We give a complete analysis of covariant measurements on two spins. We consider the cases of two parallel and two antiparallel spins, and we consider both collective measurements on the two spins and measurements that require only local quantum operations and classical communication (LOCC). In all cases we obtain the optimal measurements for arbitrary fidelities. In particular, we show that if the aim is to determine as accurately as possible the direction in which the spins are pointing, it is best to carry out measurements on antiparallel spins (as already shown by Gisin and Popescu), second best to carry out measurements on parallel spins, and worst to be restricted to LOCC measurements. If the aim is to determine as accurately as possible a direction orthogonal to that in which the spins are pointing, it is best to carry out measurements on parallel spins, whereas measurements on antiparallel spins and LOCC measurements are both less suitable but equivalent.We give a complete analysis of covariant measurements on two spins. We consider the cases of two parallel and two antiparallel spins, and we consider both collective measurements on the two spins and measurements that require only local quantum operations and classical communication (LOCC). In all cases we obtain the optimal measurements for arbitrary fidelities. In particular, we show that if the aim is to determine as accurately as possible the direction in which the spins are pointing, it is best to carry out measurements on antiparallel spins (as already shown by Gisin and Popescu), second best to carry out measurements on parallel spins, and worst to be restricted to LOCC measurements. If the aim is to determine as accurately as possible a direction orthogonal to that in which the spins are pointing, it is best to carry out measurements on parallel spins, whereas measurements on antiparallel spins and LOCC measurements are both less suitable but equivalent.

arXiv:quant-ph/0004035Physical Review ASep 19, 200055 citations

SPIN EXPERIMENTS AND DATA

WORLD SCIENTIFIC eBooksNov 1, 20070 citations

Rotational invariance and spin measurements

G. C. Ghirardi, A. Rimini, T. Weber

Physica A Statistical Mechanics and its ApplicationsAug 1, 19825 citations

Reversible quantum measurement with arbitrary spins

Hiroaki Terashima, Masahito Ueda

We propose a physically reversible quantum measurement of an arbitrary spin- $s$ system using a spin- $j$ probe via an Ising interaction. In the case of a spin- $1∕2$ system $(s=1∕2)$ , we explicitly construct a reversing measurement and evaluate the degree of reversibility in terms of fidelity. The recovery of the measured state is pronounced when the probe has a high spin $(j>1∕2)$ , because the fidelity changes drastically during the reversible measurement and the reversing measurement. We also show that the reversing measurement scheme for a spin- $1∕2$ system can serve as an experimentally feasible approximate reversing measurement for a high-spin system $(s>1∕2)$ . If the interaction is sufficiently weak, the reversing measurement can recover a cat state almost deterministically in spite of there being a large fidelity change.We propose a physically reversible quantum measurement of an arbitrary spin-$s$ system using a spin-$j$ probe via an Ising interaction. In the case of a spin-$1∕2$ system $(s=1∕2)$, we explicitly construct a reversing measurement and evaluate the degree of reversibility in terms of fidelity. The recovery of the measured state is pronounced when the probe has a high spin $(j>1∕2)$, because the fidelity changes drastically during the reversible measurement and the reversing measurement. We also show that the reversing measurement scheme for a spin-$1∕2$ system can serve as an experimentally feasible approximate reversing measurement for a high-spin system $(s>1∕2)$. If the interaction is sufficiently weak, the reversing measurement can recover a cat state almost deterministically in spite of there being a large fidelity change.

arXiv:quant-ph/0507020Physical Review AJul 17, 200611 citations

Spin Matrices

Elsevier eBooksJan 1, 20000 citations

The realization of a generalized spin measurement

David Thomas Pegg

A generalized spin measurement, as opposed to a projective measurement, can produce interesting effects such as the weak Zeno effect (Cresser et al 2006 Opt. Commun. 264 352). In the weak limit a generalized spin measurement can also lead to surprising weak values (Aharonov et al 1988 Phys. Rev. Lett. 60 1351). In this paper we show explicitly how a generalized spin measurement can be realized physically by entangling the spin to be measured with a pointer spin. Adjustment of the interaction time allows any amount of generalization to be achieved, ranging from a projective measurement to the limit of a very weak measurement.A generalized spin measurement, as opposed to a projective measurement, can produce interesting effects such as the weak Zeno effect (Cresser et al 2006 Opt. Commun. 264 352). In the weak limit a generalized spin measurement can also lead to surprising weak values (Aharonov et al 1988 Phys. Rev. Lett. 60 1351). In this paper we show explicitly how a generalized spin measurement can be realized physically by entangling the spin to be measured with a pointer spin. Adjustment of the interaction time allows any amount of generalization to be achieved, ranging from a projective measurement to the limit of a very weak measurement.

Journal of Physics A Mathematical and TheoreticalJul 11, 20080 citations

We propose a physically reversible quantum measurement of an arbitrary spin-

s

system using a spin-

j

probe via an Ising interaction. In the case of a spin-

1∕2

system

(s=1∕2)

, we explicitly construct a reversing measurement and evaluate the degree of reversibility in terms of fidelity. The recovery of the measured state is pronounced when the probe has a high spin

(j>1∕2)

, because the fidelity changes drastically during the reversible measurement and the reversing measurement. We also show that the reversing measurement scheme for a spin-

1∕2

system can serve as an experimentally feasible approximate reversing measurement for a high-spin system

(s>1∕2)

. If the interaction is sufficiently weak, the reversing measurement can recover a cat state almost deterministically in spite of there being a large fidelity change.