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Nonlocal prediction of quantum measurement outcomes

Chirag Srivastava, Aparajita Bhattacharyya, Ujjwal Sen

Abstract

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.

Nonlocal prediction of quantum measurement outcomes

Abstract

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.
Paper Structure (7 sections, 7 theorems, 34 equations, 1 figure)

This paper contains 7 sections, 7 theorems, 34 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Nonlocal predictability
  3. Pure entangled state versus its dephased counterpart
  4. Conclusion
  5. Proof of Observation \ref{['Ehsaan']}
  6. Proof of Theorem. \ref{['th1']}
  7. Proof of Theorem. \ref{['th2']}

Key Result

Theorem 1

All pure entangled states and some classically correlated states can violate the local bound on nonlocal predictability.

Figures (1)

  • Figure 1: A schematic of the considered protocol. Bob prepares a state $\rho_{AB}$ and sends subsystem $A$ to Alice: (a) through a noiseless channel (Section \ref{['sec:nonlocal_predictability']}), or (b) through a dephasing channel $\mathcal{D}_A$ (Section \ref{['sec:dephasing']}). We investigate how well Bob can predict the outcomes of a measurement $\pi$ performed by Alice on $A$.

Theorems & Definitions (16)

  • Theorem 1
  • proof
  • Theorem 2
  • proof
  • Theorem 3
  • proof
  • proof
  • proof
  • Theorem 4
  • proof
  • ...and 6 more