Figure 1

Depiction of the ideal qubit SDC protocol. Bob prepares the Bell state $|{\psi }^{+}\rangle$, and keeps half of it in a quantum memory. He sends the other half to Alice who either does an encoding (with probability $c$, solid line) or does the $Z$-basis measurement which indicates whether she prepares $|+\rangle$ or $|-\rangle$ (with probability $1-c$, dashed line). Alice sends this state to Bob who does a Bell measurement with his stored qubit and the qubit from Alice (with probability $c$, solid line) or does a $Z\otimes X$-basis measurement (with probability $1-c$, dashed line).Reuse & Permissions

Figure 2

Version 1 of the ideal qubit LM05 protocol. Bob prepares one of the four BB84 states and sends it Alice. Alice performs an encoding (with probability $c$, solid line), or a measurement in the $X$ basis followed by the sending of the postmeasurement state (with probability $1-c$, dashed line). Bob performs a measurement in the $Z$ or $X$ basis whenever he prepared states in the $Z$ or $X$ basis, respectively. Bob then does an xor of his measured bit and his preparation bit corresponding to his prepared state.Reuse & Permissions

Figure 3

A depiction of Lemma 1. An encoding that takes a quantum state and a random string as input, which is used to choose which encoding to perform, always outputs a fixed state (averaged over all encoding choices). This encoding is equivalent to the scenario where a measurement $F$ acts jointly on the same quantum state input as the encoding and half of a bipartite pure state $|\varphi \rangle$. The output of the measurement is a random string, and the other half of $|\varphi \rangle$ is then the same fixed state output from the encoding, averaged over all measurement outcomes of $F$.Reuse & Permissions

Figure 4

(Top) Log base 10 of the key rates vs the error rate (i.e., half the probability of having a state depolarized) for uncorrelated independent identical depolarizing channels. (Bottom) Log base 10 of the key rates vs the error rate (i.e., half the probability of having a state depolarized) in one channel, where the channels are correlated such that the probability of becoming depolarized through one channel is the same as the probability of being depolarized when going forwards and backwards through the same channel. The plotted key rates are as follows: two copies of the one-way BB84 protocol performed from Alice to Bob and from Bob to Alice (blue, solid), the SDC protocol (green, dashed), the LM05 protocol (cyan, dot dashed), and the Plug & Play protocol (red, dotted).Reuse & Permissions