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arXiv:0906.1885 · Physical Review A

Conditions for factorizable output from a beam splitter

Steffen Springer, Jinhyoung Lee, Marco Bellini, M. S. Kim

Published Jun 3, 2009• 9 citations
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Abstract

A beam splitter is one of the most important devices in an optics laboratory because of its handiness and versatility; equivalent devices are found in various quantum systems to couple two subsystems or to interfere them. While it is normal that two independent input fields are superposed at the beam splitter to give correlated outputs, identical Gaussian states interfere there to produce totally independent output fields. We prove that the Gaussian states with same variances are the only states which bring about factorizable output fields.

DOI
10.1103/physreva.79.062303

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A beam splitter is one of the most important devices in an optics laboratory because of its handiness and versatility; equivalent devices are found in various quantum systems to couple two subsystems or to interfere them. While it is normal that two independent input fields are superposed at the beam splitter to give correlated outputs, identical Gaussian states interfere there to produce totally independent output fields. We prove that the Gaussian states with same variances are the only states which bring about factorizable output fields.
A beam splitter is a simple, readily available device which can act to entangle output optical fields. We show that a necessary condition for the fields at the output of the beam splitter to be entangled is that the pure input states exhibit nonclassical behavior. We generalize this proof for arbitrary (pure or impure) Gaussian input states. Specifically, nonclassicality of the input Gaussian fields is a necessary condition for entanglement of the field modes with the help of a beam splitter. We conjecture that this is a general property of beam splitters: Nonclassicality of the inputs is a necessary condition for entangling fields in a beam splitter.
In general, a pair of uncorrelated Gaussian states mixed in a beam splitter (BS) produces a correlated state at the output. However, when the inputs are identical Gaussian states the output state is equal to the input, and no correlations appear, as the interference had not taken place. On the other hand, since physical phenomena do have observable effects, and the BS is there, a question arises on how to reveal the interference between the two beams. We prove theoretically and demonstrate experimentally that this is possible if at least one of the two beams is prepared in a discordant, i.e., Gaussian correlated, state with a third beam. We also apply the same technique to reveal the erasure of polarization information. Our experiment involves thermal states and the results show that Gaussian discordant states, even when they show a positive Glauber P-function, may be useful to achieve specific tasks.
A beam splitter is a basic linear optical element appearing in many optics experiments and is frequently used as a continuous-variable entangler transforming a pair of input modes from a separable Gaussian state into an entangled state. However, a beam splitter is a passive operation that can create entanglement from Gaussian states only under certain conditions. One such condition is that the input light is suitably squeezed. We demonstrate, experimentally, that a beam splitter can create entanglement even from modes which do not possess such a squeezing provided that they are correlated to, but not entangled with, a third mode. Specifically, we show that a beam splitter can create three-mode entanglement by acting on two modes of a three-mode fully separable Gaussian state without entangling the two modes themselves. This beam splitter property is a key mechanism behind the performance of the protocol for entanglement distribution by separable states. Moreover, the property also finds application in collaborative quantum dense coding in which decoding of transmitted information is assisted by interference with a mode of the collaborating party.
Entanglement is an important ingredient for quantum information processing. We discuss some sources of entanglement, namely a beam splitter and a thermal field. For the generation of entangled continuous-variable states, we consider a beam splitter and find some conditions for input fields to see entanglement in the output. While a beam splitter is a unitary device to generate an entangled state for a bipartite continuous-variable system, a thermal field is shown to mediate entanglement of two qubits.
The second-order coherence of optical fields at output ports of a beam splitter is investigated. The properties of the second-order coherence are not only strongly dependent on the input states but also quite involved with the nature of the beam splitter. When parameters of both the input states and the beam splitter are chosen appropriately, the fields at the output ports will exhibit quantum behaviour. Between the two output modes, there stands mode–mode correlation which can even be anticorrelation. Some nonclassical properties, such as the photon antibunching effect of the input fields, may be destroyed by the beam splitter.