any set of three or more pure states, state exclusion becomes possible with a finite number of copies.<n>We further show that the required number of copies may be arbitrarily large -- in particular, for every natural number $N$, we construct sets of states for which exclusion remains impossible with $N$ or fewer copies.
  arXiv  Detail & Related papers  (2026-01-20T19:15:41Z)
• Quantum Sequential Universal Hypothesis Testing [62.751483592497806]
  Quantum hypothesis testing (QHT) concerns the statistical inference of unknown quantum states.<n>We introduce the quantum sequential universal test (QSUT), a novel framework for sequential QHT in the general case of composite hypotheses.<n> QSUT builds on universal inference, and it alternates between adaptive local measurements aimed at exploring the hypothesis space and joint measurements optimized for maximal discrimination.
  arXiv  Detail & Related papers  (2025-08-29T12:50:04Z)
• Universal quantum frequency comb measurements by spectral mode-matching [39.58317527488534]
  We present the first general approach to make arbitrary, one-shot measurements of a multimode quantum optical source. This approach uses spectral mode-matching, which can be understood as interferometry with a memory effect.
  arXiv  Detail & Related papers  (2024-05-28T15:17:21Z)
• The role of shared randomness in quantum state certification with unentangled measurements [36.19846254657676]
  We study quantum state certification using unentangled quantum measurements. $Theta(d2/varepsilon2)$ copies are necessary and sufficient for state certification. We develop a unified lower bound framework for both fixed and randomized measurements.
  arXiv  Detail & Related papers  (2024-01-17T23:44:52Z)
• Quantum Simulation of Bound-State-Enhanced Quantum Metrology [1.083709868255469]
  We find that the error of the measurement can vanish due to the existence of the bound state. By both analytical and numerical simulations, we prove the $t-1$ scaling of the measurement error can be recovered when there is a bound state in the hybrid system.
  arXiv  Detail & Related papers  (2023-11-23T14:20:52Z)
• Quantum State Tomography for Matrix Product Density Operators [28.799576051288888]
  Reconstruction of quantum states from experimental measurements is crucial for the verification and benchmarking of quantum devices. Many physical quantum states, such as states generated by noisy, intermediate-scale quantum computers, are usually structured. We establish theoretical guarantees for the stable recovery of MPOs using tools from compressive sensing and the theory of empirical processes.
  arXiv  Detail & Related papers  (2023-06-15T18:23:55Z)
• Discriminating mixed qubit states with collective measurements [0.2621730497733947]
  We propose and experimentally demonstrate a protocol for distinguishing two copies of single qubit states using collective measurements. We implement our measurements on an IBM Q System One device, a superconducting quantum processor.
  arXiv  Detail & Related papers  (2023-02-17T14:02:26Z)
• Observation of partial and infinite-temperature thermalization induced by repeated measurements on a quantum hardware [62.997667081978825]
  We observe partial and infinite-temperature thermalization on a quantum superconducting processor. We show that the convergence does not tend to a completely mixed (infinite-temperature) state, but to a block-diagonal state in the observable basis.
  arXiv  Detail & Related papers  (2022-11-14T15:18:11Z)
• The gap persistence theorem for quantum multiparameter estimation [14.334779130141452]
  We show that it is impossible to saturate the Holevo Cram'er-Rao bound (HCRB) for several physically motivated problems. We further prove that if the SLDCRB cannot be reached with a single copy of the probe state, it cannot be reached with collective measurements on any finite number of copies of the probe state.
  arXiv  Detail & Related papers  (2022-08-15T18:01:22Z)
• Experimental demonstration of optimal unambiguous two-out-of-four quantum state elimination [52.77024349608834]
  A core principle of quantum theory is that non-orthogonal quantum states cannot be perfectly distinguished with single-shot measurements. Here we implement a quantum state elimination measurement which unambiguously rules out two of four pure, non-orthogonal quantum states.
  arXiv  Detail & Related papers  (2022-06-30T18:00:01Z)
• Graph-Theoretic Framework for Self-Testing in Bell Scenarios [37.067444579637076]
  Quantum self-testing is the task of certifying quantum states and measurements using the output statistics solely. We present a new approach for quantum self-testing in Bell non-locality scenarios.
  arXiv  Detail & Related papers  (2021-04-27T08:15:01Z)
• Quantum Algorithm for Quantum State Discrimination via Partial Negation and Weak Measurement [1.2691047660244335]
  A quantum algorithm using weak measurement and partial negation will be proposed to solve the quantum state discrimination problem. The proposed algorithm will be able to determine, with high probability of success, the state of the unknown qubit.
  arXiv  Detail & Related papers  (2021-02-23T21:18:19Z)

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.