Jacob E. Finesinger, M. D

Brody, Eugene B.

doi:10.1176/ajp.116.4.383

Cited by 7 publications

(10 citation statements)

References 0 publications

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“…At the suggestion of the author, Dunkl was also able to derive, in similar fashion, the Bures metric [4,26] counterpart of this Hilbert-Schmidt result (33). It took the form (Appendix D 3)…”

Section: Hilbert-schmidt and Bures Probability Distributions Overmentioning

confidence: 88%

“…Since we had previously computed [19][eqs, (33)- (41)] the moments of |ρ P T | n 2−rebit/HS , n = 1, . .…”

Section: Determinantal Product Moment Formulasmentioning

confidence: 99%

“…(cf. [9,10,33])) case-the estimates obtained by application of the procedure of Provost [29, eq. (15)] to sequences of 2,125 moments of (|ρ||ρ P T |) n (upper blue curve) and |ρ P T | n (lower red curve).…”

Section: Estimation Of Separability Probabilities Using Conjecmentioning

confidence: 99%

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Moment-based evidence for simple rational-valued Hilbert–Schmidt generic 2 × 2 separability probabilities

Slater

Dunkl

2012

J. Phys. A: Math. Theor.

122

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Employing Hilbert-Schmidt measure, we explicitly compute and analyze a number of determinantal product (bivariate) moments |ρ| k |ρ P T | n , k, n = 0, 1, 2, 3, . . ., P T denoting partial transpose, for both generic (9-dimensional) two-rebit (α = 1 2 ) and generic (15-dimensional) two-qubit (α = 1) density matrices ρ. The results are, then, incorporated by Dunkl into a general formula (Appendix D 6), parameterized by k, n and α, with the case α = 2, presumptively corresponding to generic (27-dimensional) quaternionic systems. Holding the Dyson-index-like parameter α fixed, the induced univariate moments (|ρ||ρ P T |) n and |ρ P T | n are inputted into a Legendre-polynomialbased (least-squares) probability-distribution reconstruction algorithm of Provost (Mathematica J., 9, 727 (2005)), yielding α-specific separability probability estimates. Since, as the number of inputted moments grows, estimates based on the variable |ρ||ρ P T | strongly decrease, while ones employing |ρ P T | strongly increase (and converge faster), the gaps between upper and lower estimates diminish, yielding sharper and sharper bounds. Remarkably, for α = 2, with the use of 2,325 moments, a separability-probability lower-bound 0.999999987 as large as 43, 195302 (2010)).

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Section: Hilbert-schmidt and Bures Probability Distributions Overmentioning

confidence: 88%

“…Since we had previously computed [19][eqs, (33)- (41)] the moments of |ρ P T | n 2−rebit/HS , n = 1, . .…”

Section: Determinantal Product Moment Formulasmentioning

confidence: 99%

See 1 more Smart Citation

Moment-based evidence for simple rational-valued Hilbert–Schmidt generic 2 × 2 separability probabilities

Slater

Dunkl

2012

J. Phys. A: Math. Theor.

122

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“…Although much work has been done on the subject since the first major result by Mandelstam and Tamm [1], scarce contributions [40][41][42][43][44] undertake nonunitary evolutions. In this Letter, we develop a method that allows one to derive useful saturable lower bounds for the minimal evolution time for general physical processes.…”

mentioning

confidence: 99%

Quantum Speed Limit for Physical Processes

Taddei

Escher

Filho

2013

The Rochester Conferences on Coherence and Quantum Optics and the Quantum Information and Measurement Meeting

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The evaluation of the minimal evolution time between two distinguishable states of a system is important for assessing the maximal speed of quantum computers and communication channels. Lower bounds for this minimal time have been proposed for unitary dynamics. Here we show that it is possible to extend this concept to nonunitary processes, using an attainable lower bound that is connected to the quantum Fisher information for time estimation. This result is used to delimit the minimal evolution time for typical noisy channels.

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“…Hw describes the interaction of the pseudo-spins with the phonons, 9 The acoustic phonons with wq = v q are coupled via the piezoelectric coupling constant Fqq to the Ising model in a transverse field. I n the ordered phase we have the mean values ( S z ) $: 0 and ( S z ) =/= 0, and it is appropriate to choose a new coordinate system rotating the original one used in (1) by the angle 8 in the xy plane,…”

Section: Hph Represents the Usual Haniiltonian Of The Lattice Vibratimentioning

confidence: 99%

Spin‐phonon interactions in the ising model with a transverse field

Wesselinowa

1983

Physica Status Solidi (b)

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A Green function technique is used to study the effects of spin-phonon interactions in t,he Ising model with a transverse field. The renormalized energy of the coupled mode, the damping of the spin waves, and the phonon damping are evaluated. The transverse dynamic structure factor exhibits three peaks due to the coupling of the transverse soft-mode and the acoustic phonon mode. The width of the central peak is proportional to the phonon damping.Die Methode der Greenschen Funktionen wird angewendet, um die Spin-Phonon-Wechselwirkung im Ising-Model1 mit transversalem Feld zu untersuchen. Die renormierte Energie der gekoppelten Mode und die Spinwellen-und Phonondampfung werden berechnet. Der transversale dynamische Strukturfaktor zeigt drei Peaks, verursacht durch die Kopplung der transversalen weichen Mode und der Mode der akustischen Phononen. Die Breite des Zentralpeaks ist proportional der Phonondampfung.

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Jacob E. Finesinger, M. D

Cited by 7 publications

References 0 publications

Moment-based evidence for simple rational-valued Hilbert–Schmidt generic 2 × 2 separability probabilities

Moment-based evidence for simple rational-valued Hilbert–Schmidt generic 2 × 2 separability probabilities

Quantum Speed Limit for Physical Processes

Spin‐phonon interactions in the ising model with a transverse field

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