The Measurement Bottleneck in Quantum Computing: Holevo-Limited Readout and the Role of Phase-Window Coordination in Distributed Architectures

This note clarifies a fundamental but often-misunderstood limitation of quantum computation: regardless of the exponentially large Hilbert space of an \(N\)-qubit register, the amount of classical information that can be extracted from a single run is bounded by the quantum-to-classical measurement interface. Using the accessible information framework and the Holevo bound, we show that for a system of dimension \(d\) (in particular \(d=2^N\)), the accessible classical information per run satisfies \(I_{\mathrm{acc}}\le \log d\), i.e. at most \(N\) bits for \(N\) qubits (log base 2).  

We emphasize that quantum advantage is therefore not about “reading out” exponentially many classical bits, but about how interference structures the distribution of \(O(N)\) measured bits so that they encode useful answers.  

Finally, we discuss why temporal/phase coordination becomes an architectural requirement in *distributed* quantum computing and quantum networks: without a shared phase/time reference, operations are symmetry-restricted and measurement events across nodes may fail to compose reliably. This motivates cycle-anchored phase-window coordination and reference-frame/asymmetry viewpoints as practical foundations for scalable distributed systems.  

Keywords
quantum measurement, Holevo bound, accessible information, readout bottleneck, distributed quantum computing, quantum networks, phase coordination, \(U(1)\) asymmetry.