Belgrade - On the weight of entanglement 1/15 On the weight of entanglement David Edward Bruschi Department of Physics Universit¨ at des Saarlandes Germany XIII Sept. MMXIX
Belgrade - On the weight of entanglement 2/15 Gravity
Belgrade - On the weight of entanglement 2/15 Gravity Einstein gravity We know that ALL ENERGY GRAVITATES .
Belgrade - On the weight of entanglement 2/15 Gravity Einstein gravity We know that ALL ENERGY GRAVITATES . Einstein equations G µν = 8 π G R µν . c 4 These equations have been highly successful in providing many predictions. Successes Difficulties - Precession of orbits; - Rotation curves of galaxies; - Bending of light; - Nonlinearity of equations; - Black Holes; - Gravitation of quantum objects; - Penrose process; - Quantum nature of gravity; - Gravitational waves; - Fundamental or emergent theory? - Cosmology.
Belgrade - On the weight of entanglement 3/15 Gravity Einstein gravity extended We know that ALL ENERGY GRAVITATES . Semiclassical gravity � : ˆ G µν = 8 π G T µν : � c 4 ˆ T µν : stress-energy tensor for quantum field. : · : is normal ordering. Successes Problems - Fluctuations of stress energy - Takes into account (somehow) tensor big/huge; backreaction; - Curved spacetime: inconsistent - ... renormalisation procedures; - “Strange” predictions for gravitational fields of superpositions; - ...
Belgrade - On the weight of entanglement 4/15 Current research Experiments at the overlap of relativity/quantum phys. Planning There are plans to try to test the gravitational field of small quantum objects that can be found in quantum states.
Belgrade - On the weight of entanglement 4/15 Current research Experiments at the overlap of relativity/quantum phys. Planning There are plans to try to test the gravitational field of small quantum objects that can be found in quantum states. Experiments of interest One setup - Spontaneous WF collapse; - Gravitational decoherence; - Superposition of masses; - Optomechanical systems; - Space based tests; - Atom Interferometry; - More? Figure: Micius satellite CAS
Belgrade - On the weight of entanglement 5/15 Current research Quantum Information (QI) and Thermodynamics (QT) Quantum Information Allows us to connect concepts such as entropy and quantum correlations. Quantum Thermodynamics QT investigates thermodynamics far from thermodynamic limit. Regime of interest: where fluctuations around the mean are important;
Belgrade - On the weight of entanglement 5/15 Current research Quantum Information (QI) and Thermodynamics (QT) Quantum Information Allows us to connect concepts such as entropy and quantum correlations. Quantum Thermodynamics QT investigates thermodynamics far from thermodynamic limit. Regime of interest: where fluctuations around the mean are important; Features - Small (quantum) constituents; - Few (e.g ONE) systems; - Concepts of energy and work not unique; - Fluctuation relations; - ...
Belgrade - On the weight of entanglement 5/15 Current research Quantum Information (QI) and Thermodynamics (QT) Quantum Information Allows us to connect concepts such as entropy and quantum correlations. Quantum Thermodynamics QT investigates thermodynamics far from thermodynamic limit. Regime of interest: where fluctuations around the mean are important; Features Applications - Quantum chemistry; - Small (quantum) constituents; - Quantum refrigerators; - Few (e.g ONE) systems; - Concepts of energy and work - Fundamental physics; not unique; - Connections to Information - Fluctuation relations; Theory; - ... - ...
Belgrade - On the weight of entanglement 6/15 Current research Quantum Thermodynamics (QT) Resources ρ . Unitaries ˆ U . Then, exists ˆ ρ p = ˆ ρ ˆ U † State ˆ U p : ˆ p ˆ U p . And, ˆ ρ p is “unique”.
Belgrade - On the weight of entanglement 6/15 Current research Quantum Thermodynamics (QT) Resources ρ . Unitaries ˆ U . Then, exists ˆ ρ p = ˆ ρ ˆ U † State ˆ U p : ˆ p ˆ U p . And, ˆ ρ p is “unique”. Features E = H E = H W ≤ Δ F ^ ρ U p E 0 E 0 ρ p
Belgrade - On the weight of entanglement 6/15 Current research Quantum Thermodynamics (QT) Resources ρ . Unitaries ˆ U . Then, exists ˆ ρ p = ˆ ρ ˆ U † State ˆ U p : ˆ p ˆ U p . And, ˆ ρ p is “unique”. Features Applications (PRE 91, 032118 (2015)) E = H E = H - Correlations I AB give work ( W ) ⇔ work ( W ) gives correlations I AB . W ≤ Δ F ^ ρ U p E 0 E 0 ρ p
Belgrade - On the weight of entanglement 6/15 Current research Quantum Thermodynamics (QT) Resources ρ . Unitaries ˆ U . Then, exists ˆ ρ p = ˆ ρ ˆ U † State ˆ U p : ˆ p ˆ U p . And, ˆ ρ p is “unique”. Features Applications (PRE 91, 032118 (2015)) E = H E = H - Correlations I AB give work ( W ) ⇔ work ( W ) gives correlations I AB . - Bound on correlations (work): W ≤ Δ F ^ ρ U I AB ≤ β W . p E 0 E 0 ρ p
Belgrade - On the weight of entanglement 6/15 Current research Quantum Thermodynamics (QT) Resources ρ . Unitaries ˆ U . Then, exists ˆ ρ p = ˆ ρ ˆ U † State ˆ U p : ˆ p ˆ U p . And, ˆ ρ p is “unique”. Features Applications (PRE 91, 032118 (2015)) E = H E = H - Correlations I AB give work ( W ) ⇔ work ( W ) gives correlations I AB . - Bound on correlations (work): W ≤ Δ F ^ ρ U I AB ≤ β W . p E 0 E 0 - Conclusion: Correlations must ρ p “carry energy”.
Belgrade - On the weight of entanglement 7/15 Current research Role of corrleations On the weight of entanglement (Physics Letters B 54, 182-186 (2016)) Employing semiclassical gravity: entanglement has a weight . ∝ β , where G (1) is correction to flat Einstein tensor. We find G (1) β Backreaction Backreaction Ψ = 1 ⎡ ⎤ 01 LR + 10 LR ⎣ ⎦ 2 L R ρ = α 01 01 + (1 − α ) 10 10 + β 01 10 + β 10 ⎡ 01 ⎤ ⎣ ⎦ Backreaction Backreaction
Belgrade - On the weight of entanglement 8/15 Connecting fields A gedankenexperiment The weight of a passive state U Tr ( ˆ ρ ˆ → ˆ ρ p , H 0 ˆ ρ p ) = E 0 .
Belgrade - On the weight of entanglement 8/15 Connecting fields A gedankenexperiment The weight of a passive state U Tr ( ˆ ρ ˆ → ˆ ρ p , H 0 ˆ ρ p ) = E 0 . Work from passive states ρ p ρ p ρ p ρ p
Belgrade - On the weight of entanglement 8/15 Connecting fields A gedankenexperiment The weight of a passive state U Tr ( ˆ ρ ˆ → ˆ ρ p , H 0 ˆ ρ p ) = E 0 . Work from passive states What happens - Two passive states; ρ p ρ p ρ p ρ p
Belgrade - On the weight of entanglement 8/15 Connecting fields A gedankenexperiment The weight of a passive state U Tr ( ˆ ρ ˆ → ˆ ρ p , H 0 ˆ ρ p ) = E 0 . Work from passive states What happens - Two passive states; - Same state (e.g., temperature); ρ p ρ p ρ p ρ p
Belgrade - On the weight of entanglement 8/15 Connecting fields A gedankenexperiment The weight of a passive state U Tr ( ˆ ρ ˆ → ˆ ρ p , H 0 ˆ ρ p ) = E 0 . Work from passive states What happens - Two passive states; - Same state (e.g., temperature); ρ p - Attract eachother; ρ p ρ p ρ p
Belgrade - On the weight of entanglement 8/15 Connecting fields A gedankenexperiment The weight of a passive state U Tr ( ˆ ρ ˆ → ˆ ρ p , H 0 ˆ ρ p ) = E 0 . Work from passive states What happens - Two passive states; - Same state (e.g., temperature); ρ p - Attract eachother; ρ p - Cannot extract energy from state with unitaries on both; ρ p ρ p
Belgrade - On the weight of entanglement 8/15 Connecting fields A gedankenexperiment The weight of a passive state U Tr ( ˆ ρ ˆ → ˆ ρ p , H 0 ˆ ρ p ) = E 0 . Work from passive states What happens - Two passive states; - Same state (e.g., temperature); ρ p - Attract eachother; ρ p - Cannot extract energy from state with unitaries on both; - System interacts gravitationally; ρ p ρ p
Belgrade - On the weight of entanglement 8/15 Connecting fields A gedankenexperiment The weight of a passive state U Tr ( ˆ ρ ˆ → ˆ ρ p , H 0 ˆ ρ p ) = E 0 . Work from passive states What happens - Two passive states; - Same state (e.g., temperature); ρ p - Attract eachother; ρ p - Cannot extract energy from state with unitaries on both; - System interacts gravitationally; - grav. inter.=employable energy; ρ p ρ p
Belgrade - On the weight of entanglement 8/15 Connecting fields A gedankenexperiment The weight of a passive state U Tr ( ˆ ρ ˆ → ˆ ρ p , H 0 ˆ ρ p ) = E 0 . Work from passive states What happens - Two passive states; - Same state (e.g., temperature); ρ p - Attract eachother; ρ p - Cannot extract energy from state with unitaries on both; - System interacts gravitationally; - grav. inter.=employable energy; ρ p ρ p - Employable energy= work;
Belgrade - On the weight of entanglement 8/15 Connecting fields A gedankenexperiment The weight of a passive state U Tr ( ˆ ρ ˆ → ˆ ρ p , H 0 ˆ ρ p ) = E 0 . Work from passive states What happens - Two passive states; - Same state (e.g., temperature); ρ p - Attract eachother; ρ p - Cannot extract energy from state with unitaries on both; - System interacts gravitationally; - grav. inter.=employable energy; ρ p ρ p - Employable energy= work; - Something is wrong; - (Also if GR dof in passive state);
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