# Knowledge of Quantum Hidden Variables Enables Backwards-In-Time Signaling
## 1 Introduction  
In this paper, we provide a protocol that allows any party with knowledge of quantum hidden variables [1, 2, 3] to communicate to her own past, leading to a breakdown of causality in the strong sense. By \"causality\", here we simply mean that \"a cause temporally precedes all its effects\" (in the absence of closed timelike curves [4]). We will specify better the distinction between \"cause\" and \"effect\" in Section 5. By \"hidden variables\", here we mean \"whatever information that is necessary to describe values of observables as preexisting before the measurement\", which is their usual definition. Namely, the hidden variables encode the properties that are assigned to the outcome once the measurement is performed. Our protocol is based on quantum contextuality, and the context is chosen _after_ the values of the hidden variables are discovered. Since the context determines the value of the hidden variables and different contexts will lead to different values, this value must have been \"sent back in time\". This applies to contextual hidden variables. We will not consider non-contextual hidden variables, since it is known that non-contextual hidden variables cannot be used to describe quantum mechanics [5, 6]. In other words, the _future_ choice of context affects the _past_ values of the hidden variables, and this can be used to send information back to one's own causal past as we shall show below. [PERSON]'s theorem [7, 8, 9] implies that such hidden variables are nonlocal: a measurement on one system may change the hidden variables of a distant second system that may be causally disconnected from the first. If the hidden variables exist, this type of nonlocality(which we will call \"Einstein nonlocality\") is incompatible with the conjunction of special relativity and causality. Indeed, a person with knowledge of the hidden variables will be able to communicate superluminally [10], which means that _for another observer_ the temporal order of cause and effect can be flipped. An example can illustrate this: suppose that [PERSON] uses a superluminal projectile (or signal) to shoot a distant target. The other observer, [PERSON], in uniform motion with respect to [PERSON], can see these two spacelike-separated events with opposite time ordering: he can see the target is hit before [PERSON] pulls the trigger. Interestingly, we note that superluminal signals are not, by themselves, incompatible with relativity if one relaxes causality [11]. If [PERSON] is a mafia hit-man, she will be acquitted from killing her target thanks to [PERSON]'s testimony that the target died before she even pulled the trigger. In other words, the three hypotheses (i) \"special relativity\", (ii) \"weak causality\" (a cause temporally precedes an effect) and (iii) \"superluminal signaling\" lead to a contradiction: either one has to drop causality (namely, [PERSON] walks free), or one has to drop superluminal signaling (these projectiles do not exist), or one has to drop special relativity. In other words, [PERSON]'s theorem implies that the knowledge of hidden variables violates the causal relations of another observer, under the assumption that special relativity holds. In this paper we prove a stronger statement that one can communicate with one's _own_ past without any assumption about relativity. Namely, we show that knowledge of contextual hidden variables enables Backwards-In-Time Signaling (BITS). This is a stronger statement as is evident from the observation that Newtonian mechanics is a theory that does allow superluminal communication but does not allow any communication with one's own past.