Phase retrieval in quantum mechanics

Orłowski, Arkadiusz; Paul, H.

doi:10.1103/physreva.50.r921

Cited by 44 publications

(30 citation statements)

References 17 publications

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“…The origin of quantum tomography of systems of continuous variables can be traced back to Pauli [21], who considered the problem of the reconstruction of the wavefunction of a spinless quantum particle, given its coordinate and momentum probability densities [22]. In general, the probability density and the probability current (not coordinate and momentum probability densities) allow the reconstruction of pure states [23].…”

Section: Quantum Tomographymentioning

confidence: 99%

Single plane minimal tomography of double slit qubits

Sogamoso¹,

Angulo²,

Romero³

2017

Optics Communications

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The determination of the density matrix of an ensemble of identically prepared quantum systems by performing a series of measurements, known as quantum tomography, is minimal when the number of outcomes is minimal.The most accurate minimal quantum tomography of qubits, sometimes called a tetrahedron measurement, corresponds to projections over four states which can be represented on the Bloch sphere as the vertices of a regular tetrahedron. We investigate whether it is possible to implement the tetrahedron measurement of double slit qubits of light, using measurements performed on a single plane. Assuming Gaussian slits and free propagation, we demonstrate that a judicious choice of the detection plane and the double slit geometry allows the implementation of a tetrahedron measurement. Finally, we consider possible sets of values which could be used in actual experiments.

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Section: Quantum Tomographymentioning

confidence: 99%

Single plane minimal tomography of double slit qubits

Sogamoso¹,

Angulo²,

Romero³

2017

Optics Communications

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“…(13). Integrating the result over a volume V, with boundary @V , and applying Green's theorem, gives…”

Section: Quantum Mechanicsmentioning

confidence: 99%

“…w S ðrÞ ¼ 4pqðrÞ; (13) where h is Planck's constant divided by 2p, m is the mass, x is the angular frequency, k ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi 2mx= h p is the wave number, and V(r) is a real, but otherwise arbitrary, potential that influences the scattered waves. The source q(r) of the scattered waves is due to the action of H 0 (but not of V) on w 0 .…”

Section: Quantum Mechanicsmentioning

confidence: 99%

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Extracting the Green’s function from measurements of the energy flux

Snieder

Douma

Vasconcelos

2012

The Journal of the Acoustical Society of America

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Existing methods for Green’s function extraction give the Green’s function from the correlation of field fluctuations recorded at those points. In this work it is shown that the Green’s function for acoustic waves can be retrieved from measurements of the integrated energy flux through a closed surface taken from three experiments where two time-harmonic sources first operate separately, and then simultaneously. This makes it possible to infer the Green’s function in acoustics from measurements of the energy flux through an arbitrary closed surface surrounding both sources. The theory is also applicable to quantum mechanics where the Green’s function can be retrieved from measurement of the flux of scattered particles through a closed surface.

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“…The study of correlations between the behavior of the phase and modulo of complex probability amplitudes is a relevant topic in a number of physical problems such as the "phase problem" in diffraction theory [1], the study of phase singularities [2] and the semi-classical or WKB approximation [3] to name a few. In the phase problem, for instance, the aim is to infer phase information in the diffracted wave from the observed cross section, which only involves the magnitude of the wave.…”

Section: Introductionmentioning

confidence: 99%

Geometric phase and modulus relations for probability amplitudes as functions on complex parameter spaces

Botero

2003

Journal of Mathematical Physics

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We investigate general differential relations connecting the respective behaviors of the phase and modulo of probability amplitudes of the form ψ f |ψ , where |ψ f is a fixed state in Hilbert space and |ψ is a section of a holomorphic line bundle over some complex parameter space. Amplitude functions on such bundles, while not strictly holomorphic, nevertheless satisfy generalized CauchyRiemann conditions involving the U (1) Berry-Simon connection on the parameter space. These conditions entail invertible relations between the gradients of the phase and modulo, therefore allowing for the reconstruction of the phase from the modulo (or vice-versa) and other conditions on the behavior of either polar component of the amplitude. As a special case, we consider amplitude functions valued on the space of pure states, the ray space R = CP n , where transition probabilities have a geometric interpretation in terms of geodesic distances as measured with the Fubini-Study metric. In conjunction with the generalized Cauchy-Riemann conditions, this geodesic interpretation leads to additional relations, in particular a novel connection between the modulus of the amplitude and the phase gradient, somewhat reminiscent of the WKB formula. Finally, a connection with geometric phases is established.

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Phase retrieval in quantum mechanics

Cited by 44 publications

References 17 publications

Single plane minimal tomography of double slit qubits

Single plane minimal tomography of double slit qubits

Extracting the Green’s function from measurements of the energy flux

Geometric phase and modulus relations for probability amplitudes as functions on complex parameter spaces

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