Multiple photon effective Hamiltonians in linear quantum optical networks

García‐Escartín, Juan Carlos; Gimeno, Vicent; Moyano‐Fernández, Julio José

doi:10.1016/j.optcom.2018.08.082

Cited by 11 publications

(18 citation statements)

References 20 publications

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“…These matrices have a strong structure. The only nonzero elements are in positions which correspond to transitions between states that are, at most, one photon away from each other (for input states |p and |q that only differ in the photon number in two positions, one mode giving the photon to the other [13]).…”

Section: Summary Of the Resultsmentioning

confidence: 99%

“…The map ϕ m,M is a differentiable group homomorphism [1] and it induces an algebra homomorphism, dϕ m,M , as described by the commutative diagram, , which relates the unitary groups U(m) and U(M ) containing the scattering matrix S and the n-photon evolution operator U , respectively, to the algebras u(m) and u(M ), whose elements correspond to anti-Hermitian matrices iH S and iH U which give an equivalent description of the evolution through exponentiation of the Hamiltonians H S and H U (S = e iH S and U = e iH U ) [12,13].…”

Section: B Linear Optical Evolution From the Unitary (Group) And Hermentioning

confidence: 99%

“…We can also write the elements of U from the permanent of different submatrices of S [4]. From the differential dϕ m,M [13], we can write the effective Hamiltonian H U of a linear optical transformation as…”

Section: B Linear Optical Evolution From the Unitary (Group) And Hermentioning

confidence: 99%

“…For a given iH S ∈ u(2), the corresponding element in the image subalgebra d, iH U = dϕ 2,6 (iH S ), is given by [13]…”

Section: F Example Space: Five Photons In Two Modesmentioning

confidence: 99%

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Method to determine which quantum operations can be realized with linear optics with a constructive implementation recipe

2019

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The evolution of quantum light through linear optical devices can be described by the scattering matrix S of the system. For linear optical systems with m possible modes, the evolution of n input photons is given by a unitary matrix U = ϕ m,M (S), derived from a known homomorphism, ϕ m,M , which depends on the size of the resulting Hilbert space of the possible photon states, M. We present a method to decide whether a given unitary evolution U for n photons in m modes can be achieved with linear optics or not and the inverse transformation ϕ −1 m,M when the transformation can be implemented. Together with previous results, the method can be used to find a simple optical system which implements any quantum operation within the reach of linear optics. The results come from studying the adjoint map between the Lie algebras corresponding to the Lie groups of the relevant unitary matrices.

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Section: Summary Of the Resultsmentioning

confidence: 99%

Section: B Linear Optical Evolution From the Unitary (Group) And Hermentioning

confidence: 99%

Section: B Linear Optical Evolution From the Unitary (Group) And Hermentioning

confidence: 99%

“…For a given iH S ∈ u(2), the corresponding element in the image subalgebra d, iH U = dϕ 2,6 (iH S ), is given by [13]…”

Section: F Example Space: Five Photons In Two Modesmentioning

confidence: 99%

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Method to determine which quantum operations can be realized with linear optics with a constructive implementation recipe

2019

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“…There are many results on the synthesis of linear systems from their classical description [4,7,8] and that analyze the evolution of multiple photons in those devices [10][11][12][13][14][15][16][17][18]. However, there are relatively few methods for the design of tailored quantum evolutions for multiple photons.…”

Section: Introductionmentioning

confidence: 99%

Optimal approximation to unitary quantum operators with linear optics

García‐Escartín

Gimeno

Moyano‐Fernández

2021

Quantum Inf Process

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Linear optical systems acting on photon number states produce many interesting evolutions, but cannot give all the allowed quantum operations on the input state. Using Toponogov’s theorem from differential geometry, we propose an iterative method that, for any arbitrary quantum operator U acting on n photons in m modes, returns an operator $$\widetilde{U}$$ U ~ which can be implemented with linear optics. The approximation method is locally optimal and converges. The resulting operator $$\widetilde{U}$$ U ~ can be translated into an experimental optical setup using previous results.

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