Table 1.

Subadditivity of Episodic Memory as Predicted by the Quantum Model of Fuzzy-Trace Theory in False Memory and Source-Monitoring Experiments

Memory judgment	Trace vector
	|V〉	|G〉	|N〉	Vector sum
1. Item false memory experiment
Cue = target
O?	|vO|2	|gO|2	0	|vO|2 + |gO|2
NS?	0	|gO|2	0	|gO|2
ND?	0	0	|nO|2	|nO|2
Total memory probability	|vO|2 +|gO|2 +|gO|2 + |nO|2 > 1
Cue = New-Similar
O?	|vns|2	|gns|2	0	|vns|2 + |gns|2
NS?	0	|gns|2	0	|gns|2
ND?	0	0	|nns|2	|nns|2
Total memory probability	|vns|2 +|gns|2 +|gns|2 + |nns|2 > 1
Cue = New-dissimilar
O?	|vnd|2	|gnd|2	0	|vnd|2 + |gnd|2
NS?	0	|gnd|2	0	|gnd|2
ND?	0	0	|nnd|2	|nnd|2
Total memory probability	|vnd|2 +|gnd|2 +|gnd|2 + |nnd|2 > 1
2. Source false memory experiment
Cue = List 1target
List 1?	|vL1-1|2	|gL1|2	0	|vL1-1|2 +|gL1|2
List 2?	|vL1-2|2	|gL1|2	0	|vL1-2|2 +|gL1|2
New?	0	0	|nL1|2	|nL1|2
Total memory probability	|vL1-1|2+|vL1-2|2+|g L1|2 +|g L1|2 + |nL1|2 > 1
Cue = List 2 target
List 1?	|vL2-1|2	|gL2|2	0	|vL2-1|2+|gL2|2
List 2?	|vL2-2|2	|gL2|2	0	|vL2-2|2+|gL2|2
New?	0	0	|nL2|2	|nL2|2
Total memory probability	|vL2-1|2+|vL2-2|2+| gL2|2 +| gL2|2 + |nL2|2 > 1

Note. |V〉, |G〉, and |N〉 are unit-length vectors for verbatim, gist, and nonmatching traces, respectively, which form an orthonormal basis in a three-dimensional space where memory judgments are made in false memory and source-monitoring experiments. In both types of experiments, the v_c, g_c, and n_c parameters are scalars that multiply the |V〉, |G〉, and |N〉 vectors, respectively, giving the magnitudes of these vectors, subject to the constraint that |v_c|² +|g_c|² + |n_c|² = 1 for the item false memory paradigm and |v_c-1|² +|v_c-2|² +|g_c|² + |n_c|² = 1 for the source false memory paradigm.

Psychologically, the v_c, g_c, and n_c parameters correspond to the strength/accessibility of verbatim, gist, and nonmatching traces, respectively, for the test cue c. The subscript c runs over O (old), NS (newsimilar), and ND (new-dissimilar) cues in false memory experiments, and in general, the scalars have different values for the three types of cues. The subscript c runs over L₁ (List 1), L₂ (List 2), and ND (newdissimilar) cues in source-monitoring experiments designs, and in general, the scalars have different values for the three types of cues.