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Table 1 Tables with the maximum value of \(\pmb{A_{J}^{\mathrm{max}}}\) allowed in order for the quantum teleportation protocol to work

From: Quantum teleportation of propagating quantum microwaves

Distance (m) \(\boldsymbol{\Delta\xi^{\prime2}}\) \(\boldsymbol{A_{J}^{\mathrm{max}}}\)
a1
1 0.482 0.164
1 0.500 0.155
10 0.734 0.046
20 0.867 unf.
b1
1 0.476 0.166
1 0.486 0.162
10 0.623 0.098
20 0.737 0.045
a2
1 0.789 0.020
1 0.802 0.014
10 0.895 unf.
b2
1 0.666 0.078
1 0.677 0.073
10 0.767 0.031
  1. The abbreviation ‘unf.’ means ‘unfeasible’. We assume an EPR state with the values discussed in Section 3, i.e. \(\Delta\xi^{2}\simeq0.47\), \(\Delta\xi_{\perp}^{2}\simeq16.77\), and typical values for connector losses leading to α 0.933 (\(A_{\alpha}\simeq0.036\)), β 0.891 (\(A_{\beta}\simeq0.061\)). Moreover, we assume a JPA gain \(g_{J}\simeq180\), and HEMT noise \(A_{H} \simeq7\). The noise parameter \(A_{J}^{\mathrm{max}}\) is estimated from the formulas \(\Xi\equiv(1+\Delta\xi^{\prime2} +A)^{2}\leq4\), which defines the quantum regime. Here, \(\Delta\xi^{\prime2}\) is defined in Eq. (24) and A is introduced in Eq. (27). We assume Alice and Bob symmetrically situated with respect the EPR sources. The distance is referred to the cable length from the EPR sources to Alice (Bob). The estimations take into account of the feedforward, and \(A_{J}^{\mathrm{max}}\) is evaluated for various distances and in four different situations. In a1 we assume cable power losses of 0.1 dB per meter and zero time measurement. In a2 we assume cable power losses of 0.1 dB per meter and 200 ns for measuring and processing the information in Alice. These two tables give an insight on how much the measurement duration, which result in a delay line in Bob, affects the quality of the protocol. In b1 we assume a more optimistic value for cable power losses, i.e. 0.05 dB per meter, and zero time measurement. In b2 we assume 0.05 dB of power losses per meter and 200 ns for measuring the processing the information in Alice. In all the tables, when Eq. (25) holds, we have applied a proper attenuator in Alice in order to optimise \(\Delta\xi^{\prime2}\).