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arXiv:1511.07956 · Journal of the Korean Physical Society

Conditional generation scheme for high-fidelity Yurke-Stoler states by mixing two coherent beams with a squeezed vacuum state

Sun-Hyun Youn

Published Jan 1, 2015• 1 citation
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Abstract

The numerical conditions to generate high-fidelity Yurke-Stoler states (|α > +e iψ | − α >)were found for two cascade-placed beam splitters with one squeezed state input and two coherent state inputs. Controlling the amplitudes and the phases of beams allows for various Yurke-Stoler states to be manipulated with ultra-high fidelity, and the expected theoretical fidelity is more than 0.9999.

DOI
10.3938/jkps.66.187

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The numerical conditions to generate high-fidelity Yurke-Stoler states (|α > +e iψ | − α >)were found for two cascade-placed beam splitters with one squeezed state input and two coherent state inputs. Controlling the amplitudes and the phases of beams allows for various Yurke-Stoler states to be manipulated with ultra-high fidelity, and the expected theoretical fidelity is more than 0.9999.
The numerical conditions to generate high-purity |1 >, |2 >, and |1 > + re iψ |2 > states were found from the explicit form of the probability amplitudes for two cascade-placed beam splitters with one squeezed state input and two coherent state inputs. The expected theoretical signal-tonoise ratio is more than 1000. Controlling the amplitudes and the phases of two coherent beams, as well as the transmittances of two beam splitters, allow various quantum states to be manipulated with a high signal-to-noise ratio. High-purity nonclassical states are expected to be a key element in quantum information science.
In the two-cascade-placed beam splitter system, controllable entangled states can be conditionally generated with one squeezed light and two coherent lights. By measuring one photon in one of three output ports, an entangled quantum state can be generated in the remaining two ports. Using the Schmidt decomposition technique, we calculate the degree of entanglement, and maximize the degree of entanglement by adjusting the three input beams and the transmittances of the two beam splitters. The degree of entanglement can be easily adjusted by changing the relative phase angle of the input states.
We investigate an optical scheme to conditionally engineer quantum states using a beam splitter, homodyne detection, and a squeezed vacuum as an ancillar state. This scheme is efficient in producing non-Gaussian quantum states such as squeezed single photons and superpositions of coherent states (SCSs). We show that a SCS with well defined parity and high fidelity can be generated from a Fock state of $n\ensuremath{\leqslant}4$, and conjecture that this can be generalized for an arbitrary nnn Fock state. We describe our experimental demonstration of this scheme using coherent input states and measuring experimental fidelities that are only achievable using quantum resources.
From the explicit form of the probability amplitude for two cascade-placed beam splitters (with one squeezed state input and two coherent state inputs), we calculated the probability amplitude of the output beam as a function of the transmittance of the two beam splitters and the amplitude and the relative phase of the three input states. At a certain condition, the output beam had no vacuum and was in a highly nonclassical state that contained more than one photon. Armed with explicit probability amplitude for two beam splitters and two coherent states, the squeezed vacuum state might be a very useful tool for generating highly nonclassical light.
Entangled coherent states are shown to emerge, with high fidelity, when mixing coherent and squeezed vacuum states of light on a beam-splitter. These maximally entangled states, where photons bunch at the exit of a beamsplitter, are measured experimentally by Fock-state projections. Entanglement is examined theoretically using a Bell-type nonlocality test and compared with ideal entangled coherent states. We experimentally show nearly perfect similarity with entangled coherent states for an optimal ratio of coherent and squeezed vacuum light. In our scheme, entangled coherent states are generated deterministically with small amplitudes, which could be beneficial, for example, in deterministic distribution of entanglement over long distances.
We present an optical scheme to conditionally generate even or odd squeezed superpositions of coherent states (SSCSs). The optical setup consists of an unbalanced beam splitter whose transmittance tends to unity, and additional balanced beam splitters and photodetectors in auxiliary modes. Squeezed coherent states with different amplitudes are the input states in the optical scheme. The single-qubit operations are probabilistic and employ two- and three-photon subtractions from initial beams as the driving force. Generation of the even or odd SSCSs is observed in a wide diapason of values of used parameters. We consider a possibility to realize a one-way Hadamard gate for the squeezed coherent states when the base states are transformed into superposition states. States approximating the output states of a Hadamard gate with high fidelity can be realized by imposing restrictions on the values of used parameters. Higher-order subtractions from input beams are necessary to generate the SSCSs with larger amplitudes and higher fidelities. The problem is resolved in a Wigner representation to take into account imperfections of the optical devices.