Contextual Values of Observables in Quantum Measurements

Dressel, Justin; Agarwal, Swapnil; Jordan, Andrew N.

doi:10.1103/physrevlett.104.240401

Cited by 111 publications

(195 citation statements)

References 20 publications

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“…[16,22] it is shown that one recovers the AAV weak value if one requires that the Kraus operators are positive and Hermitian (this is taken as the definition of a minimally disturbing measurement in Ref. [26]).…”

Section: B Minimal Disturbance and Uniqueness Of The Weak Valuementioning

confidence: 99%

Disturbance in weak measurements and the difference between quantum and classical weak values

Ipsen

2015

Phys. Rev. A

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The role of measurement induced disturbance in weak measurements is of central importance for the interpretation of the weak value. Uncontrolled disturbance can interfere with the postselection process and make the weak value dependent on the details of the measurement process. Here we develop the concept of a generalized weak measurement for classical and quantum mechanics. The two cases appear remarkably similar, but we point out some important differences. A priori it is not clear what the correct notion of disturbance should be in the context of weak measurements.We consider three different notions and get three different results: (1) For a 'strong' definition of disturbance, we find that weak measurements are disturbing. (2) For a weaker definition we find that a general class of weak measurements are non-disturbing, but that one gets weak values which depend on the measurement process. (3) Finally, with respect to an operational definition of the 'degree of disturbance', we find that the AAV weak measurements are the least disturbing, but that the disturbance is always non-zero.

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Section: B Minimal Disturbance and Uniqueness Of The Weak Valuementioning

confidence: 99%

Disturbance in weak measurements and the difference between quantum and classical weak values

Ipsen

2015

Phys. Rev. A

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“…Quantum violations.-The quantum mechanical equivalent of a noisy MR measurement is a weak measurement [23], as emphasized in Ref. [10].…”

Section: Generalizedmentioning

confidence: 99%

Avoiding loopholes with hybrid Bell-Leggett-Garg inequalities

Dressel

Korotkov

2014

Phys. Rev. A

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By combining the postulates of macrorealism with Bell locality, we derive a qualitatively different hybrid inequality that avoids two loopholes that commonly appear in Leggett-Garg and Bell inequalities. First, locally invasive measurements can be used, which avoids the "clumsiness" Leggett-Garg inequality loophole. Second, a single experimental ensemble with fixed analyzer settings is sampled, which avoids the "disjoint sampling" Bell inequality loophole. The derived hybrid inequality has the same form as the Clauser-Horne-Shimony-Holt Bell inequality; however, its quantum violation intriguingly requires weak measurements. A realistic explanation of an observed violation requires either the failure of Bell locality, or a preparation conspiracy of finely tuned and nonlocally correlated noise. Modern superconducting and optical systems are poised to implement this test.

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“…Often consideration is limited to its real part, as would be done in standard measurement [17,28,30] but the imaginary part also has a physical significance: the evolution U not only shifts the average position of pointer but also the average momentum of the pointer. These two, purely real, shifts are proportional to the real and imaginary parts of the weak value, respectively [30][31][32]:…”

mentioning

confidence: 99%

“…It has also been used to amplify small experimental effects [22] and as feedback for control of a quantum system [23]. Weak measurements have been demonstrated in both classical [24] and non-classical systems [25].The concept of weak measurement is universally applicable to all types of measurement [26][27][28] but here we introduce it with a standard model of measurement, the von Neumann model [29]. In it, a measurement apparatus has a pointer, in an initial position wavefunction…”

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confidence: 99%

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Procedure for Direct Measurement of General Quantum States Using Weak Measurement

2012

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Recent work [J.S. Lundeen et al. Nature, 474, 188 (2011)] directly measured the wavefunction by weakly measuring a variable followed by a normal (i.e. 'strong') measurement of the complementary variable. We generalize this method to mixed states by considering the weak measurement of various products of these observables, thereby providing the density matrix an operational definition in terms of a procedure for its direct measurement. The method only requires measurements in two bases and can be performed 'in situ', determining the quantum state without destroying it.PACS numbers: 03.65. Ta, 03.65.Wj, 42.50.Dv, The wavefunction Ψ is at the heart of quantum mechanics, yet its nature has been debated since its inception. It is typically relegated to being a calculational device for predicting measurement outcomes. Recently, Lundeen et al. proposed a simple and general operational definition of the wavefunction based on a method for its direct measurement: "it is the average result of a weak measurement of a variable followed by a strong measurement of the complementary variable [1,2]." By 'direct' it is meant that a value proportional to the wavefunction appears straight on the measurement apparatus itself without further complicated calculations or fitting. The 'wavefunction' referred to here is a special case of a general quantum state, known as a 'pure state.' The general case is represented by the density operator ρ, which can describe both pure and 'mixed' states. The latter incorporates both the effects of classical randomness (e.g., noise) and entanglement with other systems (e.g., decoherence). The density operator plays an important role in quantum statistics, quantum information, and the study of decoherence. Because of its generality and because it follows naturally from classical concepts of probability and measures, some consider ρ, rather than Ψ, to be the fundamental quantum state description. In this letter, we propose two methods to directly measure general quantum states, one of which directly gives the matrix elements of ρ.The standard method for experimentally determining the density operator is Quantum State Tomography [3]. In it, one makes a diverse set of measurements on an ensemble of identical systems and then determines the quantum state that is most compatible with the measurement results. An alternative is our direct measurement method, which may have advantages over tomography, such as simplicity, versatility, and directness. A quantitative comparison of measures such as the signal to noise ratio, resolution, and fidelity, has not been undertaken but some limitations of the direct method have been identified in [4]. As compared to tomography, which works with mixed states, the most significant limitation of the direct measurement of the wavefunction is that it has only been shown to work with pure states.Previous works have developed direct methods to measure quasi-probability distributions, such as the Wigner function [5], Husimi Q-function [6], and the GlauberSudarshan P-function [7]...

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Contextual Values of Observables in Quantum Measurements

Cited by 111 publications

References 20 publications

Disturbance in weak measurements and the difference between quantum and classical weak values

Disturbance in weak measurements and the difference between quantum and classical weak values

Avoiding loopholes with hybrid Bell-Leggett-Garg inequalities

Procedure for Direct Measurement of General Quantum States Using Weak Measurement

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