Steve Flammiasflammia

Apr 28 2017 15:04 UTC
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Apr 25 2017 02:00 UTC
Encoding schemes and error-correcting codes are widely used in information technology to improve the reliability of data transmission over real-world communication channels. Quantum information protocols can further enhance the performance in data transmission by encoding a message in quantum states, however, most proposals to date have focused on the regime of a large number of uses of the noisy channel, which is unfeasible with current quantum technology. We experimentally demonstrate quantum enhanced communication over an amplitude damping noisy channel with only two uses of the channel per bit and a single entangling gate at the decoder. By simulating the channel using a photonic interferometric setup, we experimentally increase the reliability of transmitting a data bit by greater than 20% for a certain damping range over classically sending the message twice. We show how our methodology can be extended to larger systems by simulating the transmission of a single bit with up to eight uses of the channel and a two-bit message with three uses of the channel, predicting a quantum enhancement in all cases.
Apr 19 2017 18:12 UTC
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Apr 13 2017 19:22 UTC
Apr 13 2017 19:16 UTC

Just to clarify Michel's earlier remark, the field norm for the cyclotomics defines the norm in which these vectors are equiangular, and then they will generally **not** be equiangular in the standard norm based on the Hilbert-Schmidt inner product. In the example that he quotes,
$$\|(7\pm 3 \sqrt{5})/32\|_{\mathbb{Q}(\sqrt{5})} = \left[\frac{(7\pm 3 \sqrt{5})}{32} \frac{(7\mp 3 \sqrt{5})}{32}\right]^{1/\deg(\mathbb{Q}[\sqrt{5})]} = \frac{1}{16}.$$
It might be helpful in v2 of the paper if these vectors are called "generalized equiangular" or "equiangular with respect to the field norm", as this will help avoid confusion.

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