De Broglie wavelength of a non-local four-photon state

Walther, Philip; Pan, Jian-Wei; Aspelmeyer, Markus; Ursin, Rupert; Gasparoni, Sara; Zeilinger, Anton

doi:10.1038/nature02552

Cited by 545 publications

(548 citation statements)

References 32 publications

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“…First of all it assumes the ability of creating NOON states. This is possible via some rather complicated optical schemes [57][58][59][60][61] which have only been implemented in highly refined, but post-selected experiments [61][62][63][64][65][66]. However states which possess a high fidelity with the NOON states, also for large values of N , can be simply obtained by mixing a squeezed vacuum and a coherent state at a beam splitter [67][68][69].…”

Section: Applications In Quantum Interferometrymentioning

confidence: 99%

Advances in quantum metrology

2011

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In classical estimation theory, the central limit theorem implies that the statistical error in a measurement outcome can be reduced by an amount proportional to n −1/2 by repeating the measures n times and then averaging. Using quantum effects, such as entanglement, it is often possible to do better, decreasing the error by an amount proportional to n −1 . Quantum metrology is the study of those quantum techniques that allow one to gain advantages over purely classical approaches.In this review, we analyze some of the most promising recent developments in this research field. Specifically, we deal with the developments of the theory and point out some of the new experiments. Then we look at one of the main new trends of the field, the analysis of how the theory must take into account the presence of noise and experimental imperfections.Any measurement consists in three parts: the preparation of a probe, its interaction with the system to be measured, and the probe readout. This process is often plagued by statistical or systematic errors. The source of the former can be accidental (e.g. deriving from an insufficient control of the probes or of the measured system) or fundamental (e.g. deriving from the Heisenberg uncertainty relations). Whatever their origin, we can reduce their effect by repeating the measurement and averaging the resulting outcomes. This is a consequence of the central-limit theorem: given a large number n of independent measurement results (each having a standard deviation ∆σ), their average will converge to a Gaussian distribution with standard deviation ∆σ/ √ n, so that the error scales as n −1/2 . In quantum mechanics this behavior is referred to as "standard quantum limit" (SQL) and is associated with procedures which do not fully exploit the quantum nature of the system under investigation 1 . Notably it is possible to do better when one employs quantum effects, such as entanglement among the probing devices employed for the measurements, e.g. see Refs. [1][2][3][4][5][6]. Consequently, the SQL is not a fundamental quantum mechanical bound as it can be surpassed by using "non-classical" strategies. Nonetheless, through Heisenberg-like uncertainty relations, quantum mechanics still sets ultimate limits in precision which are typically referred to as "Heisenberg bounds". In Fig. 1 we present a simple example which may be useful to un-1 In quantum optics, the n −1/2 scaling is also indicated as "shot noise", since it is connected to the discrete nature of the radiation that can be heard as "shots" in a photon counter operating in Geiger mode.derstand the quantum enhancement. Part of the emerging field of quantum technology [7], quantum metrology studies these bounds and the (quantum) strategies which allows us to attain them. More generally it deals with measurement and discrimination procedures that receive some kind of enhancement (in precision, efficiency, simplicity of implementation, etc.) through the use of quantum effects. This paper aims to review some of the most recent developmen...

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Section: Applications In Quantum Interferometrymentioning

confidence: 99%

Advances in quantum metrology

2011

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“…5,6 This is complementary to the objectives of gravitywave astronomy schemes that use squeezed light and require high circulating laser power (watts to kilowatts) in km-scale interferometry for sub-SNL performance. 7 A widespread objective of quantum metrology has been to engineer instances of 'NOON' states, 2,[8][9][10][11][12] which are path-entangled states of N photons across two modes 1 O2 N j i 0 j i þ 0 j i N j i ð Þ . They offer both super-resolution (N-fold decrease in fringe period) and supersensitivity (enhanced precision towards the Heisenberg limit -Δϕ~1/N), and they are the optimal state for low-flux sensing in the lossless regime.…”

Section: Introductionmentioning

confidence: 99%

Towards practical quantum metrology with photon counting

et al. 2016

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Quantum metrology aims to realise new sensors operating at the ultimate limit of precision measurement. However, optical loss, the complexity of proposed metrology schemes and interferometric instability each prevent the realisation of practical quantumenhanced sensors. To obtain a quantum advantage in interferometry using these capabilities, new schemes are required that tolerate realistic device loss and sample absorption. We show that loss-tolerant quantum metrology is achievable with photoncounting measurements of the generalised multi-photon singlet state, which is readily generated from spontaneous parametric downconversion without any further state engineering. The power of this scheme comes from coherent superpositions, which give rise to rapidly oscillating interference fringes that persist in realistic levels of loss. We have demonstrated the key enabling principles through the four-photon coincidence detection of outcomes that are dominated by the four-photon singlet term of the four-mode downconversion state. Combining state-of-the-art quantum photonics will enable a quantum advantage to be achieved without using post-selection and without any further changes to the approach studied here.

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“…These states are extremely difficult to generate. Measurement schemes with counted photons or ions have been performed with N ≤ 6 [6,7,8,9,10,11,12,13,14,15], but few have surpassed the standard quantum limit [12,14] and none have shown Heisenberg-limited scaling. Here we demonstrate experimentally a Heisenberg-limited phase estimation procedure.…”

mentioning

confidence: 99%

“…Recent work in quantum interferometry has focused on nphoton NOON states [5,6,7,8,9,10,11,12,21], (|n |0 + |0 |n ) / √ 2, expressed in terms of number states of the two arms of the interferometer. With this state, an improved phase sensitivity results from a decrease in the phase period from 2π to 2π/n.…”

mentioning

confidence: 99%

Entanglement-free Heisenberg-limited phase estimation

Higgins

Berry

Bartlett

et al. 2007

Nature

603

628

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Measurement underpins all quantitative science. A key example is the measurement of optical phase, used in length metrology and many other applications. Advances in precision measurement have consistently led to important scientific discoveries. At the fundamental level, measurement precision is limited by the number N of quantum resources (such as photons) that are used. Standard measurement schemes, using each resource independently, lead to a phase uncertainty that scales as 1/ √ N -known as the standard quantum limit. However, it has long been conjectured [1,2] that it should be possible to achieve a precision limited only by the Heisenberg uncertainty principle, dramatically improving the scaling to 1/N [3]. It is commonly thought that achieving this improvement requires the use of exotic quantum entangled states, such as the NOON state [4,5]. These states are extremely difficult to generate. Measurement schemes with counted photons or ions have been performed with N ≤ 6 [6, 7, 8, 9, 10, 11, 12, 13, 14, 15], but few have surpassed the standard quantum limit [12,14] and none have shown Heisenberg-limited scaling. Here we demonstrate experimentally a Heisenberg-limited phase estimation procedure. We replace entangled input states with multiple applications of the phase shift on unentangled single-photon states. We generalize Kitaev's phase estimation algorithm [16] using adaptive measurement theory [17,18,19,20] to achieve a standard deviation scaling at the Heisenberg limit. For the largest number of resources used (N = 378), we estimate an unknown phase with a variance more than 10 dB below the standard quantum limit; achieving this variance would require more than 4,000 resources using standard interferometry. Our results represent a drastic reduction in the complexity of achieving quantumenhanced measurement precision.Phase estimation is a ubiquitous measurement primitive, used for precision measurement of length, displacement, speed, optical properties, and much more. Recent work in quantum interferometry has focused on nphoton NOON states [5,6,7,8,9,10,11,12,21], (|n |0 + |0 |n ) / √ 2, expressed in terms of number states of the two arms of the interferometer. With this state, an improved phase sensitivity results from a decrease in the phase period from 2π to 2π/n. We achieve improved phase sensitivity more simply using an insight from quantum computing. We apply Kitaev's phase estimation algorithm [16,22] to quantum interferometry, wherein the entangled input state is replaced by multiple passes through the phase shift. The idea of using multi-pass protocols to gain a quantum advantage was proposed for the problem of aligning spatial reference frames [23], and further developed in relation to clock synchronization [24] and phase estimation [25,26].The conceptual circuit for Kitaev's phase estimation algorithm is shown in Fig. 1a. The algorithm yields, with K + 1 bits of precision, an estimate φ est of a classical phase parameter φ, where e iφ is an eigenvalue of a unitary operator U . It requires us t...

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De Broglie wavelength of a non-local four-photon state

Cited by 545 publications

References 32 publications

Advances in quantum metrology

Advances in quantum metrology

Towards practical quantum metrology with photon counting

Entanglement-free Heisenberg-limited phase estimation

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