The Einstein-Podolsky-Rosen (EPR) entanglement of a neutral K-meson (kaon) pair enjoys the peculiar quantum behaviour of mixing, charge-parity CP violation (C charge conjugation, P parity) and two non-orthogonal eigenstates of definite time evolution KL and KS with very different lifetimes. The dynamics of this "strange entanglement", experimentally accessible at the Phi-factory, makes possible the search for novel phenomena not accessible in any other system, i.e. at interference times and at decoherence times of the single partners after their disentanglement, in order to unveil the nature of the correlation between the two neutral kaons. Until now, the studies have been concentrated on the single kaon intensity distribution between the two decay times t1 and t2 with Delta t = t2-t1 > 0. Here we focus on the study of the two single time distributions, before each decay, which are physical in both senses: "from past to future", leading to the state of the living partner at time t2 from the observation of the first decay channel at t1, but also "from future to past", leading to the past state of the decayed kaon at time t1 from the observation of the second decay channel at t2.
The latter constitutes a surprising novel effect, which leads to the affirmative answer to the title: it does, the past decayed state depends on the result of the future measurement for the living partner.
This effect has been discussed for the first time in a very recent work; the deepening of its theoretical implications and its experimental investigation which might lead to its first observation are the subject of the present proposal.
Entanglement has played a fundamental role in quantum physics since the EPR discovery of quantum correlations and its physical implications with the Bell's inequalities. The coherent behaviour is translated into instantaneous information transfer - between the two partners - not subjected to the rules of a signal propagation, when a measurement on one partner is performed. In these studies, a space-like interval between the two partners is therefore preferred.
In the case of entangled neutral mesons in the C = ( -) state, the dynamics before the first decay was considered to be trivial, even with mixing, as corresponding to a definite time evolution with the total width of the system. Hence the experimental studies were concentrated in the observation of the single kaon decay rate distribution between the two decays depending on Delta t. The first decay acts as a filtering preparation of the initial single state of the living partner.
This is consistent with the description in terms of observables like: What is the state of the living partner at the time t2 of the second decay?, a well defined "speakable" question after the measurement of the first decay channel f1 at t1.
It is worth mentioning here that these concepts have been instrumental in recent years for identifying initial and final neutral meson states and connect the experimental intensities to be measured with the transition probabilities needed for genuine tests of antiunitary discrete symmetries like Time Reversal T and CPT [21-24].
Asking What was the state of the first decayed kaon?, however, was considered to be unspeakable. Our study of the FTP effect leads to the conclusion that this last contention is only valid as long as no future observation is made.
The present research has gone indeed a step further and seems to recognize that the correlation between the two partners survives their explicit dynamics, with a transition from the quantum correlation of entanglement to a classical correlation of separable KS KL states. The information transfer from a future measurement on the living partner - f2 decay channel at t2 - to the state of the decayed meson at t1 is most surprising. Entering into the entangled region, i.e. just before the first decay, is not an artefact of the formalism, but a precise experimental observable through the t1 distribution of decays in any channel.
These measurements can be performed by the KLOE-2 Collaboration, as described in the previous sections. This is so for even situations of decoherence, Eq.(4), a physical situation only reachable for strange entanglement with the two very different lifetimes of KL and KS.
The relevance of the FTP effect and its first experimental evidence
would be very important for the Foundations of Quantum Mechanics.
The effect, connected with the non-local nature of QM (but it cannot be exploited for superluminal communication!) is directly observable at KLOE/KLOE-2.
Moreover as an outstanding corollary, the FTP effect provides the solution of the KS tag problem in particle physics:
Since the discovery of CP violation and the non-orthogonality of the stationary states
there is no decay channel able to tag either KS or KL on an event-by-event basis.
The FTP effect is the only known FAPP method to actually post-pare a KS beam (i.e. the short-lived stationary state) with arbitrary high purity (depending on Dt and eta_2), preparation otherwise impossible with other methods.
In general the present project helps in the understanding of the surprising influence of a future observation on the past element of reality - in the EPR terminology - with a seeming violation of causality. It merits further thinking to unveil what kind of reality is behind the undefined lack of local realism.
[21] Bernabeu, J., Martinez-Vidal, F., and Villanueva-Perez, P. Time Reversal Violation from the entangled B0-antiB0 system. JHEP 08, 064 (2012).
[22] Lees, J. P. et al. Observation of Time Reversal Violation in the B0 Meson System. Phys. Rev. Lett. 109, 211801 (2012).
[23] Bernabeu, J., Di Domenico, A., Villanueva-Perez, P. Direct test of time reversal symmetry in the entangled neutral kaon system at a -factory. Nucl. Phys. B 868, 102¿119 (2013).
[24] Bernabeu, J., Di Domenico, A., Villanueva-Perez, P. Probing CPT in transitions with entangled neutral kaons. JHEP 10, 139 (2015).