Multiparticle quantum interference in Bogoliubov bosonic transformations

Jabbour, Michael G.; Cerf, Nicolas J.

doi:10.1103/physrevresearch.3.043065

Cited by 3 publications

(8 citation statements)

References 48 publications

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“…It should be stressed that the derivation of D is far from obvious because it requires the evaluation of non-Gaussian matrix elements of Gaussian unitaries in the Fock basis. This is where the generating function comes into play because it enables expressing these matrix elements by using the Gaussian toolbox only [12]. Actually, the trick is not to access these matrix elements individually, but to exploit the recurrence equation that they obey (as implied by the generating function) in order to prove the majorization ladder (4).…”

Section: Discussion and Perspectivesmentioning

confidence: 99%

“…has a closed analytical expression when ÛG is chosen to be the unitary of a beam-splitter or two-mode squeezer, see Ref. [12]. It should be noted here that multi-index sequences are simply associated with multivariate generating functions, with one variable associated with each index.…”

Section: Generating Function Of Transition Probabilitiesmentioning

confidence: 99%

“…3 can thus be retrieved from h(x, z). Expression (12) holds for both the noisy loss channel E N η and noisy amplifier A N g provided f (x, y, z, 1) is replaced by its appropriate expression as found in Ref. [12].…”

Section: Generating Function Of Transition Probabilitiesmentioning

confidence: 99%

“…Expression (12) holds for both the noisy loss channel E N η and noisy amplifier A N g provided f (x, y, z, 1) is replaced by its appropriate expression as found in Ref. [12]. In the case of the conjugated amplifier ÃN g , the partial trace is done over the first mode, so that the generating function is h(x, z) = (1 − y) f (x, y, 1, z).…”

Section: Generating Function Of Transition Probabilitiesmentioning

confidence: 99%

“…In Section II, we lay the general sketch of our proof, which relies on the construction of a column-stochastic matrix linking the eigenvalues of the output states associated with subsequent Fock states for any BCG. The matrix is built by exploiting a recently found recurrence relation on the transition probabilities in Gaussian unitaries [12]. In Section III, we use the generating function as a mathematical tool in order to derive a recurrence relation satisfied by the output states of any BCG.…”

Section: Introductionmentioning

confidence: 99%

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Majorization ladder in bosonic Gaussian channels

Herstraeten¹,

Jabbour²,

Cerf³

2022

Preprint

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We show the existence of a majorization ladder in bosonic Gaussian channels, that is, we prove that the channel output resulting from the nth energy eigenstate (Fock state) majorizes the channel output resulting from the (n+1)th energy eigenstate (Fock state). This reflects a remarkable link between the energy at the input of the channel and a disorder relation at its output as captured by majorization theory. This result was previously known in the special cases of a pure-loss channel and quantum-limited amplifier, and we achieve here its nontrivial generalization to any singlemode phase-covariant (or -contravariant) bosonic Gaussian channel. The key to our proof is the explicit construction of a column-stochastic matrix that relates the outputs of the channel for any two subsequent Fock states at its input, which is made possible by exploiting a recently found recurrence relation on multiphoton transition probabilities for Gaussian unitaries [M. G. Jabbour and N. J. Cerf, Phys. Rev. Research 3, 043065 (2021)]. We then discuss possible generalizations and implications of our results. a

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Section: Discussion and Perspectivesmentioning

confidence: 99%

Section: Generating Function Of Transition Probabilitiesmentioning

confidence: 99%

Section: Generating Function Of Transition Probabilitiesmentioning

confidence: 99%

Section: Generating Function Of Transition Probabilitiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Majorization ladder in bosonic Gaussian channels

Herstraeten¹,

Jabbour²,

Cerf³

2022

Preprint

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Families of bosonic suppression laws beyond the permutation symmetry principle

Bezerra,

Shchesnovich

2023

New J. Phys.

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Exact cancellation of quantum amplitudes in multiphoton interferences with Fock states at the input, the so-called suppression or zero transmission laws generalizing the Hong-Ou-Mandel dip, are useful tools in quantum information and computation. It was recently suggested that all bosonic suppression laws follow from a common permutation symmetry in the input quantum state and the unitary matrix of the interferometer. By using the recurrence relations for the interference of Fock states, we find a wealth of suppression laws on the beamsplitter and tritter interferometers that do not follow from the permutation symmetry principle. Our results reveal the existence of whole families of suppression laws for an arbitrary total number of bosons with only a fraction of them being accounted for by the permutation symmetry principle, suggested as the general principle behind the suppression laws.

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Majorization ladder in bosonic Gaussian channels

Herstraeten

Jabbour

Cerf

2023

AVS Quantum Science

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We show the existence of a majorization ladder in bosonic Gaussian channels, that is, we prove that the channel output resulting from the [Formula: see text] energy eigenstate (Fock state) majorizes the channel output resulting from the [Formula: see text] energy eigenstate (Fock state). This reflects a remarkable link between the energy at the input of the channel and a disorder relation at its output as captured by majorization theory. This result was previously known in the special cases of a pure-loss channel and quantum-limited amplifier, and we achieve here its non-trivial generalization to any single-mode phase-covariant (or -contravariant) bosonic Gaussian channel. The key to our proof is the explicit construction of a column-stochastic matrix that relates the outputs of the channel for any two subsequent Fock states at its input. This is made possible by exploiting a recently found recurrence relation on multiphoton transition probabilities for Gaussian unitaries [Jabbour and Cerf, Phys. Rev. Res. 3, 043065 (2021)]. Possible generalizations and implications of these results are then discussed.

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Multiparticle quantum interference in Bogoliubov bosonic transformations

Cited by 3 publications

References 48 publications

Majorization ladder in bosonic Gaussian channels

Majorization ladder in bosonic Gaussian channels

Families of bosonic suppression laws beyond the permutation symmetry principle

Majorization ladder in bosonic Gaussian channels

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