Predicting quantum measurement outcomes for a local observer makes sense before, but not after, the measurement. However, for a remote observer, predicting measurement outcomes even after measurement remains a valid question. We define remote predictability as the degree to which one observer can predict a measurement outcome of a spatially separated observer, given full knowledge of the shared quantum state and measurement setting. We show that the remote predictability before and after the measurement remains the same for product states, whereas it increases for all pure entangled states and for some classically correlated states. Perfect remote predictability for arbitrary projective measurements occurs only for maximally entangled states among all pure states, underscoring their special role. Comparing pure entangled states with their dephased versions, we find that dephasing on one subsystem can enhance remote predictability for a broad class of states and measurements - a counterintuitive, noise-induced advantage that vanishes for maximally entangled states under any projective measurement.
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11 pages, 1 figure; Revised title and corresponding modifications to the abstract, introduction, and conclusion
Predicting quantum measurement outcomes for a local observer makes sense before, but not after, the measurement. However, for a remote observer, predicting measurement outcomes even after measurement remains a valid question. We define remote predictability as the degree to which one observer can predict a measurement outcome of a spatially separated observer, given full knowledge of the shared quantum state and measurement setting. We show that the remote predictability before and after the measurement remains the same for product states, whereas it increases for all pure entangled states and for some classically correlated states. Perfect remote predictability for arbitrary projective measurements occurs only for maximally entangled states among all pure states, underscoring their special role. Comparing pure entangled states with their dephased versions, we find that dephasing on one subsystem can enhance remote predictability for a broad class of states and measurements - a counterintuitive, noise-induced advantage that vanishes for maximally entangled states under any projective measurement.
A central aspect of quantum information is that correlations between spacelike separated observers sharing entangled states cannot be reproduced by local hidden variable (LHV) models, a phenomenon known as Bell nonlocality. If one wishes to explain such correlations by classical means, a natural possibility is to allow communication between the parties. In particular, LHV models augmented with two bits of classical communication can explain the correlations of any two-qubit state. Would this still hold if communication is restricted to measurement outcomes? While in certain scenarios with a finite number of inputs the answer is yes, we prove that if a model must reproduce all projective measurements, then for any qubit-qudit state the answer is no. In fact, a qubit-qudit under projective measurements admits an LHV model with outcome communication if and only if it already admits an LHV model without communication. On the other hand, we also show that when restricted sets of measurements are considered (for instance, when the qubit measurements are in the upper hemisphere of the Bloch ball), outcome communication does offer an advantage. This exemplifies that trivial properties in standard LHV scenarios, such as deterministic measurements and outcome-relabelling, play a crucial role in the outcome communication scenario.
Nonclassicality, defined through nonpositivity of quasiprobability distributions such as the Wigner and Kirkwood-Dirac distributions, underlies key quantum advantages. We show that it can be remotely activated: local measurements by a correlated partner alone can drive a party whose reduced state is classical into a genuinely nonclassical conditional state. For two-qubit systems we obtain closed forms for the maximal single-branch effect and for its probability-weighted average under the best two-outcome projective measurement, the latter proven optimal over all measurements when the shared state carries no local bias. Local noise on the steered party, evaluated relative to its own noise-updated reference basis, can enhance the effect when non-unital and misaligned with that party's axis, whereas no unital channel ever helps. This nonclassicality is shown to unlock, for the same reference observable, anomalous weak values unavailable to the unsteered state under arbitrary postselection. An exactly solvable hybrid qubit-oscillator model shows the same mechanism generates Wigner negativity. These results identify measurement-induced steering as an operational resource for remotely activating nonclassicality.
The predictions that quantum theory makes about the outcomes of measurements are generally probabilistic. This has raised the question whether quantum theory can be considered complete, or whether there could exist alternative theories that provide improved predictions. Here we review recent work that considers arbitrary alternative theories, constrained only by the requirement that they are compatible with a notion of "free choice" (defined with respect to a natural causal order). It is shown that quantum theory is "maximally informative", i.e., there is no other compatible theory that gives improved predictions. Furthermore, any alternative maximally informative theory is necessarily equivalent to quantum theory. This means that the state a system has in such a theory is in one-to-one correspondence with its quantum-mechanical state (the wave function). In this sense, quantum theory is complete.
One of the major remaining questions concerning foundations of the quantum mechanical theory is how superpositions are measured such that definite outcomes are obtained. Here a resolution to that issue is proposed. It is shown how to obtain state vectors associated with measurements on the separated subystems of an entangled state, revealing how a single wavefunction encodes a special kind of set of statistical measurement outcomes. The result explains why measurements on the subsystems give definite outcomes and why measurements on one subsystem are correlated with those on the other. It is therefore concluded that the theory of quantum mechanics, without nonlinearities or \emph{ad hoc} assertions, can explain both the mechanism of state vector collapse and the reason for the paradoxical nonlocal correlations between separated subsystems. The theory also explains why nonlocal correlations do not require any kind of interaction between the subsystems.
The entangled Schrodinger cat state obtained immediately upon measurement of a superposed two-state quantum system is often considered paradoxical because it appears to predict two macroscopically different outcomes, such as an alive and dead cat. However, nonlocal interferometry experiments testing momentum-entangled photon pairs over all phases demonstrate that the cat state does not fit this description and is not paradoxical. Both experiment and theory imply that it instead represents a superposition of two nonlocally coherent (i.e. phase-dependent) statistical correlations between its sub-systems. This is not paradoxical. Standard quantum theory rigorously predicts the experimentally-observed outcomes of this state. Neither sub-system is superposed; rather, the correlations between the states of the subsystems are superposed. This resolves the problem of definite outcomes. The nonlocal properties of entanglement then ensure that only one outcome occurs while the other outcome simultaneously does not occur, resolving a problem posed by Einstein in 1927. The single outcome that occurs then triggers an irreversible process leading to macroscopic registration of the outcome. This resolves the quantum measurement problem. Collapse occurs because of entanglement and does not require a special collapse postulate. Collapse is a consequence of standard quantum physics and the irreversible nature of the macroscopic registration.
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.