## 6 The Unstructured ack-QKD Protocol  
In the ack-QKD protocol, most of the bi-qubits pulses sent by [PERSON] arrive to [PERSON]'s station as single pulses that behave as BB84 pulses. Usually, in QKD implementations, it is necessary to reduce after-pulsing errors in the protocol. To achieve this, [PERSON] sends pulses at well-defined times, and [PERSON] accepts a detection click only during a narrow time window, discarding events outside these time windows. For any QKD system, one major limitation is the dead time of the avalanche photo diodes (APD), which is the hold-off time following each detection event during which no photon can be  
Figure 5: A representation of the non-orthogonal states of the three-quantum-flow protocol (3Q) protocol in the three-dimensional Bloch sphere. The polarization states, \(\left|0_{X}\right\rangle\), \(\left|0_{Y}\right\rangle\) and \(\left|0_{Z}\right\rangle\), are mutually non-orthogonal. The conjugated basis measurements are \(X\), \(Y\) and \(Z\). detected. If a photon click occurs in a certain pulse, the probability to have one or more photon clicks within the next few gate pulses immediately following the avalanche is very low (see [13]). In such a case, it seems suitable to hold-off on an appropriate number of gate pulses after each registered detection click. However, in the ack-QKD protocol, we must not hold off gate pulses in order to allow [PERSON]'s detectors to be capable of detecting consecutive photonic pulses. We will introduce the unstructured ack-QKD protocol, where [PERSON] chooses, as usually in the ack-QKD, the pairs of quantum states, parallel and non-orthogonal, but she sends the quantum states as single qubits, choosing to send each of them randomly (See Table 4). After [PERSON] measures the quantum states choosing randomly the basis measurement, \(X\) or \(Z\), for each pulse, [PERSON] reveals the bi-qubit pairs, but she does not specify if each pair corresponds to parallel or non-orthogonal states. Once [PERSON] reveals the bi-qubit pairs, [PERSON] is able to look for the matching and non-matching detection events, allowing himself, after this step, to follow the sifting procedure of the ack-QKD protocol. Suppose [PERSON] wants to send the following quantum pairs of the ack-QKD protocol: \((\ket{0_{X}},\ket{0_{Z}})_{1},(\ket{1_{X}},\ket{0_{Z}})_{2},(\ket{0_{X}},\ket{1 _{Z}})_{3},(\ket{1_{X}},\ket{1_{Z}})_{4},(\ket{1_{Z}},\ket{1_{Z}})_{5},(\ket{0 _{X}},\ket{1_{X}})_{6},(\ket{0_{Z}},\ket{0_{Z}})_{7}\). However, as can be seen in the Step 1, [PERSON] sends such states individually and randomly. In Step 2, [PERSON] chooses the measurement basis for each incoming quantum state at random. Then, in Step 3, [PERSON] announces publicly the corresponding quantum states, so [PERSON] determines on which cases he applied correctly his basis measurement. Once [PERSON] reveals her bi-qubit pairs, [PERSON] is able to look for the matching and non-matching detection events, allowing himself, after this step, to follow the sifting procedure of the ack-QKD protocol. In this example, [PERSON] applied the same basis measurement over the quantum pairs, 1, 3, 4 and 7. Since the probability of getting the correct (same) basis measurement for the corresponding pair of pulses is 50%, the photonic gains decrease by a half. The unstructured ack-QKD protocol is feasible, because the photonic gains depend on the final computation of two independent detection probabilities, which can be consecutive events or not. It should be noticed that the unstructured ack-QKD protocol can be applied to the 3Q version of the protocol. To the best of our knowledge, the ack-QKD is the first protocol that uses qubits of two \"colors\", namely the non-orthogonal bi-qubit and the parallel bi-qubit, which are useful for composing two quantum flows randomly interleaved. We believe that this may open up new possibilities to increase the ultimate security of the QKD protocols towards the achievement of a device independent protocol.