Corrigendum: Informational approach to the quantum symmetrization postulate (2015 New J. Phys.17 013043)

Q Q , * p p = ( ) ( ) and equation (19), Q 1, p =  ( ) only hold for permutations p that are self-inverses, , 1 p p = not for all p as stated. As it turns out, the remainder of the argument, contained in subpart (ii) and continuing thereafter, can be minimallymodified in such away that it does not requiremaking use of equation (2) at all.We now give this modification. For the sake of clarity, we give themodified argument, culminating in the final expression for H , ,..., , N 1 2 a a a p p p ( ) ! in full. (ii)Establishing Q Q p p = ¢ ( ) ( )whenever p and p¢ are both odd or both even. In equation (A11), let k , , , i i i a d d = + p p p p p ¢ ( ) where k is some constant. Then, using equations (A18), namely

where 1 pdenotes the inverse permutation to , p that is 1 ppis the identity permutation .
1 p The reason is that, under reversal, the permutation p with amplitude a p yields the amplitude 1 a¢ p -for the permutation 1 p -(see figure 1). Consequently, the unnumbered equation that follows and equation (19), only hold for permutations p that are self-inverses, , 1 p p = not for all p as stated. As it turns out, the remainder of the argument, contained in subpart (ii) and continuing thereafter, can be minimally modified in such a way that it does not require making use of equation (2) That is, any two permutations, , , p p that are connected by a pair of transpositions have the same Q-value. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
But every even permutation can be written as a product of an even number of transpositions and the identity permutation. Therefore, all even permutations have the same Q-value, Q e . Similarly, every odd permutation can be written as a product of an even number of transpositions and a given odd permutation. Therefore, all odd permutations have the same Q-value, Q o . Finally, equation (3)  where sgn p ( ) takes the value 1 + or 1 according to whether p is even or odd.
Insofar as the probability of the transition of the system of N indistinguishable particles is concerned, the multiplicative phase factor Q 1 p ( )and the complex conjugation are irrelevant. More generally, consider a system, ,  that consists of subsystems 1  and , 2  where 1  consists of N indistinguishable particles of one type (say, electrons). Suppose, first, that 2  only contains particles that can be distinguished from those in . be performed on 1  at times t 1 and t 2 . Additionally, let measurements U and V be performed on 2  at t 1 and t 2 , respectively, yielding outcomes u and v. Let a p be the amplitude of the transition of  from (ℓ: u) to (m: v) in which the particles in 1  are treated as distinguishable and make the transition described by .
p Then, by the same argument as described above, the amplitude of the process from (ℓ: u) to (m: v) where the particles in 1  are treated as indistinguishable is given by H , ,..., , N 1 2 a a a p p p (˜˜˜) ! and the transition probability is again unaffected by the overall sign or complex conjugation of H. In the case that 2  does contain, say, M particles that are indistinguishable from those in , 1  the boundaries of 1  must be redrawn to encompass them. The resulting situation, namely a system composed of subsystem , 1  ¢ containing N + M indistinguishable particles, and subsystem , 2  ¢ containing only particles that are distinguishable from those in , 1  ¢ is of the same type the as one previously considered. Therefore, in general, the overall multiplicative factor Q , 1 p ( ) which has modulus unity 2 , and the complex conjugation in equation (5b), are irrelevant insofar as predictions are concerned, and can be discarded without any loss of generality. Hence, without loss of generality, we can take equation (5a) with Q 1, 1 p = ( ) namely ℓ ℓ ℓ at t 2 . The amplitude of this process can be computed in two different ways. As shown on the left, one can first take the amplitude of the indistinguishableparticle process with the measurements in their original order, and then take its complex-conjugate to get H , ; , where 0 s = or 1 s = is the only remaining degree of freedom, corresponding respectively to bosons and fermions.
The above result for the amplitude holds for a particular labelling of the outcomes at times t 1 and t 2 . However, the corresponding transition probability is invariant under relabelling of these outcomes. To see this, suppose that the outcomes at t 1 and t 2 are relabelled such that i