arXiv:quant-ph/0010085 · Physical Review Letters

Entangled Quantum States as Direction Indicators

Asher Peres, Petra F. Scudo

Published Apr 30, 2001• 89 citations

Abstract

We consider the use of $N$ spin- $\frac{1}{2}$ particles for indicating a direction in space. If $N>2$, their optimal state is entangled. For large $N$, the mean square error decreases as ${N}^{\ensuremath{-}2}$ (rather than ${N}^{\ensuremath{-}1}$ for parallel spins).

DOI: 10.1103/physrevlett.86.4160

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arXiv:quant-ph/0010085 · Physical Review Letters

Entangled Quantum States as Direction Indicators

Asher Peres, Petra F. Scudo

Published Apr 30, 2001• 89 citations

arXiv HTML PDF

Abstract

We consider the use of

N

spin-

\frac{1}{2}

particles for indicating a direction in space. If

N>2

, their optimal state is entangled. For large

N

, the mean square error decreases as

{N}^{\ensuremath{-}2}

(rather than

{N}^{\ensuremath{-}1}

for parallel spins).

DOI: 10.1103/physrevlett.86.4160

Related papers

Unspeakable quantum information

Asher Peres, Petra F. Scudo

arXiv:quant-ph/0201017Jan 6, 20029 citations

The existence of maximally multipartite entangled states of N particles may depend on their spin

Jay Lawrence, Mario Gaeta, Andrei Klimov

Bulletin of the American Physical SocietyMar 3, 20150 citations

Detecting entanglement by the mean value of spin on a quantum computer

Andrij Romanovych Kuzmak, V. M. Tkachuk

arXiv:2003.01011Physics Letters AMay 20, 202017 citations

Optimal estimation of SU(d) using exact and approximate 2-designs

Manuel A. Ballester

We consider the problem of estimating an SU(d) quantum operation when n copies of it are available at the same time. It is well known that, if one uses a separable state as the input for the unitaries, the optimal mean square error will decrease as 1/n. However it is shown here that, if a proper entangled state is used, the optimal mean square error will decrease at a 1/n^2 rate. It is also shown that spherical 2-designs (e.g. complete sets of mutually unbiased bases and symmetric informationally complete positive operator valued measures) can be used to design optimal input states. Although 2-designs are believed to exist for every dimension, this has not yet been proven. Therefore, we give an alternative input state based on approximate 2-designs which can be made arbitrarily close to optimal. It is shown that measurement strategies which are based on local operations and classical communication between the ancilla and the rest of the system can be optimal.We consider the problem of estimating an SU(d) quantum operation when n copies of it are available at the same time. It is well known that, if one uses a separable state as the input for the unitaries, the optimal mean square error will decrease as 1/n. However it is shown here that, if a proper entangled state is used, the optimal mean square error will decrease at a 1/n^2 rate. It is also shown that spherical 2-designs (e.g. complete sets of mutually unbiased bases and symmetric informationally complete positive operator valued measures) can be used to design optimal input states. Although 2-designs are believed to exist for every dimension, this has not yet been proven. Therefore, we give an alternative input state based on approximate 2-designs which can be made arbitrarily close to optimal. It is shown that measurement strategies which are based on local operations and classical communication between the ancilla and the rest of the system can be optimal.

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arXiv:quant-ph/9907042Physical Review AApr 10, 200014 citations

We consider the use of

N

spin-

\frac{1}{2}

particles for indicating a direction in space. If

N>2

, their optimal state is entangled. For large

N

, the mean square error decreases as

{N}^{\ensuremath{-}2}

(rather than

{N}^{\ensuremath{-}1}

for parallel spins).

We consider a quantum computer with

n

quantum bits (``qubits''), where each qubit is coupled independently to an environment affecting the state in a dephasing or depolarizing way. For mixed states we define a parameter indicating quantum uncertainty on the macroscopic level. We illustrate in which sense a large parameter can be seen as an indicator for large entanglement and give hypersurfaces enclosing the set of separable states. Using methods of the classical theory of maximum likelihood estimation we prove that this parameter is decreasing with

1/\sqrt{n}

for all those states which have been exposed to the environment. Furthermore we consider a quantum computer with perfect 1-qubit gates and two-qubit gates with a depolarizing error and show that any state which can be obtained from a separable initial state lies inbetween a family of pairs of certain hypersurfaces parallel to those enclosing the separable ones.