TY - JOUR

T1 - Majorization relations and entanglement generation in a beam splitter

AU - Gagatsos, C. N.

AU - Oreshkov, O.

AU - Cerf, N. J.

PY - 2013/4/4

Y1 - 2013/4/4

N2 - We prove that a beam splitter, one of the most common optical components, fulfills several classes of majorization relations, which govern the amount of quantum entanglement that it can generate. First, we show that the state resulting from k photons impinging on a beam splitter majorizes the corresponding state with any larger photon number k′>k, implying that the entanglement monotonically grows with k. Then we examine parametric infinitesimal majorization relations as a function of the beam-splitter transmittance and find that there exists a parameter region where majorization is again fulfilled, implying a monotonic increase of entanglement by moving towards a balanced beam splitter. We also identify regions with a majorization default, where the output states become incomparable. In this latter situation, we find examples where catalysis may nevertheless be used in order to recover majorization. The catalyst states can be as simple as a path-entangled single-photon state or a two-mode squeezed vacuum state.

AB - We prove that a beam splitter, one of the most common optical components, fulfills several classes of majorization relations, which govern the amount of quantum entanglement that it can generate. First, we show that the state resulting from k photons impinging on a beam splitter majorizes the corresponding state with any larger photon number k′>k, implying that the entanglement monotonically grows with k. Then we examine parametric infinitesimal majorization relations as a function of the beam-splitter transmittance and find that there exists a parameter region where majorization is again fulfilled, implying a monotonic increase of entanglement by moving towards a balanced beam splitter. We also identify regions with a majorization default, where the output states become incomparable. In this latter situation, we find examples where catalysis may nevertheless be used in order to recover majorization. The catalyst states can be as simple as a path-entangled single-photon state or a two-mode squeezed vacuum state.

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U2 - 10.1103/PhysRevA.87.042307

DO - 10.1103/PhysRevA.87.042307

M3 - Article

AN - SCOPUS:84876115217

SN - 1050-2947

VL - 87

JO - Physical Review A - Atomic, Molecular, and Optical Physics

JF - Physical Review A - Atomic, Molecular, and Optical Physics

IS - 4

M1 - 042307

ER -