Partial Collapse and Uncollapse of a Wavefunction: Theory and Experiments (What Is “Inside” Collapse) Alexander Korotkov EE Dept

UCR, 5/06/10 Partial collapse and uncollapse of a wavefunction: theory and experiments (what is “inside” collapse) Alexander Korotkov EE dept. (& Physics), University of California, Riverside

Outline: • Bayesian formalism for quantum measurement • Persistent Rabi oscillations (+ expt.) • Wavefunction uncollapse (+ expts.)

Acknowledgements: Funding: Theory: R. Ruskov, A. Jordan, K. Keane Expt.: UCSB (J. Martinis, N. Katz et al.), Saclay (D. Esteve, P. Bertet et al.) Alexander Korotkov University of California, Riverside Quantum mechanics is weird…

Niels Bohr: “If you are not confused by quantum physics then you haven’t really understood it”

Richard Feynman: “I think I can safely say that nobody understands quantum mechanics”

Weirdest part is quantum measurement

Alexander Korotkov University of California, Riverside Quantum mechanics = Schrödinger equation (evolution) + collapse postulate (measurement)

2 1) Probability of measurement result pr =||〈ψψr 〉 | 2) Wavefunction after measurement = ψ r • State collapse follows from common sense • Does not follow from Schrödinger Eq. (contradicts)

What is “inside” collapse? What if collapse is stopped half-way?

Alexander Korotkov University of California, Riverside What is the evolution due to measurement? (What is “inside” collapse?) • controversial for last 80 years, many wrong answers, many correct answers • solid-state systems are more natural to answer this question Various approaches to non-projective (weak, continuous, partial, generalized, etc.) quantum measurements Names: Davies, Kraus, Holevo, Mensky, Caves, Knight, Plenio, Walls, Carmichael, Milburn, Wiseman, Gisin, Percival, Belavkin, etc. (very incomplete list)

Key words: POVM, restricted path integral, quantum trajectories, quantum filtering, quantum jumps, stochastic master equation, etc.

Our limited scope: solid-state qubit (simplest system, experimental setups) detector I(t), noise S Alexander Korotkov University of California, Riverside “Typical” setup: double-quantum-dot (DQD) qubit + quantum point contact (QPC) detector Gurvitz, 1997 |1Ò |1Ò H = H + H + H H |2Ò |2Ò QB DET INT e ε |2Ò |1Ò HH=+σ σ QB 2 ZX I(t) ΔI It()=+ I zt () +ξ () t I(t) 0 2 const + signal + noise

Two levels of average detector current: I1 for qubit state |1〉, I2 for |2〉

Response: ΔI= I1 –I2 Detector noise: white, spectral density SI For low-transparency QPC

†† †† HDET =++∑∑∑lrl Eaall l+ Eaarrr ,r Taa()rl aa l r †††† SeI= 2 HINT =Δ∑lr, T()() cc11 − cc 22 aarrll + aa I

5/38 Alexander Korotkov University of California, Riverside Bayesian formalism for DQD-QPC system

Qubit evolution due to measurement (quantum back-action): HQB =0 ρ ()t |1Ò ψ ()tt= αβ ()|1〉+ ()|2 t 〉 or ij H e 1) |α(t)|2 and |β(t)|2 evolve as probabilities, |2Ò i.e. according to the Bayes rule (same for ρii) 2) phases of α(t) and β(t) do not change I(t) 1/2 (no dephasing!), ρij /(ρii ρjj) = const (A.K., 1998) 1 τ Bayes rule (1763, Laplace-1812): Itdt() τ ∫0 posterior prior measured probab. likelihood probability I1 I2 PA()(res|)ii P A PA(|res)i = So simple because: ∑k P(APkk ) (res | A ) 1) no entaglement at large QPC voltage 2) QPC happens to be an ideal detector 3) no Hamiltonian evolution of the qubit

Alexander Korotkov University of California, Riverside Bayesian formalism for a single qubit Vg V H e • Time derivative of the quantum Bayes rule I(t) • Add unitary evolution of the qubit I(t) 2e • Add decoherence γ (if any)

•• 2ΔI ρρ11=- 22 =- ρρρ2ImHI12 + 11 22 []It()- 0 SI • ΔI ρ 12 =+ ρiiH ρερ 12 ()()[]11 - 22+ 12 11 - 22 It() --I0γ ρ 12 SI

2 (A.K., 1998) γ =-ΓΔ()/4,ISI Γ−ensemble decoherence γ = 0 for QPC detector Averaging over result I(t) leads to conventional master equation with Γ Evolution of qubit wavefunction can be monitored if γ=0 (quantum-limited) Natural generalizations: • add classical back-action • entangled qubits Alexander Korotkov University of California, Riverside Assumptions needed for the Bayesian formalism: • Detector voltage is much larger than the qubit energies involved eV >> ÑΩ, eV >> ÑΓ, Ñ/eV << (1/Ω,1/Γ), Ω=(4H2+ε2)1/2 (no coherence in the detector, classical output, Markovian approximation)

• Simpler if weak response, |ΔI | << I0, (coupling C ~ Γ/Ω is arbitrary) Derivations: 1) “logical”: via correspondence principle and comparison with decoherence approach (A.K., 1998) 2) “microscopic”: Schr. eq. + collapse of the detector (A.K., 2000) ρ n()t ij nt()k classical qubit detector pointer information quantum frequent n – number of electrons interaction quantum collapse passed through detector 3) from “quantum trajectory” formalism developed for quantum optics (Goan-Milburn, 2001; also: Wiseman, Sun, Oxtoby, etc.) 4) from POVM formalism (Jordan-A.K., 2006) 5) from Keldysh formalism (Wei-Nazarov, 2007) Alexander Korotkov University of California, Riverside Why not just use Schrödinger equation for the whole system?

qubit

detector information Impossible in principle!

Technical reason: Outgoing information (measurement result) makes it an open system Philosophical reason: Random measurement result, but deterministic Schrödinger equation Einstein: God does not play dice Heisenberg: unavoidable quantum-classical boundary Alexander Korotkov University of California, Riverside Quantum limit for ensemble decoherence 2 “measurement time” (S/N=1) Γ = (ΔI) /4SI + γ 2 τ m =Δ2/()SI I ensemble single-qubit decoherence rate decoherence 1 Γτ m ≥ ~ information flow [bit/s] 2 A.K., 1998, 2000 S. Pilgram et al., 2002 2 γ ≥ 0 ⇒ Γ ≥ (ΔI) /4SI A. Clerk et al., 2002 D. Averin, 2000,2003 γ ()/4ΔIS2 η =-1 = I detector ideality (quantum efficiency) ΓΓ η ≤ 100%

Translated into energy sensitivity: (ε ε )1/2 ≥ =/2 Danilov, Likharev, O BA Zorin, 1983 εO, εBA: sensitivities [J/Hz] limited by output noise and back-action Known since 1980s (Caves, Clarke, Likharev, Zorin, Vorontsov, Khalili, etc.) 2 1/2 2 2 (εO εBA - εO,BA ) ≥ =/2 ⇔ Γ ≥ (ΔI) /4SI + K SI/4 Quantum limits for measurement are due to quantum (informational) back-action 10/38 Alexander Korotkov University of California, Riverside POVM vs. Bayesian formalism

General quantum measurement (POVM formalism) (Nielsen-Chuang, p. 85,100): † Measurement (Kraus) operator M ψ MMρ r ρ → rr M (any linear operator in H.S.) : ψ → or † r ||Mrψ || Tr(MMrrρ ) 2 † Probability : PMrr=||ψ || or PMMrrr= Tr(ρ ) † (People often prefer linear evolution Completeness : ∑r MMrr= 1 and non-normalized states)

• POVM is essentially a projective measurement in an extended Hilbert space • Easy to derive: interaction with ancilla + projective measurement of ancilla • For extra decoherence: incoherent sum over subsets of results † Relation between POVM and decomposition MUMMrrrr= quantum Bayesian formalism: unitary Bayes Mathematically POVM and quantum Bayes are almost equivalent We focus not on the mathematical structures, but on particular setups and experimental consequences

Alexander Korotkov University of California, Riverside Can we verify the Bayesian formalism experimentally?

Direct way:

partial control projective prepare measur. (rotation) measur.

A.K.,1998

However, difficult: bandwidth, control, efficiency (expt. realized only for supercond. phase qubits)

Tricks are needed for real experiments (proposals 1999-2010)

Alexander Korotkov University of California, Riverside Non-decaying (persistent) Rabi oscillations excited - Relaxes to the ground state if left alone (low-T) left right - Becomes fully mixed if coupled to a high-T (non-equilibrium) environment ground - Oscillates persistently between left and right z if (weakly) measured continuously (measure left-right) to verify: stop& check z 1.0 |left〉 ρ11 0.5 |e〉 ••• |g〉 Reρ11 |right〉 0.0 Imρ11 -0.5 0 5 10 15 20 25 30 time A.K., PRB-1999 Direct experiment is difficult

Alexander Korotkov University of California, Riverside Indirect experiment: spectrum

of persistent Rabi oscillations A.K., LT’1999 C A.K.-Averin, 2000 qubit detector ΔI I(t) It()=+ I0 zt () +ξ () t z is Bloch 2 coordinate 12 (const + signal + noise) C=13 10 Ω =2H SI (ω) amplifier noise ﬂ higher pedestal, 1 0 8 10 2 poor quantum efficiency, )/S CIHS=Δ()/ I ηÜ1

ω 6 0

( but the peak is the same!!! I 012ω/Ω S 4 integral under the peak ‹ variance ‚z2Ú 3 2 1 How to distinguish experimentally 0 0.3 0.00.51.01.52.0 persistent from non-persistent? Easy! ω/Ω Ω - Rabi frequency perfect Rabi oscillations: ·z2Ò=·cos2Ò=1/2 peak-to-pedestal ratio = 4η≤4 imperfect (non-persistent): ·z2ÒÜ1/2 ΩΔ22()I Γ quantum (Bayesian) result: ·z2Ò =1 (!!!) SS()ω =+ I 0 ()ω 22222−Ω +Γ ω (demonstrated in Saclay expt.) Alexander Korotkov University of California, Riverside z |left〉 How to understand ·z2Ò =1? |e〉 ••• |g〉 qubit |right〉 ΔI It()=+ I0 zt () +ξ () t I(t) 2 detector First way (mathematical) We actually measure operator: z →σz (What does it mean? 2 2 Difficult to say…) z →σz =1 Second way (Bayesian) ΔΔII2 SS()ω =+ S()ωω + S () I ξξ 42zz ξ z quantum back-action changes z Equal contributions (for weak in accordance with the noise ξ coupling and η=1) “what you see is what you get”: observation becomes reality Can we explain it in a more reasonable way (without spooks/ghosts)? +1 z(t)? No (under assumptions of macrorealism; -1 Leggett-Garg, 1985) or some other z(t)? 15/38 Alexander Korotkov University of California, Riverside Leggett-Garg-type inequalities for continuous measurement of a qubit Ruskov-A.K.-Mizel, PRL-2006 qubit detector I(t) Jordan-A.K.-Büttiker, PRL-2006

Assumptions of macrorealism Leggett-Garg,1985 6 SI (ω) (similar to Leggett-Garg’85): 0 Kij = ·Qi QjÒ 4 0 )/S It()= I+Δ ( I /2)() zt +ξ () t if Q = ±1, then 4S ≤ 0 (ω 2 1+K +K +K ≥0 I |()|1,zt≤〈 ξ ()( t zt +〉τ )= 0 12 23 13 S K12+K23+K34 -K14 £2 0 012ω/Ω Then for correlation function quantum result violation KItIt()τ = 〈+〉 ()(τ ) 3 3 KKK()ττττ+−+≤Δ () ( ) ( I /2)2 (/2)ΔI 2 × 1212 2 2 and for area under narrow spectral peak π 2 [()Sf−≤ Sdf ] (8/)(/2)π 22 Δ I (/2)ΔI 2 × ∫ I 0 8 η is not important! Experimentally measurable violation (Saclay experiment) Alexander Korotkov University of California, Riverside Experiment with supercond. qubit (Saclay group) courtesy of Patrice Bertet

〈〉=n 0.23 〈n〉=3.9 photons photons A. Palacios-Laloy, F. Mallet, F. Nguyen, P. Bertet,D.Vion, D. Esteve, and A. Korotkov, Nature Phys., 2010 spectral density (z) spectral frequency (MHz) • superconducting charge qubit LGI violation 1.00 1 2 (transmon) in circuit QED setup 0.75 8/π 2/3 (microwave reflection from cavity) 0.50 • driven Rabi oscillations (this fig. 0.25 peak area unpub.) 0.00 • perfect spectral peaks 0 5 10 15 20 25 f (MHz) • LGI violation (both K & S)

Alexander Korotkov University of California, Riverside Next step: quantum feedback (Useful?) Goal: persistent Rabi oscillations with zero linewidth (synchronized) Types of quantum feedback: Bayesian Direct “Simple” Best but very difficult a la Wiseman-Milburn Imperfect but simple (monitor quantum state (1993) (do as in usual classical and control deviation) (apply measurement signal to ΔH feedback) desired evolution fb control with minimal processing) = F ×φm feedback H

control stage signal comparison control

(barrier height) circuit ΔH /sin()HF=Ω t fb X qubit × cos (Ω t), τ-average ρij(t) ⎛⎞It()− I qubit C<<1 detector 0 C<<1 I(t) φ I(t) Bayesian × −Ωcos t m H ⎜⎟ equations detector local oscil. e I /2 ⎝⎠Δ Y × sin (Ω t), τ-average 1.0 rel. phase environment Δ=×ΔHHF/ ϕ fb 0.8 1.0 η = 1 C = 0.1 1.00 eff 0.6 0.8 2 τ [(ΔI) /SI] = 1 averaging time 0.5 0 0.95 τ a = (2π/Ω)/10 0.4 0.6 C=1 0.5 C /C = 0 0.1 0.5 ε/H = 1 env det 0.2 η =1 0 0.90 0.4 0 C=C =1 0.2 0.1 det (feedback fidelity) =0.2 0.0 Ω/CΩ τ =0 0.2 Δ 0.85 a D 0.0 0.2 0.4 0.6 0.8

(feedback fidelity) 0.1 F (feedbackF(f db k strength)t th) (feedback fidelity) D 0.80 0.0

D 012345678910 0.0 0.2 0.4 0.6 0.8 F (feedback strength) Ruskov & A.K., 2002 F/C (feedback strength) Ruskov & A.K., 2002 A.K., 2005 Alexander Korotkov University of California, Riverside Quantum feedback in optics

First experiment: Science 304, 270 (2004)

First detailed theory: H.M. Wiseman and G. J. Milburn, Phys. Rev. Lett. 70, 548 (1993)

Alexander Korotkov University of California, Riverside Quantum feedback in optics

First experiment: Science 304, 270 (2004)

drawn r with pape

PRL 94, 203002 (2005) also withdrawn

First detailed theory: Recent experiment: H.M. Wiseman and G. J. Milburn, Cook, Martin, Geremia, Phys. Rev. Lett. 70, 548 (1993) Nature 446, 774 (2007) (coherent state discrimination) 20/38 Alexander Korotkov University of California, Riverside Undoing a weak measurement of a qubit (“uncollapse”) A.K. & Jordan, PRL-2006 It is impossible to undo “orthodox” quantum measurement (for an unknown initial state) Is it possible to undo partial quantum measurement? (To restore a “precious” qubit accidentally measured) Yes! (but with a finite probability) If undoing is successful, an unknown state is fully restored

l ccessfu ψ (still ψ su 0 ψ weak (partial) 1 unknown) 0 (partially unsuc (unknown) measurement cessful collapsed) ψ uncollapse 2 (information erasure)

Alexander Korotkov University of California, Riverside Quantum erasers in optics Quantum eraser proposal by Scully and Drühl, PRA (1982)

Interference fringes restored for two-detector correlations (since “which-path” information is erased) Our idea of uncollapsing is quite different: we really extract quantum information and then erase it Alexander Korotkov University of California, Riverside Uncollapse of a qubit state

Evolution due to partial (weak, continuous, etc.) measurement is non-unitary, so impossible to undo it by Hamiltonian dynamics. How to undo? One more measurement!

|1〉 |1〉 |1〉

× =

| 0〉 | 0〉 | 0〉 need ideal (quantum-limited) detector

(Figure partially adopted from (similar to Koashi-Ueda, PRL-1999) Jordan-A.K.-Büttiker, PRL-06) Alexander Korotkov University of California, Riverside Uncollapsing for DQD-QPC system A.K. & Jordan, 2006

H=0 first (“accidental”) uncollapsing measurement measurement Qubit r(t) r I(t) (DQD) 0

Detector (QPC) t Simple strategy: continue measuring until result r(t) becomes zero! Then Meas. result: ΔI t any initial state is fully restored. rt() [ I(t')dt' It] =-∫0 0 (same for an entangled qubit) SI If r = 0, then no information However, if r = 0 never happens, then and no evolution! uncollapsing procedure is unsuccessful. |r | e- 0 Probability of success: PS = ||rr00-|| eeρρ11(0) + 22 (0)

Alexander Korotkov University of California, Riverside General theory of uncollapsing MMρ † POVM formalism rr Measurement operator Mr : ρ → † (Nielsen-Chuang, p.100) Tr(MMrrρ ) Probability : † Completeness : MM† 1 PMMrrr= Tr(ρ ) ∑r rr=

−1 (to satisfy completeness, Uncollapsing operator: CM× r eigenvalues cannot be >1) † max(Cpp )= minii , i– eigenvalues of MMrr

min Pr Probability of success: PS ≤ A.K. & Jordan, 2006 Pr ()ρin

Pr(ρin) – probability of result r for initial state ρin,

min Pr – probability of result r minimized over all possible initial states

Averaged (over r) probability of success: PPav ≤ ∑r min r (cannot depend on initial state, otherwise get information) (similar to Koashi-Ueda, 1999) 25/38 Alexander Korotkov University of California, Riverside Partial collapse of a Josephson phase qubit N. Katz, M. Ansmann, R. Bialczak, E. Lucero, R. McDermott, M. Neeley, M. Steffen, E. Weig, A. Cleland, J. Martinis, A. Korotkov, Science-06 |1〉 Γ How does a qubit state evolve |0〉 in time before tunneling event? (What happens when nothing happens?)

Main idea: ⎧|out〉 , if tunneled ⎪ ψ αβ|0〉+ |1 〉 → ψ (t ) αβ|0〉+ e-Γt /2eiϕ |1〉 ==⎨ , if not tunneled ⎪ 22-Γt ⎩ ||αβ+ ||e (better theory: L. Pryadko & A.K., 2007) amplitude of state |0〉 grows without physical interaction finite linewidth only after tunneling! continuous null-result collapse (similar to optics, Dalibard-Castin-Molmer, PRL-1992) Alexander Korotkov University of California, Riverside Superconducting phase qubit at UCSB Courtesy of Nadav Katz (UCSB) XY Iμw 10ns Flux Z 3ns bias Iz Iμw Qubit Reset Compute Meas. Readout I +I time dc z SQUID Idc IS VS

Is 0 1 Vs Repeat 1000x prob. 0,1 |1〉 |0〉 ω01

1 Φ0

Alexander Korotkov University of California, Riverside Experimental technique for partial collapse Nadav Katz et al. (John Martinis group)

Protocol: 1) State preparation (via Rabi oscillations) 2) Partial measurement by lowering barrier for time t 3) State tomography (microwave + full measurement)

Measurement strength p = 1 - exp(-Γt ) is actually controlled by Γ, not by t p=0: no measurement p=1: orthodox collapse

Alexander Korotkov University of California, Riverside Experimental tomography data Nadav Katz et al. (UCSB, 2005) ψ in = p =0 p =0.06 p =0.14 | 0〉+|1 〉 2

θy

θx p =0.23 p =0.32 p =0.43

π π/2

p =0.56 p =0.70 p =0.83

Alexander Korotkov University of California, Riverside Partial collapse: experimental results N. Katz et al., Science-06

• In case of no tunneling lines - theory phase qubit evolves dots and squares – expt.

Polar angle no fitting parameters in (a) and (b) • Evolution is described by the Bayesian theory probability p without fitting parameters

• Phase qubit remains coherent in the process of continuous collapse

Azimuthal angle (expt. ~80% raw data,

pulse ampl. ~96% corrected for T1,T2)

quantum efficiency

Visibility in (c) T1=110 ns, T2=80 ns (measured) η0 > 0.8 probability p 30/38 Alexander Korotkov University of California, Riverside Uncollapse of a phase qubit state A.K. & Jordan, 2006 1) Start with an unknown state 2) Partial measurement of strength p 3) π-pulse (exchange |0Ú ↔ |1Ú) 4) One more measurement with the same strength p pe=-1 -Γt 5) π-pulse |1〉 Γ If no tunneling for both measurements, |0〉 then initial state is fully restored!

αβ|0〉+eeiφ −Γt /2 |1〉 αβ|0〉+ |1 〉→ → Norm eeiiφφαβ−Γtt/2 |0〉+ ee−Γ /2 |1〉 = eiφ (|0αβ〉+ |1) 〉 Norm phase is also restored (spin echo)

Alexander Korotkov University of California, Riverside Experiment on wavefunction uncollapse partial partial N. Katz, M. Neeley, M. Ansmann, state measure p measure p tomography & preparation final measure R. Bialzak, E. Lucero, A. O’Connell, π H. Wang, A. Cleland, J. Martinis, and A. Korotkov, PRL-2008 Iμw

p p Idc

time Nature News 10 ns 7 ns 10 ns 7 ns Nature-2008 Physics Uncollapse protocol: - partial collapse - π-pulse - partial collapse (same strength) State tomography with X, Y, and no pulses |0〉+ |1 〉 ψ in = 2 Background PB should be subtracted to find qubit density matrix

Alexander Korotkov University of California, Riverside Experimental results on the Bloch sphere Initial |0〉−i |1 〉 |0〉+ |1 〉 N. Katz et al. |1〉 | 0〉 state 2 2

Partially collapsed

Uncollapsed uncollapsing works well!

Both spin echo (azimuth) and uncollapsing (polar angle) Difference: spin echo – undoing of an unknown unitary evolution, uncollapsing – undoing of a known, but non-unitary evolution

Alexander Korotkov University of California, Riverside Quantum process tomography N. Katz et al. (Martinis group)

p = 0.5

uncollapsing works with good fidelity!

Why getting worse at p>0.6?

Energy relaxation pr = t/T1= 45ns/450ns = 0.1 Selection affected when 1-p ~ pr Overall: uncollapsing is well-confirmed experimentally

Alexander Korotkov University of California, Riverside Experiment on uncollapsing using single photons Kim et al., Opt. Expr.-2009

initial state

after partial collapse

after uncollapse • very good fidelity of uncollapsing (>94%) • measurement fidelity is probably not good (normalization by coincidence counts) 35/38 Alexander Korotkov University of California, Riverside Suppression of T1-decoherence by uncollapsing A.K. & K. Keane, Protocol: π π PRA-2010 ρ11 storage period t

(low temperature) )

χ 1.0

Ideal t/T1 1-p)

, F - ( partial collapse uncollapse s 0.9 1-e pu= almost

towards ground (measurem. av state (strength p) strength p ) F 0.8 complete u p suppression pu= 0.7 -t/T1 0.3 without e = 1(1)exp(/)p ptT 0.6 best for -=-u -1 uncollapsing 0.5 0.00.20.40.60.81.0

Ideal case (T during storage only) QPT fidelity ( 1 measurement strength p for initial state |ψin〉=α |0〉 +β |1〉 |ψ 〉= |ψ 〉 with probability (1-p)e-t/T1 f in Trade-off: fidelity vs. probability 2 2 -t/T1 -t/T1 |ψf〉= |0〉 with (1-p) |β| e (1-e ) procedure preferentially selects events without energy decay

Alexander Korotkov University of California, Riverside Realistic case (T1 and Tϕ at all stages)

1.0 fidelity 0.8 (1-p ) κ κ = (1-p) κ κ as in u 3 4 1 2 expt. 0.6 }without κ2 = 0.3 uncollapsing p 0.4 ro κ = 1, 0.95 • Easy to realize experimentally bab ϕ ili κ κ κ 1, 0.999, ty 1= 3= 4= (similar to existing experiment) −tT/ 0.2 κ = e i 1 0.99. 0.9 i −tT/

QPT fidelity, probability Σ ϕ κϕ = e • Improved fidelity can be observed 0.0 0.00.20.40.60.81.0with just one partial measurement measurement strength p

• Tϕ-decoherence is not affected Uncollapse seems the only way to protect against T -decoherence • fidelity decreases at p→1 due to T 1 1 without quantum error correction between 1st π-pulse and 2nd meas.

A.K. & K. Keane, Trade-off: fidelity vs. selection probability PRA-2010

Alexander Korotkov University of California, Riverside Conclusions

● It is easy to see what is “inside” collapse: simple Bayesian formalism works for many solid-state setups

● Rabi oscillations are persistent if weakly measured

● Collapse can sometimes be undone if we manage to erase extracted information (uncollapsing)

● Continuous/partial measurements and uncollapsing may be useful

● Three direct solid-state experiments have been realized, many interesting experimental proposals are still waiting

38/38 Alexander Korotkov University of California, Riverside