Firewall vs. Scrambling 2 1 Review of Firewall argument Review of - - PowerPoint PPT Presentation
Firewall vs. Scrambling 2 1 Review of Firewall argument Review of Hayden-Preskill 4 3 State-independent interior operators Interior operator from HP recovery 6 5 Resolution of the puzzle Effect of infalling observer 7 Discussions Beni
Review of Firewall argument Review of Hayden-Preskill State-independent interior operators Effect of infalling observer Resolution of the puzzle Discussions
Interior operator from HP recovery
State-independent interior operators Effect of infalling observer Resolution of the puzzle Discussions
Interior operator from HP recovery
Review of Firewall argument Review of Hayden-Preskill
Review of Firewall argument Review of Hayden-Preskill State-independent interior operators Effect of infalling observer Resolution of the puzzle Discussions
Interior operator from HP recovery
Review of Firewall argument Review of Hayden-Preskill State-independent interior operators Discussions
Interior operator from HP recovery
Effect of infalling observer Resolution of the puzzle
Review of Firewall argument Review of Hayden-Preskill State-independent interior operators Effect of infalling observer Resolution of the puzzle Discussions
Interior operator from HP recovery
(Each phrase will be defined more precisely later)
involving the distant radiation ever. It “avoids” previous no-go results. (Each phrase will be defined more precisely later)
involving the distant radiation ever. It “avoids” previous no-go results.
and disentangles the outgoing mode from the early radiation, no matter how she falls. (Each phrase will be defined more precisely later)
involving the distant radiation ever. It “avoids” previous no-go results.
and disentangles the outgoing mode from the early radiation, no matter how she falls. (Each phrase will be defined more precisely later)
experience cannot be influenced by any operation on the early radiation.
Review of Firewall argument Review of Hayden-Preskill State-independent interior operators Effect of infalling observer Resolution of the puzzle Discussions
Interior operator from HP recovery
From the outside (Bob)
(a)
C : Remaining black hole D : Outgoing mode R : Early radiation
e r = 2GM + ✏ c ly r > 3GM
From the outside (Bob)
(a)
I(D, R) ⇡ max I(C, D) ⇡ 0 (
“old” black hole
C : Remaining black hole D : Outgoing mode R : Early radiation
e r = 2GM + ✏ c ly r > 3GM
From the outside (Bob)
(a)
From the inside (Alice)
(b)
I(D, R) ⇡ max I(C, D) ⇡ 0 (
“old” black hole
C : Remaining black hole D : Outgoing mode R : Early radiation
e r = 2GM + ✏ c ly r > 3GM
From the outside (Bob)
(a)
From the inside (Alice)
(b)
: Rindler modes
I(D, ¯ D) ⇡ max
D ¯ D
I(D, R) ⇡ max I(C, D) ⇡ 0 (
“old” black hole
C : Remaining black hole D : Outgoing mode R : Early radiation
e r = 2GM + ✏ c ly r > 3GM
From the outside (Bob)
(a)
From the inside (Alice)
(b)
: Rindler modes
I(D, ¯ D) ⇡ max
D ¯ D
I(D, R) ⇡ max I(C, D) ⇡ 0 (
“old” black hole
C : Remaining black hole D : Outgoing mode R : Early radiation
e r = 2GM + ✏ c ly r > 3GM
From the outside (Bob)
(a)
From the inside (Alice)
(b)
: Rindler modes
I(D, ¯ D) ⇡ max
D ¯ D
I(D, R) ⇡ max I(C, D) ⇡ 0 (
“old” black hole
C : Remaining black hole D : Outgoing mode R : Early radiation
e r = 2GM + ✏ c ly r > 3GM I(D, ¯ D) ≈ 0 (
firewall?
From the outside (Bob)
(a)
From the inside (Alice)
(b)
: Rindler modes
I(D, ¯ D) ⇡ max
D ¯ D
I(D, R) ⇡ max I(C, D) ⇡ 0 (
“old” black hole
C : Remaining black hole D : Outgoing mode R : Early radiation
e r = 2GM + ✏ c ly r > 3GM I(D, ¯ D) ≈ 0 (
firewall? Monogamy of entanglement
(a)
(a)
Place R at a far distant universe. “A = RB” approach, “ER = EPR” approach (This is how quantum gravity works?)
(a)
Place R at a far distant universe. “A = RB” approach, “ER = EPR” approach (This is how quantum gravity works?)
Two-sided AdS black hole
(a)
Place R at a far distant universe. “A = RB” approach, “ER = EPR” approach (This is how quantum gravity works?)
Two-sided AdS black hole
Review of Firewall argument Review of Hayden-Preskill State-independent interior operators Effect of infalling observer Resolution of the puzzle Discussions
Interior operator from HP recovery
IFQ lecture (4th week)
EPR
C : Remaining BH D : Late radiation R : Early radiation
radiation and reconstruct the original state.
EPR
C : Remaining BH D : Late radiation R : Early radiation
radiation and reconstruct the original state.
V : recovery unitary “Black hole as mirrors” (Hayden-Preskill)
A : input C : remaining BH D : late radiation R : early radiation
EPR
existence of V. (2015)
hOA(0)OD(t)O†
A(0)O† D(t)i ⌘ 1
d Tr
AU †O† DU
C : remaining BH D : late radiation R : early radiation
EPR
existence of V. (2015)
hOA(0)OD(t)O†
A(0)O† D(t)i ⌘ 1
d Tr
AU †O† DU
C : remaining BH D : late radiation R : early radiation
2I(2)(A0,RD) = Z dOAdOD hOA(0)OD(t)O†
A(0)O† D(t)i
“state representation” of U
EPR EPR
EPR
2I(2)(A0,RD) = Z dOAdOD hOA(0)OD(t)O†
A(0)O† D(t)i
EPR EPR
⇡
EPR EPR
.
A : input C : remaining BH D : late radiation R : early radiation “partner operator“
existence of V. (2015)
hOA(0)OD(t)O†
A(0)O† D(t)i ⌘ 1
d Tr
AU †O† DU
EPR EPR
D ¯ D
“Decoding protocol”
projection
D ¯ D
EPR EPR
D ¯ D
“Decoding protocol”
projection
“Traversable wormhole”
D ¯ D
EPR EPR
D ¯ D
“Decoding protocol”
projection
Review of Firewall argument Review of Hayden-Preskill State-independent interior operators Effect of infalling observer Resolution of the puzzle Discussions
Interior operator from HP recovery
(BY 2018)
EPR EPR
⇡
EPR EPR
C : Remaining BH D : Outgoing mode R : Radiation
EPR D C R EPR D C R
=
Split R into AB
C : Remaining BH D : Outgoing mode R : Radiation
EPR D C R EPR D C R
= A B
Reconstruct on CA.
C : Remaining BH D : Outgoing mode R : Radiation
EPR D C R D
= A B Split R into AB EPR C R
A B
Reconstruct on CA.
C : Remaining BH D : Outgoing mode R : Radiation
EPR D C R D
= A B Split R into AB EPR C R
A B
Rotate the figure…
e =
C : Remaining BH D : Outgoing mode R : Radiation
e =
AMPS Reconstruct D (outgoing) from C (remaining BH) and A (early mode) Reconstruct A (early mode) from B (initial BH) and D (outgoing) HP
C : Remaining BH D : Outgoing mode R : Radiation
e =
C : Remaining BH D : The zone R : Radiation
e =
(I ⌦ K)|EPRi
C : Remaining BH D : The zone R : Radiation
Alice Bob
If Alice takes A, then Alice possesses the EPR pair If Alice didn’t take A, then Bob possesses the EPR pair AB : Radiation (R) D : outgoing mode C : remaining black hole
Alice Bob
If Alice takes A, then Alice possesses the EPR pair If Alice didn’t take A, then Bob possesses the EPR pair AB : Radiation (R) D : outgoing mode C : remaining black hole
Alice Bob
If Alice takes A, then Alice possesses the EPR pair If Alice didn’t take A, then Bob possesses the EPR pair AB : Radiation (R) D : outgoing mode C : remaining black hole
Review of Firewall argument Review of Hayden-Preskill State-independent interior operators Effect of infalling observer Resolution of the puzzle Discussions
Interior operator from HP recovery
(BY 2018) (BY 2019)
EPR
(I ⌦ K)|EPRi
Generic two-sided AdS = K is arbitrary, BH not evaporating
EPR
At : propagating modes Bt : modes at stretched horizo
boundary modes
Generic two-sided AdS = K is arbitrary, BH not evaporating
EPR
(a)
EPR SWAP Prepare ancillary EPR and apply SWAP
At : propagating modes Bt : modes at stretched horizo
boundary modes
Generic two-sided AdS = K is arbitrary, BH not evaporating
EPR
(a)
EPR SWAP Prepare ancillary EPR and apply SWAP
EPR
At : propagating modes Bt : modes at stretched horizo
boundary modes
Generic two-sided AdS = K is arbitrary, BH not evaporating
EPR
(a)
EPR SWAP Prepare ancillary EPR and apply SWAP
without ever accessing R EPR
At : propagating modes Bt : modes at stretched horizo
boundary modes
Generic two-sided AdS = K is arbitrary, BH not evaporating
EPR
EPR
EPR
EPR
Rt : high-energy radiation At : modes on the zone Bt : modes at stretched horizon
Rt : high-energy radiation At : modes on the zone Bt : modes at stretched horizon
BH
e ≈ 2SBH-dimensional
in Hcode.
Coarse-grained Hilbert space , determined by M, J, Q…
in Hcode.: wavefunctions with the same classical geometry
“S-qubit” toy model
BH
e ≈ 2SBH-dimensional
in Hcode.
Coarse-grained Hilbert space , determined by M, J, Q…
in Hcode.: wavefunctions with the same classical geometry
“S-qubit” toy model
thermalization time scrambling time
er ≈ rS log rS er ≈ rS
BH
e ≈ 2SBH-dimensional
in Hcode.
Coarse-grained Hilbert space , determined by M, J, Q…
in Hcode.: wavefunctions with the same classical geometry
“S-qubit” toy model
Review of Firewall argument Review of Hayden-Preskill State-independent interior operators Effect of infalling observer Resolution of the puzzle Discussions
Interior operator from HP recovery
D ˜ D
M becomes gravitational shockwave. Bob’s entanglement is disturbed. Due to decay of OTOCs.
D ˜ D
M becomes gravitational shockwave. Bob’s entanglement is disturbed. Due to decay of OTOCs.
D ˜ D
M becomes gravitational shockwave. Bob’s entanglement is disturbed. Due to decay of OTOCs.
) =
EPR
Small OTOC
I(C, D) ⇡ max
D is not entangled with R “Proof”
D ˜ D
M becomes gravitational shockwave. Bob’s entanglement is disturbed. Due to decay of OTOCs.
) =
EPR
Small OTOC
I(C, D) ⇡ max
D is not entangled with R “Proof”
D ˜ D
I(2)(D, EC) ⇡ max
I(2)(D, EC) ⇡ max
falls in !
I(2)(D, EC) ⇡ max
falls in !
D
˜ D
without Alice
D
˜ D
without Alice
D D
with Alice
D
˜ D
without Alice
D D
with Alice
by RHS. D
D
˜ D
without Alice
D D
with Alice
by RHS. D
˜ D Resolution of non-locality problem
Review of Firewall argument Review of Hayden-Preskill State-independent interior operators Effect of infalling observer Resolution of the puzzle Discussions
Interior operator from HP recovery
early radiation
mode
early radiation
mode
entangled
early radiation
mode
entangled BH
entangled
early radiation
mode
entangled BH
entangled firewall ?
BH early radiation
mode
entangled
entangled
BH early radiation
mode
entangled
entangled same ?
BH early radiation
mode
entangled
entangled same ? shockwave ?
BH early radiation
mode
entangled
BH early radiation
mode
entangled entangled Alice
Perform the Hayden-Preskill recovery !
EPR EPR projection
D ¯ D
Perform the Hayden-Preskill recovery !
EPR EPR projection
D ¯ D
Perform the Hayden-Preskill recovery !
EPR EPR projection
D ¯ D
Perform the Hayden-Preskill recovery !
https://doi.org/10.1038/s41586-019-0952-6
Verified quantum information scrambling
. Yao2,4 & C. Monroe1,5 Quantum scrambling is the dispersal of local information into many-body quantum entanglements and correlations distributed throughout an entire system. This concept accompanies the dynamics of thermalization in closed quantum systems, and has recently emerged as a powerful tool for characterizing chaos in black holes1–4. However, the direct experimental measurement
complexity of ergodic many-body entangled states. One way to characterize quantum scrambling is to measure an out-of-time-
leads to their decay, OTOCs do not generally discriminate between quantum scrambling and ordinary decoherence. Here we implement a quantum circuit that provides a positive test for the scrambling features of a given unitary process5,6. This approach conditionally teleports a quantum state through the circuit, providing an unambiguous test for whether scrambling has occurred, while simultaneously measuring an OTOC. We engineer quantum scrambling processes through a tunable three-qubit unitary
per cent, and enable us to experimentally bound the scrambling- induced decay of the corresponding OTOC measurement. The dynamics of strongly interacting quantum systems lead to the For example, non-unitary time-evolution arising from depolarization
the absence of quantum scrambling. A similar decay can also originate from even slight mismatches between the purported forward and back- wards time-evolution of W t ˆ ( ) (refs 6,16 and 24). Although full quantum tomography can in principle distinguish scrambling from decoherence and experimental noise, this requires a number of measurements that scales exponentially with system size and is thus impractical. In this work, we overcome this challenge and implement a quantum teleporation protocol that robustly distinguishes information scram- bling from both decoherence and experimental noise5,6. Using this pro- tocol, we demonstrate verifiable information scrambling in a family
scrambling observed in the experiments. The intuition behind our approach lies in a re-interpretation of the black-hole information paradox9,10, under the assumption that the dynamics of the black hole can be modelled as a random unitary oper- ation U ˆ (Fig. 1). Schematically, an observer (Alice) throws a secret quantum state into a black hole, while an outside observer (Bob) attempts to reconstruct this state by collecting the Hawking radiation emitted at a later time1,10. An explicit decoding protocol has been recently proposed5,6, which enables Bob to decode Alice’s state using a quantum memory, an ancil-
Experiment of HP recovery protocol Nature 567 (7746), 61
https://doi.org/10.1038/s41586-019-0952-6
Verified quantum information scrambling
. Yao2,4 & C. Monroe1,5 Quantum scrambling is the dispersal of local information into many-body quantum entanglements and correlations distributed throughout an entire system. This concept accompanies the dynamics of thermalization in closed quantum systems, and has recently emerged as a powerful tool for characterizing chaos in black holes1–4. However, the direct experimental measurement
complexity of ergodic many-body entangled states. One way to characterize quantum scrambling is to measure an out-of-time-
leads to their decay, OTOCs do not generally discriminate between quantum scrambling and ordinary decoherence. Here we implement a quantum circuit that provides a positive test for the scrambling features of a given unitary process5,6. This approach conditionally teleports a quantum state through the circuit, providing an unambiguous test for whether scrambling has occurred, while simultaneously measuring an OTOC. We engineer quantum scrambling processes through a tunable three-qubit unitary
per cent, and enable us to experimentally bound the scrambling- induced decay of the corresponding OTOC measurement. The dynamics of strongly interacting quantum systems lead to the For example, non-unitary time-evolution arising from depolarization
the absence of quantum scrambling. A similar decay can also originate from even slight mismatches between the purported forward and back- wards time-evolution of W t ˆ ( ) (refs 6,16 and 24). Although full quantum tomography can in principle distinguish scrambling from decoherence and experimental noise, this requires a number of measurements that scales exponentially with system size and is thus impractical. In this work, we overcome this challenge and implement a quantum teleporation protocol that robustly distinguishes information scram- bling from both decoherence and experimental noise5,6. Using this pro- tocol, we demonstrate verifiable information scrambling in a family
scrambling observed in the experiments. The intuition behind our approach lies in a re-interpretation of the black-hole information paradox9,10, under the assumption that the dynamics of the black hole can be modelled as a random unitary oper- ation U ˆ (Fig. 1). Schematically, an observer (Alice) throws a secret quantum state into a black hole, while an outside observer (Bob) attempts to reconstruct this state by collecting the Hawking radiation emitted at a later time1,10. An explicit decoding protocol has been recently proposed5,6, which enables Bob to decode Alice’s state using a quantum memory, an ancil-
Experiment of HP recovery protocol Experiment of firewall ! Nature 567 (7746), 61
Review of Firewall argument Review of Hayden-Preskill State-independent interior operators Effect of infalling observer Resolution of the puzzle Discussions
Interior operator from HP recovery
cannot see the EPR pair?
a) (b)
cannot see the EPR pair?
a) (b)
Alice see very close to the singularity.
ts D
cannot see the EPR pair?
a) (b)
Alice see very close to the singularity.
ts D
The quality of the EPR pair becomes bad ? y T =
1 2πρ
To have small , we need s ∆t ' rS log rS '
where ρ
cannot see the EPR pair?
a) (b)
Alice see very close to the singularity.
ts D
The quality of the EPR pair becomes bad ? y T =
1 2πρ
To have small , we need s ∆t ' rS log rS '
where ρ
Even if they are not entangled, it won’t create a firewall (low energy)?
a) (b)
interior operator in the entanglement wedge?
The shift is in the opposite direction!
The shift is in the opposite direction! black hole horizon cosmological horizon N S
r = ∞
singularity
The shift is in the opposite direction! Alice cannot really cross the de Sitter horizon? black hole horizon cosmological horizon N S
r = ∞
singularity
2015 Chaos in quantum channel Hosur, Qi, Roberts, BY 2015 Chaos and complexity by design Roberts, BY 2017 Efficient decoding for Hayden-Preskill protocol Kitaev, BY 2018 Verified quantum information scrambling Landsman, BY et al 2018 Soft mode and interior operators in Hayden-Preskill thought experiment, BY 2019 Firewalls vs. scrambling, BY Relevant work 2012 Black hole entanglement and quantum error-correction, Verlinde-Verlinde
same states EPR
same states EPR
Alice jumps into a black hole and returns to the outside with the interior mode ?
D
same states EPR
U † Alice jumps into a black hole and returns to the outside with the interior mode ?
D