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arXiv:1202.2948

Einstein-Podolsky-Rosen State of Neutral Mesons: The Entangled Partner of K_L Is Not K_S

Yu Shi

Published Feb 14, 2012• 0 citations
arXivHTMLPDF

Abstract

In a $ϕ$ factory, neutral kaons are produced in Einstein-Podolsky-Rosen (EPR) states, furthermore, a $K_S$ is tagged if its entangled partner is detected as $K_L$, and vice versa. Here we point out that upon its detection as $K_L$, one of the EPR-entangled particles is projected into one of the orthogonal basis states, consequently the other particle should be projected to the state orthogonal to $K_L$, denoted as $K_{\perp L}$, rather than $K_S$, because $K_S$ is not orthogonal to $K_L$. Therefore the semileptonic charge asymmetry of what was previously regarded as $K_S$ is really that of $K_{\perp L}$. Based on this re-tagging, we modify the experimentally determined values of several parameters, including the one describing the violation of $ΔS = ΔQ$ rule, the one describing CPT violation for $ΔS = ΔQ$ transitions, and the time-like CPT- and Lorentz-violating coefficient for the two valence quarks in a kaon.

DOI
10.48550/arxiv.1202.2948

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In a ϕϕϕ factory, neutral kaons are produced in Einstein-Podolsky-Rosen (EPR) states, furthermore, a KSK_SKS​ is tagged if its entangled partner is detected as KLK_LKL​, and vice versa. Here we point out that upon its detection as KLK_LKL​, one of the EPR-entangled particles is projected into one of the orthogonal basis states, consequently the other particle should be projected to the state orthogonal to KLK_LKL​, denoted as K⊥LK_{\perp L}K⊥L​, rather than KSK_SKS​, because KSK_SKS​ is not orthogonal to KLK_LKL​. Therefore the semileptonic charge asymmetry of what was previously regarded as KSK_SKS​ is really that of K⊥LK_{\perp L}K⊥L​. Based on this re-tagging, we modify the experimentally determined values of several parameters, including the one describing the violation of ΔS=ΔQΔS = ΔQΔS=ΔQ rule, the one describing CPT violation for ΔS=ΔQΔS = ΔQΔS=ΔQ transitions, and the time-like CPT- and Lorentz-violating coefficient for the two valence quarks in a kaon.
The Einstein-Podolsky-Rosen (EPR) entanglement of a neutral K-meson (kaon) pair enjoys the peculiar quantum behaviour of mixing, charge-parity CP{\cal CP}CP violation (C{\cal C}C - charge conjugation, P{\cal P}P - parity) and two non-orthogonal eigenstates of definite time evolution KLK_LKL​ and KSK_SKS​ with very different lifetimes. The dynamics of this strange entanglement, experimentally accessible at the ϕ\phiϕ-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 t1t_1t1​ and t2t_2t2​ with Δt=t2−t1>0\Delta t = t_2 - t_1 > 0Δt=t2​−t1​>0. Here we show that the entire two single time distributions, before each decay, are physical in both senses: past to future, leading to the state of the living partner at time t2t_2t2​ from the observation of the first decay channel at t1t_1t1​, and future to past, leading to the past state of the decayed kaon at time t1t_1t1​ from the observation of the second decay channel at t2t_2t2​. Our results thus demonstrate an affirmative answer to the title: it does, the past decayed state depends on the result of the future measurement for the living partner. This novel effect is truly observable through the first decay time distributions. Besides the implications for quantum physics for all Δt\Delta tΔt, at large decoherence times the resulting first decayed state is always KSK_SKS​, providing a genuine tag of this kaon state in the decoherence region, and a unique and important experimental tool to prepare a pure KSK_SKS​ beam.
A local realistic theory of single neutral kaons and of correlated neutral kaon pairs is formulated by deducing the most general consequences of three assumptions: (i) the Einstein-Podolsky-Rosen (EPR) reality criterion, (ii) locality, and (iii) no retroactive causality. Variables must be introduced for every kaon determining the stable CP\mathrm{CP}CP value and the variable value of strangeness S.S.S. Instantaneous SSS jumps are shown to take place. If kaon pairs are produced in \ensuremath{\Phi} meson decays, the local realistic probability of observing K‾0K‾0{\overline{K}}^{0}{\overline{K}}^{0}K0K0 pairs at certain different proper times necessarily differs by 30% from the quantum-mechanical predictions. The size of this difference justifies our systematic neglect of CP\mathrm{CP}CP violation. A \ensuremath{\Phi} factory is thus shown to provide a unique tool for the study of the EPR problem
The quantum interference between the decays of entangled neutral kaons is a very powerful tool for testing the quantum coherence of the entangled kaon pair state. The studied process ϕ→KSKL→π+π−π+π−\phi\rightarrow K_SK_L\rightarrow\pi^+\pi^-\pi^+\pi^-ϕ→KS​KL​→π+π−π+π− exhibits the characteristic Einstein-Podolsky-Rosen correlations that prevent both kaons to decay into π+π−\pi^+\pi^-π+π− at the same time. The newly published result is based on data sample collected with the KLOE detector at DAΦ\PhiΦNE and corresponds to an integrated luminosity of about 1.7 fb−1^{-1}−1 , i.e. to ∼\sim∼ 1.7 ×\times× 109^99 ϕ→KSKL\phi\rightarrow K_SK_Lϕ→KS​KL​ decays. From the fit to the observed time difference distribution of the two kaon decays, the decoherence and CPT violation parameters of various phenomenological models are measured. A stringent upper limit on the branching ratio of the ϕ→KSKS,KLKL\phi \rightarrow K_S K_S , K_L K_Lϕ→KS​KS​,KL​KL​ decay is also derived. Independently, the comparison of neutral meson transition rates between flavour and CP eigenstates allows direct and model independent tests of time-reversal T and CPT symmetries to be conducted, through ratios of rates of two classes of processes: KSKL→(π±e∓ν)(3π0)K_S K_L \to (\pi^{\pm}e^{\mp}\nu)(3\pi^0)KS​KL​→(π±e∓ν)(3π0) and KSKL→(π+π−)(π±e∓ν)K_S K_L \to (\pi^{+}\pi^{-})(\pi^{\pm}e^{\mp}\nu)KS​KL​→(π+π−)(π±e∓ν). In addition to this a straightforward extension to the case of CPT symmetry is performed providing the first model independent test of CPT symmetry violation in transitions of neutral kaons.
The quantum interference between the decays of entangled neutral kaons is studied in the process ϕ→KSKL→π+π−π+π−ϕ\rightarrow K_S K_L \rightarrowπ^+π^-π^+π^-ϕ→KS​KL​→π+π−π+π−, which exhibits the characteristic Einstein--Podolsky--Rosen correlations that prevent both kaons to decay into π+π−π^+π^-π+π− at the same time. This constitutes a very powerful tool for testing at the utmost precision the quantum coherence of the entangled kaon pair state, and to search for tiny decoherence and CPT violation effects, which may be justified in a quantum gravity framework. The analysed data sample was collected with the KLOE detector at DAΦΦΦNE, the Frascati ϕϕϕ-factory, and corresponds to an integrated luminosity of about 1.7 fb−1^{-1}−1, i.e. to about 1.7×1091.7 \times 10^91.7×109 ϕ→KSKLϕ\rightarrow K_S K_Lϕ→KS​KL​ decays produced. From the fit of the observed ΔtΔtΔt distribution, being ΔtΔtΔt the difference of the kaon decay times, the decoherence and CPT violation parameters of various phenomenological models are measured with a largely improved accuracy with respect to previous analyses. The results are consistent with no deviation from quantum mechanics and CPT symmetry, while for some parameters the precision reaches the interesting level at which -- in the most optimistic scenarios -- quantum gravity effects might show up. They provide the most stringent limits up to date on the considered models.
We discuss the demise of flavour tagging due to the loss of the particle–antiparticle identity of neutral B -mesons in the Einstein–Podolsky–Rosen correlated states. Such a situation occurs in cases where the CPT operator is ill-defined, as happens, for example, in quantum gravity models with induced decoherence in the matter sector. The time evolution of the perturbed B 0 – B ¯ 0 initial state, as produced in B -factories, is sufficient to generate new two-body states. For flavour specific decays at equal times, we discuss two definite tests of the two body entanglement: (i) search for the would-be forbidden B 0 B 0 and B ¯ 0 B ¯ 0 states; (ii) deviations from the indistinguishable probability between the permuted states B ¯ 0 B 0 and B 0 B ¯ 0 .
Abstract Novel quantum phenomena have been recently discussed [1] in association to a peculiar time correlation between entangled neutral kaons produced at a ϕ-factory: the past state of the first decayed kaon, when it was still entangled before its decay, is post-tagged by the result and the time of the future observation on the other kan decay. This surprising “from future to past” effect is fully observable and leads to the unique experimental tag of the KS state, an unsolved problem since the discovery of CP violation. The first preliminary results obtained on the analysis of data collected by the KLOE experiment at the DAΦNE collider, and showing experimental evidence of this new effect are presented.