Optimal measurements for relative quantum information

Abstract

We provide optimal measurement schemes for estimating relative parameters of the quantum state of a pair of spin systems. We prove that the optimal measurements are joint measurements on the pair of systems, meaning that they cannot be achieved by local operations and classical communication. We also demonstrate that in the limit where one of the spins becomes macroscopic, our results reproduce those that are obtained by treating that spin as a classical reference direction.

6 pages, 1 figure, published version

References in corpus (20)

• Separability Criterion for Density Matrices
• Noiseless Quantum Codes
• Quantum Nonlocality without Entanglement
• Loop Quantum Gravity
• Robust polarization-based quantum key distribution over collective-noise channel
• Distillability and partial transposition in bipartite systems
• Decoherence-Free Quantum Information Processing with Four-Photon Entangled States
• Decoherence-Free Subspaces in Quantum Key Distribution
• Classical and quantum communication without a shared reference frame
• Superselection rules and quantum protocols
• Entanglement constrained by superselection rules
• Quantum nonlocality in the presence of superselection rules and data hiding protocols
• Entangled quantum states as direction indicators
• Quantum multimeters: A programmable state discriminator
• Transmission of a Cartesian Frame by a Quantum System
• Aligning Reference Frames Using Quantum States
• Quantum reverse-engineering and reference frame alignment without non-local correlations
• Photon-number superselection and the entangled coherent-state representation
• Universal measurement apparatus controlled by quantum software
• Elliptic Rydberg states as direction indicators

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• Quantum Key Distribution and Communication using a Two-way Quantum Channel
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• Experimental quantum secure direct communication with single photons
• A relational quantum computer using only two-qubit total spin measurement and an initial supply of highly mixed single qubit states
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• Entanglement-assisted communication in the absence of shared reference frame
• Quantum coherence between subspaces: State transformation, Cohering Power, $k$-coherence and other properties
• The power of a shared singlet state, compared with a shared reference frame
• Experimental benchmarking of quantum state overlap estimation strategies with photonic systems
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• Interconversion between block coherence and multipartite entanglement in many-body systems
• Are right angles special? The optimal primitive reference frame
• Power of unentangled measurements on two antiparallel spins
• Testing identity of collections of quantum states: sample complexity analysis