Welcome to the Bosonic/analog c-q Kingdom.

Bosonic c-q code Bosonic code designed for transmission of classical information through non-classical channels. Typically, such codes encode real numbers into coherent states for transmission over a quantum channel and decoding with a quantum-enhanced receiver. Parents: Classical-quantum (c-q) code. Parent of: Coherent FSK (CFSK) c-q code, Niset-Andersen-Cerf code, On-off keyed (OOK) c-q code, PPM c-q code. Cousins: Bosonic code, Coherent-state constellation code, Sphere packing.
Coherent FSK (CFSK) c-q code[1][2] Bosonic c-q code encoding into coherent states that are frequency-shifted with certain initial relative phase. Codewords are coherent states \(|\alpha_m\rangle\), where \begin{align} \alpha_m = \alpha e^{i(\omega_0+[m-1]\Delta\omega)t+i(m-1)\Delta\theta} \end{align} for common frequency \(\omega_0\), frequency shift \(\Delta\omega < 2\pi/T\), total time \(T\), and phase shift \(\Delta\theta\). Parents: Bosonic c-q code. Parent of: PSK c-q code. Cousins: Frequency-shift keyring (FSK) code.
Niset-Andersen-Cerf code[3] Bosonic c-q code encoding two-mode coherent states \(\{|\alpha\rangle, |\beta\rangle\}\) into four modes such that the complex values \((\alpha,\beta)\) are recoverable after a single-mode erasure. There are two variations of the storage procedure: a deterministic protocol that offers recovery against a single mode erasure, and a probabalistic that can protect against multiple errors with post selection. This code is effectively protecting classical information stored in \((\alpha,\beta)\) using quantum operations. Protection: The deterministic protocol protects against a single erasure error on a known mode. This recovers one state perfectly and the other state with fidelity \(F = \frac{1}{1 + e^{-2 r}}\) for an initial EPR pair squeezed with variance \(e^{-2r}\). The probabalistic protocol utilizes post-selection to protect against multiple erasures with state-dependent fidelity. Parents: Bosonic c-q code. Cousins: Quadrature-amplitude modulation (QAM) code. Cousin of: Homological bosonic code.
On-off keyed (OOK) c-q code[4] Bosonic c-q binary code whose encoding is either in the vacuum \(|0\rangle\) or in a nonzero coherent state \(|\alpha\rangle\). Parents: Bosonic c-q code. Cousins: BPSK c-q code.
PPM c-q code[5] A \(q\)-PPM c-q code is a bosonic c-q code whose \(j\)th codeword corresponds to a tensor-product state of zero-amplitude coherent states at all modes except mode \(j\). For example, a 3-PPM encoding corresponds to the three-mode states \(|\alpha\rangle|0\rangle|0\rangle\), \(|0\rangle|\alpha\rangle|0\rangle\), and \(|0\rangle|0\rangle|\alpha\rangle\) for some complex \(\alpha\). Parents: Bosonic c-q code. Cousins: Pulse-position modulation (PPM) code.
PSK c-q code[6] Bosonic c-q \(q\)-ary code whose \(j\)th codeword corresponds to a coherent state whose phase is the \(j\)th multiple of \(2\pi/q\). Parents: Coherent FSK (CFSK) c-q code. Parent of: BPSK c-q code. Cousins: Phase-shift keyring (PSK) code, Cat code.
BPSK c-q code Bosonic c-q binary code encoding one bit of information into coherent states \(|\pm\alpha\rangle\) for complex \(\alpha\). Parents: PSK c-q code. Cousins: Binary PSK (BPSK) code, Two-component cat code. Cousin of: On-off keyed (OOK) c-q code.


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