## 1 Introduction  
In the Bennett-Brassard (BB84) protocol [1], ideally, the quantum states that [PERSON] sends to [PERSON] correspond to single photons. However, due to perfect single photon sources not being technologically available yet [2], many quantum key distribution (QKD) implementations use laser pulses, which are attenuated to a very low level. On average, these laser pulses contain a very small number of photons, typically around 0.2 photons per pulse, distributed according to a Poissonian distribution. In other words, most pulses actually contain no photons; few pulses only contain just one photon, and only a very small amount of pulses contain two or more photons. The photon Number Splitting (PNS) attack can be resumed as follow. If a laser pulse contains more than one photon [PERSON] can split off the extra photons from it. Then, she allows just one photon to reach [PERSON]'s detector. In doing that, [PERSON] can store the photons she got from the pulse and wait until [PERSON] reveals the measurement basis he applied. [PERSON] measures the stored photons with the same measurement basis as [PERSON], obtaining information about the key. [PERSON]'s activity on the quantum channel is unnoticed by [PERSON] and [PERSON]. References related with security proofs on the PNS attack can be found in [3; 4; 5; 6; 7]. Few protocols are known to be PNS resistant: Decoy QKD [8], Scarani-Acin-Ribordy-Gisin (SARG04) [9], the Differential Phase Shift Keying (DPSK) [10] and Coherent One Way (COW) [11]. One of the most promissory alternatives is the decoy method. In this protocol additional states are interleaved to the standard BB84 states with the purpose to detect an eavesdropper. These are called decoy states. The decoy states are generated by applying, to the photonic source, different mean photonic numbers (\(\mu\)). The only difference between the standard BB84 protocol states and the decoy states is \(\mu\). [PERSON] cannot make difference between decoy states and BB84 states. When [PERSON] intercepts the decoy states to steal photons, she modifies the mean photonic number on the decoy pulses arriving to [PERSON]'s detector. In this way the decoy method reveals the presence of an eavesdropper. Decoy QKD enhances the security of the BB84 protocol against PNS attacks while allowing high key rates. The same as the BB84 protocol, the decoy QKD method establishes a single photonic gain in the quantum channel. Unfortunately, decoy QKD can be successfully attacked if [PERSON] is able to adjust the gain of the quantum channel in order to set the QBER to zero. In this paper, we introduce a novel QKD protocol, named ack-QKD, which is simultaneously immune to a PNS attack and changes on the gain of the quantum channel. These two main features of the ack-QKD protocol are possible if two photonic quantum flows, from parallel and non-orthogonal states, are interleaved to produce two or more quantum gains that cannot be simultaneously adjusted, by changing the gain of the quantum channel, in order to set the two QBER to zero. Our method to detect the PNS attack using the ack-QKD protocol can be summarized in the following:  
(1) In the PNS attack, the eavesdropper blocks the one-photon states, but she stores the multi-photon states, allowing at least one photon to reach [PERSON]'s detection system. (2) [PERSON] cannot substitute the quantum channel, because she cannot adjust simultaneously the multiple channel gain, QPEG, from single and double detection events. As a consequence, [PERSON] is forced to measure the one-photon states, from single and double states, in order to guess the quantum states sent by [PERSON]. In measuring the single states, parallel and non-orthogonal, the eavesdropper produces QBER=0.25 (as in the BB84). On the otherside, in measuring the double (non-empty) states, parallel and non-orthogonal, [PERSON] produces QBER=0.5. (3) The QBER from the multi-photonic non-orthogonal states decrease by half for each copy of the quantum states in [PERSON]'s memory.