## 2 New Measurement Tools Involving the Reference Wires
### Deterministic Measurement and Evaluation of Entangled States and Their Superposition in INBL  
Suppose [PERSON] sets up a two-noise-bit system (\(M=2\)) with a superposition signal \(S(t)\) containing entanglement (similar to the Einstein-Rosen-Podolsky [1] problem's superposition and the related Bell states):  
\[S(t)\ =\ R_{10}(t)R_{21}+R_{11}(t)R_{20}(t). \tag{7}\]  
This 0(1),1(2) + 1(1),0(2) superposition is unknown by [PERSON] except in the conditions that it consists of the sum of any of the possible \(R_{ij}(t)R_{pq}(t)\) two-bit strings \(i,p\in\{1,2\};\ j,q\in\{0,1\}\), with the restriction that a given value of a given bit can exist at most in a single string. For example, alternative superpositions could be 0(1),0(2) + 1(1),1(2), that is, \(R_{10}(t)R_{20}(t)+R_{11}(t)R_{21}(t)\); or single strings such as 0(1),1(2), that is, \(R_{10}(t)R_{21}(t)\); 1(1),0(2), that is, \(R_{11}(t)R_{20}(t)\); 0(1),0(2), that is, \(R_{10}(t)R_{20}(t)\); or 1(1),1(2), that is, \(R_{11}(t)R_{21}(t)\).  
[PERSON]'s job is to measure \(S(t)\) and decide which is the actual superposition from these different possibilities. To identify strings, statistical methods exist, e.g., [9; 11; 12; 14] and some of them, like the time-shifted RTW scheme [9] and the Stacho [11] method, require only polynomial computation complexity versus the number of noise-bits. However, these methods used on superposition would require _exponential complexity_ with expanding \(M\) (except when the job is to identify a single string and the rest of the superposition is known [14]).  
Here we show that, by utilizing operations on the reference wires, the measurement and analysis can be done in a fast way, which is deterministic, with polynomial complexity. The procedure takes place during a clock time \(t\) when the superposition signal amplitude is non-zero, that is, \(S(t)\
eq 0\):  
(i) [PERSON] first checks the existence of the reference signal \(R_{10}(t)\) in the superposition \(S(t)\
eq 0\) by grounding (forcing zero on) the reference wire of the _inverse bit value_ of \(R_{10}(t)\), that is, forcing \(R_{11}(t)\ =\ 0\), and then checking if the resulting superposition signal \(S_{2}(t)\) is zero. In the above example, see Equation (7), the superposition gets reduced to:  
\[S_{2}(t)\ =\ R_{10}(t)R_{21}(t) \tag{8}\]  
which means \(S_{2}(t)\
eq 0\).  
In alternative cases, when the grounding causes \(S_{2}(t)\ =\ 0\), [PERSON] jumps to step (iii) below. In the present situation, \(S_{2}(t)\
eq 0\) (see Equations (7) and (8)), [PERSON] needs to evaluate which value of the second bit is entangled with the 0 value of the first bit. This string can be evaluated in various known statistical ways, e.g., [9; 11; 14] but here we again propose a deterministic tool by utilizing the reference wires:  
(ii) While still being in the same clock period \(t\) and keeping \(R_{11}(t)\ =\ 0\), [PERSON] also grounds the 0 value of the second bit, \(R_{20}(t)\ =\ 0\), and gets the superposition \(S_{3}(t)\). If \(S_{3}(t)\ =\ 0\), then \(R_{20}(t)\) is the entangled bit signal. If \(S_{3}(t)\
eq 0\), then \(R_{21}(t)\) is the bit value in question, which is the case in the present example.  
Note, [PERSON] can proceed in an alternative way: He grounds the reference \(R_{21}(t)\), \(R_{21}(t)\ =\ 0\), while keeping the grounding \(R_{11}(t)\ =\ 0\). If \(S_{3}(t)\ =\ 0\), then \(R_{21}(t)\) represents the entangled bit value.  
(iii) Now, [PERSON] repeats the above procedures (i-ii) with swapped bit values. He first checks the existence of the reference signal \(R_{11}(t)\) in the superposition by grounding the reference wire of the inverse bit value (forcing \(R_{10}(t)\ =\ 0\)). If the reference signal \(R_{11}(t)\) is not in the original superposition (Equation (7)), then \(S_{2}(t)\ =\ 0\) and [PERSON] has completed the evaluation. Otherwise, he proceeds with the swapped bit values as described in the above procedure (i-ii).