Optimal quantum rotosensors

Chryssomalakos, Chryssomalis; Hernández-Coronado, H.

doi:10.1103/physreva.95.052125

Cited by 27 publications

(37 citation statements)

References 13 publications

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“…Next, suppose that only the rotation angle η is welldefined while the rotation axis is not known, as described in [15]. This situation occurs, for example, when spins prepared in the state |ψ are-during the measurement sequence-subjected to a magnetic field whose direction randomly fluctuates on a time scale much larger than the Larmor period.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Optimal Detection of Rotations about Unknown Axes by Coherent and Anticoherent States

Martin

Weigert

Giraud

2020

Quantum

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Coherent and anticoherent states of spin systems up to spin j=2 are known to be optimal in order to detect rotations by a known angle but unknown rotation axis. These optimal quantum rotosensors are characterized by minimal fidelity, given by the overlap of a state before and after a rotation, averaged over all directions in space. We calculate a closed-form expression for the average fidelity in terms of anticoherent measures, valid for arbitrary values of the quantum number j. We identify optimal rotosensors (i) for arbitrary rotation angles in the case of spin quantum numbers up to j=7/2 and (ii) for small rotation angles in the case of spin quantum numbers up to j=5. The closed-form expression we derive allows us to explain the central role of anticoherence measures in the problem of optimal detection of rotation angles for arbitrary values of j.

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Section: Introduction and Main Resultsmentioning

confidence: 99%

Optimal Detection of Rotations about Unknown Axes by Coherent and Anticoherent States

Martin

Weigert

Giraud

2020

Quantum

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“…Another possible direction of investigation concerns quantum metrology. As anticoherent states have been shown to be optimal in detecting rotations [20] and for reference frame alignment [21], it would be worth investigating the connections between our measures of anticoherence and the efficiency of a state for such tasks.…”

Section: Discussionmentioning

confidence: 99%

“…In other words, no experiments relying on the measurement of the product of at most two spin operators will allow us to determine whether the system has been rotated or not. Surprisingly, the transition probability between a spin-2 state and the state obtained from it by a rotation has been shown to be minimized by (2) for a large range of angles, making it an optimal state in detecting rotations [20]. The state (2) was also shown to be optimal for reference frame alignment [21].…”

Section: A Examples and Propertiesmentioning

confidence: 99%

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Anticoherence measures for pure spin states

Baguette

Martin

2017

Phys. Rev. A

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The set of pure spin states with vanishing spin expectation value can be regarded as the set of the less coherent pure spin states. This set can be divided into a finite number of nested subsets on the basis of higher order moments of the spin operators. This subdivision relies on the notion of anticoherent spin state to order t: A spin state is said to be anticoherent to order t if the moment of order k of the spin components along any directions are equal for k = 1, 2, . . . , t. Most spin states are neither coherent nor anticoherent, but can be arbitrary close to one or the other. In order to quantify the degree of anticoherence of pure spin states, we introduce the notion of anticoherence measures. By relying on the mapping between spin-j states and symmetric states of 2j spin-1/2 (Majorana representation), we present a systematic way of constructing anticoherence measures to any order. We briefly discuss their connection with measures of quantum coherence. Finally, we illustrate our measures on various spin states and use them to investigate the problem of the existence of anticoherent spin states with degenerated Majorana points.

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“…For SLOCC transformation SL(2, C) ⊗4 , there exists a set of four independent polynomial invariants. The first polynomial invariant of degree 2 is Cayley's hyperdeterminant defined by [44] H ≡ Γ 0000 Γ 1111 − Γ 0001 Γ 1110 − Γ 0010 Γ 1101 + Γ 0011 Γ 1100 − Γ 0100 Γ 1011 + Γ 0101 Γ 1010 + Γ 0110 Γ 1001 − Γ 0111 Γ 1000 , (18) and the other two independent polynomial invariants of degree 4 are two determinants given by [44] L ≡…”

Section: Four-qubit States and Beyondmentioning

confidence: 99%

Three-tangle of a general three-qubit state in the representation of Majorana stars

Kam

Liu

2020

Phys. Rev. A

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Majorana stars, the 2 j spin coherent states that are orthogonal to a spinj state, offer a visualization of general quantum states and may disclose deep structures in quantum states and their evolutions. In particular, the genuine tripartite entanglement -the three-tangle of a symmetric three-qubit state, which can be mapped to a spin-3/2 state, is measured by the normalized product of the distance between the Majorana stars. However, the Majorana representation cannot applied to general non-symmetric n-qubit states. We show that after a series of SL(2, C) transformations, non-symmetric three-qubit states can be transformed to symmetric three-qubit states, while at the same time the three-tangle is unchanged. Thus the genuine tripartite entanglement of general threequbit states has the geometric representation of the associated Majorana stars. The symmetrization and hence the Majorana star representation of certain genuine high-order entanglement for more qubits are possible for some special states. In general cases, however, the constraints on the symmetrization may prevent the Majorana star representation of the genuine entanglement.

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Optimal quantum rotosensors

Cited by 27 publications

References 13 publications

Optimal Detection of Rotations about Unknown Axes by Coherent and Anticoherent States

Optimal Detection of Rotations about Unknown Axes by Coherent and Anticoherent States

Anticoherence measures for pure spin states

Three-tangle of a general three-qubit state in the representation of Majorana stars

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