Uncollapsing the wavefunction by undoing quantum measurements

Jordan, Andrew N.; Korotkov, Alexander N.

doi:10.1080/00107510903385292

Cited by 38 publications

(41 citation statements)

References 46 publications

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“…In this limit, we can readily extremize the value of R s while keeping θ s fixed in Eqs. (14), which is accomplished by fixing the ratio ∆ 2 1 /∆ 0 and then varying only ∆ 1 . This procedure determines the maximum radius to be a constant, R max = 1/ 1/η + 2τ m /T 2 < 1, that is achieved when ∆ 1 = sin θ s /(τ m R max ).…”

Section: B Stationary States For Markovian Feedbackmentioning

confidence: 99%

Linear feedback stabilization of a dispersively monitored qubit

Chantasri

García-Pintos

et al. 2017

Phys. Rev. A

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The state of a continuously monitored qubit evolves stochastically, exhibiting competition between coherent Hamiltonian dynamics and diffusive partial collapse dynamics that follow the measurement record. We couple these distinct types of dynamics together by linearly feeding the collected record for dispersive energy measurements directly back into a coherent Rabi drive amplitude. Such feedback turns the competition cooperative, and effectively stabilizes the qubit state near a target state. We derive the conditions for obtaining such dispersive state stabilization and verify the stabilization conditions numerically. We include common experimental nonidealities, such as energy decay, environmental dephasing, detector efficiency, and feedback delay, and show that the feedback delay has the most significant negative effect on the feedback protocol. Setting the measurement collapse timescale to be long compared to the feedback delay yields the best stabilization.

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Section: B Stationary States For Markovian Feedbackmentioning

confidence: 99%

Linear feedback stabilization of a dispersively monitored qubit

Chantasri

García-Pintos

et al. 2017

Phys. Rev. A

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“…Such inverse measurements in general can be understood as a combination of unitary rotations and a dispersive measurement, using the singular value decomposition of the measurement operator, discussed in Sec. III [49].…”

Section: A Generic Rank Two Qubit Measurementmentioning

confidence: 99%

Time reversal symmetry of generalized quantum measurements with past and future boundary conditions

Manikandan

Jordan

2019

Quantum Stud.: Math. Found.

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We expand the time reversal symmetry arguments of quantum mechanics, originally proposed by Wigner in the context of unitary dynamics, to contain situations including generalized measurements for monitored quantum systems. We propose a scheme to derive the time reversed measurement operators by considering the Schrödinger picture dynamics of a qubit coupled to a measuring device, and show that the time reversed measurement operators form a Positive Operator Valued Measure (POVM) set. We present three particular examples to illustrate time reversal of measurement operators : (1) the Gaussian spin measurement, (2) a dichotomous POVM for spin, and (3) the measurement of qubit fluorescence. We then propose a general rule to unravel any rank two qubit measurement, and show that the backward dynamics obeys the retrodicted equations of the forward dynamics starting from the time reversed final state. We demonstrate the time reversal invariance of dynamical equations using the example of qubit fluorescence. We also generalize the discussion of a statistical arrow of time for continuous quantum measurements introduced by Dressel et al. [Phys. Rev. Lett. 119, 220507 (2017)]: we show that the backward probabilities can be computed from a process similar to retrodiction from the time reversed final state, and extend the definition of an arrow of time to ensembles prepared with pre-and post-selections, where we obtain a non-vanishing arrow of time in general. We discuss sufficient conditions for when time's arrow vanishes and show our method also captures the contributions to time's arrow due to natural physical processes like relaxation of an atom to its ground state. As a special case, we recover the time reversibility of the weak value as its complex conjugate using our method, and discuss how our conclusions differ from the time-symmetry argument of Aharonov-Bergmann-Lebowitz (ABL) rule. I. INTRODUCTIONAlthough most 1 of the microscopic laws of physics are invariant under a suitable time reversal symmetry operation, there seems to exist a preferred ordering in which events are more likely to happen than otherwise, in the macroscopic world. This is true for a box of an ideal gas -where one can practically keep track of the dynamics of every single molecule given their initial conditions, and knowing all the microscopic interactions, while the second law of thermodynamics dictates that the gas molecules within the box re-distribute themselves and evolve towards a final state where the entropy is a maximum [4] -and in cosmology, from the observation of an expanding universe [5]. These apparent asymmetrical notions of time are also manifest in our everyday experiences as conscious observers; According to Wheeler, our notion of a past corresponds to experiencing a definite, informative, thus recordable set of events [6,7], and from an information theory perspective, they correspond to processes where entropy always increases or remains constant [7]. Understanding how a definite arrow of time emerges from a time reversal invar...

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“…In particular, the last constraint demands that c m j /min j λ m j ≤ 1, which bounds c m j . The bound on c m j also bounds the probability of reversing the measurement [6]. This proves that it is always possible to construct another POVM element which corresponds to the inverse of the first POVM element.…”

Section: Time Reversal Symmetry For Janus Measurement Sequencesmentioning

confidence: 99%

“…a measurement may be stochastically reversed, unless the measurement is a perfect projection operator [5,6]. This suggests that for any physical measurement process, a dynamical time symmetry may be restored.…”

Section: Futurementioning

confidence: 99%

Janus sequences of quantum measurements and the arrow of time

Jordan

Chantasri

Murch³

et al. 2017

AIP Conference Proceedings

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Abstract. We examine the time reversal symmetry of quantum measurement sequences by introducing a forward and backward Janus sequence of measurements. If the forward sequence of measurements creates a sequence of quantum states in time, starting from an initial state and ending in a final state, then the backward sequence begins with the time-reversed final state, exactly retraces the intermediate states, and ends with the time-reversed initial state. We prove that such a sequence can always be constructed, showing that unless the measurements are ideal projections, it is impossible to tell if a given sequence of measurements is progressing forward or backward in time. A statistical arrow of time emerges only because typically the forward sequence is more probable than the backward sequence.

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Uncollapsing the wavefunction by undoing quantum measurements

Cited by 38 publications

References 46 publications

Linear feedback stabilization of a dispersively monitored qubit

Linear feedback stabilization of a dispersively monitored qubit

Time reversal symmetry of generalized quantum measurements with past and future boundary conditions

Janus sequences of quantum measurements and the arrow of time

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