= Bose--Marletto--Vedral experiment
{c}
The <Bose--Marletto--Vedral experiment> is a family of proposals to test <gravitationally induced entanglement> between initially independent <masses>. <Sougato Bose> and collaborators, and independently <Chiara Marletto> and <Vlatko Vedral>, described the idea in 2017. Each <mass> occupies two distinguishable spatial branches, encoding a <qubit>. Different branch separations give different <Newtonian gravitational potential energies> and hence different <relative phases>.<A Spin Entanglement Witness for Quantum Gravity by Sougato Bose and others>[Figure 1(a), equations (1)–(3), spatial branches and gravitational phases]{ref}
For stationary branches at separations $r_{ab}$ held for duration $\tau$, the ideal model gives
$$
|\psi\rangle=\frac12\sum_{a,b=0}^1e^{i\phi_{ab}}|ab\rangle,\qquad \phi_{ab}=\frac{Gm_1m_2\tau}{\hbar r_{ab}}.
$$
The positive phase follows from negative <Newtonian gravitational potential energy> in $e^{-iV\tau/\hbar}$. A direct algebraic check separates local rephasing from genuine <entanglement>: the determinant of the two-by-two coefficient matrix vanishes exactly when
$$
\Delta\phi=\phi_{00}+\phi_{11}-\phi_{01}-\phi_{10}=0\pmod{2\pi}.
$$
Thus a large common <phase> alone is insufficient. For this ideal <pure state>, the <concurrence> is $|\sin(\Delta\phi/2)|$, reaching one at an odd multiple of $\pi$.
The spin-based proposal uses two <Stern-Gerlach interferometers>: embedded <spins> label the spatial branches, the <masses> interact, and <recombination> transfers the branch information into measurable <spin> <correlations>. Measurements in different <spin> bases supply an <entanglement witness>. Unwanted <electromagnetic interactions> and <quantum decoherence> must be controlled for the gravitational interpretation.<A Spin Entanglement Witness for Quantum Gravity by Sougato Bose and others>[Figure 1(b), pp. 2–3, spin-dependent splitting, recombination and correlation readout]{ref}
The mediator inference assumes initially unentangled systems, local coupling through a mediator, and no other entangling interaction. Under those assumptions, a mediator described only by commuting <observables> cannot generate the observed <entanglement>; at least two incompatible <observables> are required. This is an indirect test of nonclassical mediation, without selecting a complete high-energy theory of <quantum gravity>.<Gravitationally-induced entanglement between two massive particles is sufficient evidence of quantum effects in gravity by Chiara Marletto and Vlatko Vedral>[Pages 2–3, mediator argument and locality assumptions]{ref}
Back to article page
