Path detection and the uncertainty principle

Storey, Pippa; Tan, S. M.; Collett, M. J.; Walls, D. F.

doi:10.1038/367626a0

Cited by 150 publications

(135 citation statements)

References 4 publications

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“…It has been debated, particularly around the mid-1990s [14][15][16] , whether the WPD principle, closely related to Bohr's complementarity principle 17 , is equivalent to another fundamental quantum idea with no classical analogue: Heisenberg's uncertainty principle 18 . The latter states that there are certain pairs of observables, such as position and momentum or two orthogonal components of spin angular momentum, which cannot simultaneously be known or jointly measured.…”

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confidence: 99%

Equivalence of wave–particle duality to entropic uncertainty

2014

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Interferometers capture a basic mystery of quantum mechanics: a single particle can exhibit wave behaviour, yet that wave behaviour disappears when one tries to determine the particle's path inside the interferometer. This idea has been formulated quantitatively as an inequality, for example, by Englert and Jaeger, Shimony and Vaidman, which upper bounds the sum of the interference visibility and the path distinguishability. Such wave-particle duality relations (WPDRs) are often thought to be conceptually inequivalent to Heisenberg's uncertainty principle, although this has been debated. Here we show that WPDRs correspond precisely to a modern formulation of the uncertainty principle in terms of entropies, namely, the min-and max-entropies. This observation unifies two fundamental concepts in quantum mechanics. Furthermore, it leads to a robust framework for deriving novel WPDRs by applying entropic uncertainty relations to interferometric models. As an illustration, we derive a novel relation that captures the coherence in a quantum beam splitter.

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confidence: 99%

Equivalence of wave–particle duality to entropic uncertainty

2014

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“…Opening additional photon channels allows "which-path" information and reduces the visibility of the singlephoton interference, but results in nearly perfect visibility when photons are counted in coincidence. A simplified theoretical model accounts for these complementary observations and attributes them directly to the relations among the vacuum fields at the different crystals.Complementarity, often discussed in quantum optics as wave-particle dualism, is a fundamental principle of undiminished interest [1][2][3][4]. "Which-path" information about a single photon is possible only at the cost of decreasing interference fringe visibility V .…”

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confidence: 99%

“…Complementarity, often discussed in quantum optics as wave-particle dualism, is a fundamental principle of undiminished interest [1][2][3][4]. "Which-path" information about a single photon is possible only at the cost of decreasing interference fringe visibility V .…”

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Induced Coherence, Vacuum Fields, and Complementarity in Biphoton Generation

Heuer

Menzel

2015

Phys. Rev. Lett.

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We describe spontaneous parametric down-conversion experiments in which induced coherence across two coupled interferometers results in high-visibility single-photon interference. Opening additional photon channels allows "which-path" information and reduces the visibility of the singlephoton interference, but results in nearly perfect visibility when photons are counted in coincidence. A simplified theoretical model accounts for these complementary observations and attributes them directly to the relations among the vacuum fields at the different crystals.Complementarity, often discussed in quantum optics as wave-particle dualism, is a fundamental principle of undiminished interest [1][2][3][4]. "Which-path" information about a single photon is possible only at the cost of decreasing interference fringe visibility V . This can be expressed quantitatively by the formula K 2 + V 2 ≤ 1, where the "contrast" K is a measure of which-path information [5]. Recent work [6,7] demonstrated among other things that single-photon interference is determined by the mode function associated with the photon, as quantum field theory predicts [6]. In this paper we describe experiments on spontaneous photon down-conversion (SPDC) demonstrating that which-path information in single-photon interference reduces fringe visibility but results in very high visibility in second-order interference measurements. These experiments may serve to clarify the roles of mode functions and vacuum fields in SPDC, which has for many years been a primary platform for fundamental studies in quantum optics and conceptual foundations of quantum theory.Although the signal and idler photons in SPDC have no fixed phase relation, the combined entity, or biphoton, carries observable phase information about the pump field [8,9]. In particular, by varying the phase delay between the pump fields for two crystals, first-order singlephoton interference has been observed [10]. In these experiments the idler photon modes i1 and i2 of crystals BBO1 and BBO2 (Figure 1) were aligned and indistinguishable, and interference of the signal photon channels s1 and s2 was observed as a consequence of induced coherence between BBO1 and BBO2.Suppose now that a third pumped crystal (BBO3) is added. If the s1 and s3 modes are aligned and indistinguishable, the possibility of generating a signal photon at BBO1 or at BBO3 might suggest that single-photon interference between the channels s1 and s3 should be observable at detector A behind beam splitter BS1. But we now have "which-path" information: detection of photons i3 with a detector D behind the beam splitter BS2, for instance, implies that a photon pair (i3,s3) must have been emitted from crystal BBO3. In spite of this which-path information, however, we observe highvisibility signal-photon interference fringes at A when these signal photons are counted in coincidence with idler photons at D.The experimental setup employed three BBO crystals for biphoton generation (Figure 1). All three crystals had a length of 4 mm and were...

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“…They are therefore of special interest in the context of postselected subensembles. In particular, they have been used to "resolve" [2] Hardy's Paradox [3]; to interpret and extend novel cavity-QED experiments [4,5]; to reconcile diverging views on which-path experiments and uncertainty [6,7,8]; and to address the long-standing controversy over tunneling times [9]. Often, it is of interest to discuss the weak value of a nonlocal observable (especially, of course, in proposals to study locality [2,3,10]); unfortunately, it is usually difficult or impossible to carry out such measurements [2,11].…”

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Extracting Joint Weak Values with Local, Single-Particle Measurements

2004

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Weak measurement is a new technique which allows one to describe the evolution of postselected quantum systems. It appears to be useful for resolving a variety of thorny quantum paradoxes, particularly when used to study properties of pairs of particles. Unfortunately, such nonlocal or joint observables often prove difficult to measure weakly in practice (for instance, in optics -a common testing ground for this technique -strong photon-photon interactions would be needed). Here we derive a general, experimentally feasible, method for extracting these values from correlations between single-particle observables.

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Path detection and the uncertainty principle

Cited by 150 publications

References 4 publications

Equivalence of wave–particle duality to entropic uncertainty

Equivalence of wave–particle duality to entropic uncertainty

Induced Coherence, Vacuum Fields, and Complementarity in Biphoton Generation

Extracting Joint Weak Values with Local, Single-Particle Measurements

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