https://haifei.pro/en/tags/haar-measure/Recent content in Haar Measure on Haifei's HomeHugoenhfwang132@gmail.com (hfwang132)hfwang132@gmail.com (hfwang132)This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.Fri, 30 May 2025 02:53:53 +0800https://haifei.pro/en/post_20250530_%E9%87%8F%E5%AD%90%E6%80%81%E7%9A%84%E7%BB%8F%E5%85%B8%E9%98%B4%E5%BD%B1-classical-shadows/Fri, 30 May 2025 02:53:53 +0800hfwang132@gmail.com (hfwang132)https://haifei.pro/en/post_20250530_%E9%87%8F%E5%AD%90%E6%80%81%E7%9A%84%E7%BB%8F%E5%85%B8%E9%98%B4%E5%BD%B1-classical-shadows/<h2 id="i-quantum-state-tomography">I. Quantum State Tomography</h2> <p>At present, quantum states composed of hundreds or thousands of qubits can already be prepared (twenty references omitted here).</p> <p>But how do we know that the prepared quantum state \(\rho\) is indeed the one we want \(\rho\)? Or, more broadly: how can we learn (some or all) information about a quantum state \(\rho\)?</p> <p>To learn a quantum state \(\rho\), we first need to prepare \(\rho\), then measure it in different measurement bases to obtain probability distribution functions, and finally use these probability distribution functions to learn \(\rho\). This process is called <strong>quantum state tomography</strong>.</p>