Direct measurement of the Kirkwood-Rihaczek distribution for the spatial properties of a coherent light beam

Bollen, Viktor; Sua, Yong Meng; Lee, Kim Fook

doi:10.1103/physreva.81.063826

Cited by 11 publications

(24 citation statements)

References 48 publications

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“…A simple case, in which ρ = 1/d, is detailed in Appendix A of [37]. Recent weak measurements [10][11][12][13][31][32][33][34][35], some used to infer KD distributions, inspired our weakÃ ρ -measurement proposal. We review weak measurements, a Kraus-operator model for measurements, and theÃ ρ -measurement scheme.…”

Section: Weak-measurement and Interference Schemes For Inferringãρmentioning

confidence: 99%

“…(4) Evolve the system forward under U . In many recent experiments, only one weak measurement is performed per trial [10,12,31]. A probability P weak must be approximated to first order in the coupling constant g(x).…”

Section: From This Probability One Infers the Quasiprobabilitỹmentioning

confidence: 99%

“…The KD distribution features in quantum optics. Experimentalists have inferred the quasiprobability from weak measurements of photons [10][11][12][13][31][32][33][34] and superconducting qubits [35,36].…”

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confidence: 99%

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Quasiprobability behind the out-of-time-ordered correlator

2018

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Two topics, evolving rapidly in separate fields, were combined recently: The out-of-time-ordered correlator (OTOC) signals quantum-information scrambling in many-body systems. The Kirkwood-Dirac (KD) quasiprobability represents operators in quantum optics. The OTOC was shown to equal a moment of a summed quasiprobability [Yunger Halpern, Phys. Rev. A 95, 012120 (2017)]. That quasiprobability, we argue, is an extension of the KD distribution. We explore the quasiprobability's structure from experimental, numerical, and theoretical perspectives. First, we simplify and analyze Yunger Halpern's weak-measurement and interference protocols for measuring the OTOC and its quasiprobability. We decrease, exponentially in system size, the number of trials required to infer the OTOC from weak measurements. We also construct a circuit for implementing the weak-measurement scheme. Next, we calculate the quasiprobability (after coarse-graining) numerically and analytically: We simulate a transverse-field Ising model first. Then, we calculate the quasiprobability averaged over random circuits, which model chaotic dynamics. The quasiprobability, we find, distinguishes chaotic from integrable regimes. We observe nonclassical behaviors:The quasiprobability typically has negative components. It becomes nonreal in some regimes. The onset of scrambling breaks a symmetry that bifurcates the quasiprobability, as in classical-chaos pitchforks. Finally, we present mathematical properties. We define an extended KD quasiprobability that generalizes the KD distribution. The quasiprobability obeys a Bayes-type theorem, for example, that exponentially decreases the memory required to calculate weak values, in certain cases. A time-ordered correlator analogous to the OTOC, insensitive to quantum-information scrambling, depends on a quasiprobability closer to a classical probability. This work not only illuminates the OTOC's underpinnings, but also generalizes quasiprobability theory and motivates immediate-future weak-measurement challenges.2. Bayes-type theorem and retrodiction with the KD quasiprobability chain example. Discrete systems are governed by quasiprobabilities, which resemble probabilities. Continuous systems are governed by quasiprobability densities, which resemble probability densities. Our quasiprobabilities can be replaced with quasiprobability densities, and our sums can be replaced with integrals, in, e.g., quantum field theory.

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Section: Weak-measurement and Interference Schemes For Inferringãρmentioning

confidence: 99%

Section: From This Probability One Infers the Quasiprobabilitỹmentioning

confidence: 99%

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Quasiprobability behind the out-of-time-ordered correlator

2018

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“…However, the distribution of x and p, t and ω of the spatial light field can be measured simultaneously with high resolution by using two local oscillator fields. The use of two local oscillator fields in a balanced heterodyne detection scheme is also called two-window technique [1,2]. The optical phase-space tomography (OPST) [1,3] is Wigner distribution [4,5] W(x, p, ω, t), will offer the correlation information of x, p, t, and ω of a wave field through the distributions of x − p, ω − t, x − t, p − t, x − ω, and p − ω, where the two variables are plotted by fixing the other two variables.…”

Section: Introductionmentioning

confidence: 99%

“…(iii), the LO and signal fields in Eq. 3 can be rewritten in terms of the input field z = 0 as described in [2],…”

Section: Introductionmentioning

confidence: 99%

Optical phase-space-time-frequency tomography

Rojas¹,

Blaser²,

Sua³

et al. 2011

Opt. Express

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We present a new approach for constructing optical phase-space-time-frequency tomography (OPSTFT) of an optical wave field. This tomography can be measured by using a novel four-window optical imaging system based on two local oscillator fields balanced heterodyne detection. The OPSTFT is a Wigner distribution function of two independent Fourier Transform pairs, i.e., phase-space and time-frequency. From its theoretical and experimental aspects, it can provide information of position, momentum, time and frequency of a spatial light field with precision beyond the uncertainty principle. Besides the distributions of x-p and t-ω, the OPSTFT can provide four other distributions such as x-t, p-t, x-ω and p-ω. We simulate the OPSTFT for a light field obscured by a wire and a single-line absorption filter. We believe that the four-window system can provide spatial and temporal properties of a wave field for quantum image processing and biophotonics.

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Entropic uncertainty relations for quantum information scrambling

2019

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Different fields of physics characterize differently how much two quantum operations disagree: quantum information theory features uncertainty relations cast in terms of entropies. The higher an uncertainty bound, the less compatible the operations. In condensed matter and high-energy physics, initially localized, far-apart operators come to disagree as entanglement spreads through a quantum many-body system. This spread, called "scrambling," is quantified with the out-of-time-ordered correlator (OTOC). We unite these two measures of operation disagreement by proving entropic uncertainty relations for scrambling. The uncertainty bound depends on the quasiprobability (the nonclassical generalization of a probability) known to average to the OTOC. The quasiprobability strengthens the uncertainty bound, we find, when a spin chain scrambles in numerical simulations. Hence our entropic uncertainty relations reflect the same incompatibility as scrambling, uniting two fields' notions of quantum-operation disagreement.

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Direct measurement of the Kirkwood-Rihaczek distribution for the spatial properties of a coherent light beam

Cited by 11 publications

References 48 publications

Quasiprobability behind the out-of-time-ordered correlator

Quasiprobability behind the out-of-time-ordered correlator

Optical phase-space-time-frequency tomography

Entropic uncertainty relations for quantum information scrambling

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