Detecting metrologically useful asymmetry and entanglement by a few local measurements
Summary (2 min read)
Introduction
- Yet, this usually requires experimental and computational resources which increase exponentially with the system size.
- Indeed, the presented method requires neither the knowledge of the state and the parameter-encoding Hamiltonian nor global measurements performed on all the constituent subsystems.
- Also, verifying their presence is necessary, but not sufficient to guarantee a computational advantage.
II. RELATING ASYMMETRY TO OBSERVABLES
- Note that tomography demands to prepare O(22n) system copies and perform a measurement on each of them [2].
- It is also possible to extract the swap value by single qubit interferometry [23–25].
- Experimentally measuring coherence, and in particular asymmetry, is hard [27,28].
- In fact, the quantum Fisher information quantifies the instantaneous response to a perturbation [11,30].
III. WITNESSING METROLOGICALLY USEFUL ENTANGLEMENT
- The authors extend the analysis to multipartite systems, proving that nonlinear speed scaling witnesses useful entanglement.
- Given Eq. (4), entanglementenhanced precision in estimating a phase shift τ is verified if Sτ (ρ,Hn) > n/4. (5) The overlap detection network for n-qubit systems and additive Hamiltonians is depicted in Fig.
- Evaluating the SLDF is an appealing strategy to verify an advantage given by entanglement, rather than just detecting quantum correlations [22,33–38].
- The authors proposal has two peculiar advantages.
- First, it is applicable to any probe state ρ without a priori information and assumptions, e.g., invariance under permutation of the subsystems.
IV. EXPERIMENTAL ASYMMETRY AND ENTANGLEMENT DETECTION
- While employing state tomography would require fifteen measurements, the authors verify that the proposed protocol needs six.
- Two photon pairs (photons 3–6) are generated via single BBO crystals (beamlike type-II phase matching).
- A 90◦ rotated QWP swaps the Bell states, |φ±〉 → |φ∓〉, generating a π phase shift between H,V polarizations.
- That is, three projections are required for evaluating purity and overlap, respectively.
1. Error sources
- The authors discuss the efficiency of the experimental setup.
- This poses the problem to rule out the case of BSMs measuring two photon pairs emitted by a single SPDC source [46].
- Single source double down conversion can also occur because of high-order emission noise, which has been minimized by setting a low pump power.
- Here the main error source is the imperfection of the three Hang-Ou-Mandel interferometers (one for the PBS and each BSM), which have a visibility of 0.91.
- This is due to the temporal distinguishability between the interfering photons, determined by the pulse duration.
A. Quantum Fisher information as measures of state sensitivity
- Quantum information geometry studies quantum states and channels as geometric objects.
- This means that they have the appealing feature to be the unique class of contractive Riemannian metrics under completely positive trace preserving (CPTP) maps : d( (ρ), (σ )) d(ρ,σ ),∀ρ,σ, [51,52].
- The dynamics of the quantum Fisher information for closed and open quantum systems has been studied in Ref. [7].
- All such metrics reduce to the classical Fisher-Rao metric∑ i (dtλi(t)) 2/(λi(t)) for stochastic dynamics of probability distributions {λi(t)}, represented at any time by a diagonal density matrix.
VI. CONCLUSION
- The authors showed how to extract quantitative bounds to metrologically useful asymmetry and entanglement in multipartite systems from a limited number of measurements, demonstrating the method in an all-optical experiment.
- The scalability of the scheme may make possible to certify quantum speedup in large scale registers [1,11,38], and to study critical properties of many-body systems [14,15,39], by limited laboratory resources.
- On this hand, the authors remark that they here compared their method with state tomography, as the two approaches share the common assumption that no a priori knowledge about the input state and the Hamiltonian is given.
- An interesting followup work would test the efficiency of their entanglement witness against two-time measurements of the classical Fisher information, when local measurements on the subsystems are only available.
- A further development would be to investigate macroscopic quantum effects via speed detection, as they have been linked to quadratic precision scaling in phase estimation [IF (ρ,Hn) = O(n2)] [20,31,40].
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"Detecting metrologically useful asy..." refers background in this paper
...This means that distant laboratories can verify quantum speed-up due to entanglement in a shared system S by local operations and classical communication [1], providing each laboratory with two copies of a subsystem S i....
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...The sensitivity of a quantum system to a quantum operation described by a parametrized channel Φt [1], where t is the time, is determined by how fast its state ρt := Φt(ρ0) evolves....
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...Consider a phase estimation protocol, a building block of quantum computation and metrology schemes [1, 3, 11]....
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...Quantum coherence and entanglement can generate nonclassical speed-up in information processing [1]....
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...The scalability of the scheme may make possible to certify quantum speed-up in large scale registers [1, 11, 39], and to study critical properties of many-body systems [14, 15, 38], by limited laboratory resources....
[...]
3,931 citations
"Detecting metrologically useful asy..." refers methods in this paper
...To quantify the sensitivity of a probe state ρ = ∑ i λi|i〉〈i| to the unitary transformation Ut, we employ the symmetric logarithmic derivative quantum Fisher information (SLDF), a widely employed quantity in quantum metrology and quantum information [29]:...
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2,977 citations
"Detecting metrologically useful asy..." refers background in this paper
...Consider a phase estimation protocol, a building block of quantum computation and metrology schemes [1, 3, 11]....
[...]
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Q2. What have the authors stated for future works in "Detecting metrologically useful asymmetry and entanglement by a few local measurements" ?
The scalability of the scheme may make possible to certify quantum speedup in large scale registers [ 1,11,38 ], and to study critical properties of many-body systems [ 14,15,39 ], by limited laboratory resources. A further development would be to investigate macroscopic quantum effects via speed detection, as they have been linked to quadratic precision scaling in phase estimation [ IF ( ρ, Hn ) = O ( n2 ) ] [ 20,31,40 ].