International Journal of Physics and Mathematics

Local measurement in entangled systems: Conditional states, quantum instruments, and the no-signalling theorem

Sachin .

Published Jul 1, 2025• 0 citations

Abstract

A local measurement on one member of an entangled composite system is said to change the distant member's state instantaneously. Taken without qualification, this is misleading. A selective measurement changes the conditional state assigned to the remote subsystem once a local outcome is specified; a non-selective measurement, where that outcome is ignored, leaves the remote reduced density operator unchanged. This distinction reconciles quantum state update with operational no-signalling and provides the setting for Einstein–Podolsky–Rosen steering. This review develops measurement using density operators, completely positive instruments, Kraus representations, partial traces, conditional states, and steering assemblages. It derives the invariance of remote marginal statistics under local trace-preserving operations and contrasts this with Bell-local factorization. It examines the hierarchy among entanglement, steering, and Bell nonlocality, joint measurability, remote state preparation, and one-sided device-independent protocols. The article considers spacelike-separated measurements, microcausality in relativistic quantum theory, and ontological readings of selective state update offered by Everettian, Bohmian, collapse, and relational approaches. Decoherence is treated as the process through which local outcomes become records, while quantum Darwinism accounts for their redundant local accessibility. It highlights gaps in literature, and concludes that entanglement permits nonclassical conditional correlations, but local measurement supplies no controllable superluminal signal.

DOI: 10.33545/26648636.2025.v7.i2.257

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