Joint measurements via quantum cloning

Abstract

We explore the possibility of achieving optimal joint measurements of noncommuting observables on a single quantum system by performing conventional measurements of commuting self adjoint operators on optimal clones of the original quantum system. We consider the case of both finite dimensional and infinite dimensional Hilbert spaces. In the former we study the joint measurement of three orthogonal components of a spin 1/2, in the latter we consider the case of the joint measurements of any pair of noncommuting quadratures of one mode of the electromagnetic field. We show that universally covariant cloning is not ideal for joint measurements, and a suitable non universally covariant cloning is needed.

8 pages

References in corpus (8)

• Phase covariant quantum cloning
• Universal cloning of continuous quantum variables
• Optimal Quantum Cloning via Stimulated Emission
• Universal teleportation with a twist
• Bell Measurements and Observables
• Information transfer and fidelity in quantum copiers
• Two-mode heterodyne phase detection
• Continuous variable cloning via network of parametric gates

Cited by in corpus (20)

• An Invitation to Quantum Incompatibility
• Optimal Non-Universally Covariant Cloning
• Covariant quantum measurements which maximize the likelihood
• Coexistence of qubit effects
• Lower bound on the relative error of mixed-state cloning and related operations
• Foundations of quantum theory and quantum information applications
• Optimal Pure-State Qubit Tomography via Sequential Weak Measurements
• Approximate joint measurement of qubit observables through an Arthur-Kelly type model
• Cloning and Joint Measurements of Incompatible Components of Spin
• A quantum measurement of the spin direction
• Surmounting intrinsic quantum-measurement uncertainties in Gaussian-state tomography with quadrature squeezing
• Cloning of spin-coherent states
• Determining complementary properties with quantum clones
• Trace distance from the viewpoint of quantum operation techniques
• Cloning of observables
• How to perform the coherent measurement of a curved phase space by continuous isotropic measurement. I. Spin and the Kraus-operator geometry of $\mathrm{SL}(2,\mathbb{C})$
• Effects of the free evolution in the Arthurs-Kelly model of simultaneous measurement and in the retrodictive predictions of the Heisenberg uncertainty relations
• Approximate joint measurements of qubit observables
• Characterising a universal cloning machine by maximum-likelihood estimation
• Postponing the choice: advantage of deferred measurements in quantum information processing