We define nonlocal predictability as how well one observer can predict another's measurement outcomes without classical communication, given full knowledge of the shared quantum state and measurement settings. The local bound on nonlocal predictability is defined as the maximum probability with which one observer can correctly predict the other's measurement outcome prior to measurement. We show that product states always meet this bound, while all pure entangled states and some classically correlated states can exceed it. This demonstrates a nonlocal phenomenon since the predictability of measurement outcomes increases after the measurement. Perfect nonlocal 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 nonlocal predictability for a broad class of states and measurements - a counterintuitive, noise-induced advantage that vanishes for maximally entangled states under any projective measurement.
We define nonlocal predictability as how well one observer can predict another's measurement outcomes without classical communication, given full knowledge of the shared quantum state and measurement settings. The local bound on nonlocal predictability is defined as the maximum probability with which one observer can correctly predict the other's measurement outcome prior to measurement. We show that product states always meet this bound, while all pure entangled states and some classically correlated states can exceed it. This demonstrates a nonlocal phenomenon since the predictability of measurement outcomes increases after the measurement. Perfect nonlocal 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 nonlocal 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.
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 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.
We present a bipartite protocol inspired by the Monty Hall puzzle that operationally distinguishes quantum coherence from classical ignorance. A principal qutrit is entangled with an ancillary qutrit via a controlled unitary, preparing ∣Ψ⟩=31(∣A,0⟩+∣B,1⟩+∣C,2⟩). A rank-1 projective discard then eliminates one basis state, leaving a coherent superposition of the two remaining states. Finally, the ancilla and qutrit are measured, yielding joint probabilities that encode the interplay between superposition and measurement back-action.
We show that the conditional probability P(B∣anc=0) takes the value 1/4 in both quantum mechanics and the classical ignorant-host model, making it unsuitable as a witness. The true quantum-classical separation emerges in conditional joint probabilities that correlate ancilla outcomes with specific discard operations. We define witnesses Wi,j=P(anc=i,qutrit=j∣discard k) where j differs from the ancilla-implied state. Quantum mechanics predicts W=1/4, while any classical epistemic model with perfect initial correlations yields W=0.
We provide the explicit 9×9 unitary matrix, a complete analysis of all measurement outcomes, and a detailed proof of the violation. The witness is fully immune to white noise and robust against moderate dephasing. The protocol requires only a single pair of entangled qutrits and sequential measurements -- no spatial separation, no multiple copies, and no complex sets of incompatible observables. This makes it suitable for advanced undergraduate laboratories and provides a pedagogically accessible test of the ontic-epistemic distinction in quantum foundations.
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.