Two entangled two-level system (or qubits) is the fundamental ‘brick’ in the construcion of quantum logic gates, which are the base of quantum networks. Quantum entanglement is also at the core of the duality principle relating fringe visibility and acquisition of which way information in a two-ways interferometer. We present here a quantum logic gate — the Symmetric Quanton-Detecton System, for which each qubit can play the role of quanton or which-way detector. Applying the results of Englert [Phys. Rev. Lett. 77 , 2154 (1996).] we derive a pair of coupled duality relations for the system. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Two entangled two-level system (or qubits) is the fundamental ‘brick’ in the construcion of quantum logic gates, which are the base of quantum networks. Quantum entanglement is also at the core of the duality principle relating fringe visibility and acquisition of which way information in a two-ways interferometer. We present here a quantum logic gate — the Symmetric Quanton-Detecton System, for which each qubit can play the role of quanton or which-way detector. Applying the results of Englert [Phys. Rev. Lett. 77 , 2154 (1996).] we derive a pair of coupled duality relations for the system. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
We introduce a measure Q of the ``quality'' of a quantum which-way detector, which characterizes its intrinsic ability to extract which-way information in an asymmetric two-way interferometer. The ``quality'' Q allows one to separate the contribution to the distinguishability of the ways arising from the quantum properties of the detector from the contribution stemming from a priori which-way knowledge available to the experimenter, which can be quantified by a predictability parameter P. We provide an inequality relating these two sources of which-way information to the value of the fringe visibility displayed by the interferometer. We show that this inequality is an expression of duality, allowing one to trace the loss of coherence to the two reservoirs of which-way information represented by Q and P. Finally, we illustrate the formalism with the use of a quantum logic gate: the symmetric quanton-detecton system (SQDS). The SQDS can be regarded as two qubits trying to acquire which-way information about each other. The SQDS will provide an illustrating example of the reciprocal effects induced by duality between system and which-way detector.
We propose for the experimental verification of an inequality concerning wave-particle duality by Englert [Phys. Rev. Lett. 77, 2154 (1996)] relating (or setting) an upper limit on distinguishability and visibility in a two-way interferometer. The inequality, quantifies the concept of wave-particle duality. The considered two-way interferometer is a Young's double-slit experiment involving two four-level atoms and is a slightly modified version of that of the recent experiment by Eichmann et al. [Phys. Rev. Lett. 70, 2359 (1993)]. The fringe visibility depends on the detected polarization direction of the scattered light and a read out of the internal state of one of the two atoms provides a partial which-way information.
According to the relevant theories on duality relation, the summation of the extractable information of a quanton’s wave and particle properties, which are characterized by interference visibility V and path distinguishability D, respectively, is limited. However, this relation is violated upon quantum superposition between the wave-state and particle-state of the quanton, which is caused by the quantum beamsplitter (QBS). Along another line, recent studies have considered quantum coherence C in the l1-norm measure as a candidate for the wave property. In this study, we propose an interferometer with a quantum which-path detector (QWPD) and examine the generalized duality relation based on C. We find that this relationship still holds under such a circumstance, but the interference between these two properties causes the full-particle property to be observed when the QWPD system is partially present. Using a pair of polarization-entangled photons, we experimentally verify our analysis in the two-path case. This study extends the duality relation between coherence and path information to the quantum case and reveals the effect of quantum superposition on the duality relation.
To test the principle of complementarity and wave-particle duality quantitatively, we need a quantum composite system that can be controlled by experimental parameters. Here, we demonstrate that a double-path interferometer consisting of two parametric downconversion crystals seeded by coherent idler fields, where the generated coherent signal photons are used for quantum interference and the conjugate idler fields are used for which-path detectors with controllable fidelity, is useful for elucidating the quantitative complementarity. We show that the source purity μs is tightly bounded by the entanglement measure E by the relation μs=1−E2 and the visibility V and detector fidelity F determine the coherence of the quantons, i.e., C=V∣F∣. The quantitative complementarity of the double-path interferometer we developed recently is explained in terms of the quanton-detector entanglement or quanton source purity that are expressed as functions of injected seed photon numbers. We further suggest that the experimental scheme utilizing two stimulated parametric downconversion processes is an ideal tool for investigating and understanding wave-particle duality and complementarity quantitatively.
A quantum system (quanton) traverses an interferometer with N equally probable paths and interacts with another quantum system (detector) that stores path information in a set of symmetric states. In this framework, we present a systematic quantitative study of wave-particle duality based on entropic trade-off relations between quantum coherence, characterized by the relative entropy of coherence of the quanton state, and which-path knowledge, quantified by the mutual information obtained through detector-state discrimination. Unlike prior upper-bound-based formulations, we obtain an exact quantification of which-path knowledge for the discrimination strategies considered here, encompassing previous strategies and extending beyond them. A general optimal measurement is implemented through a state-separation map governed by a continuous parameter ξ∈[0,1], followed by minimum-error (ME) discrimination of either the successful outputs only (standard approach) or both successful and failure outputs (concatenated approach). Our framework identifies a strategy-dependent hierarchy that generally emerges in the tightness of the resulting duality relations. At ξ=0, both approaches reduce to the ME measurement, which typically yields the tightest relation. For ξ>0, each approach yields a distinct relation that generally becomes less tight as ξ increases, with the concatenated strategy always yielding a relation at least as tight as its standard counterpart. We further characterize saturation of these relations by identifying the detector-state sets that lead to it and show that nontrivial saturation occurs only for interferometers with a nonprime number of paths. From these sets, we elucidate how the underlying structure of the quanton-detector correlations gives rise to this behavior and explains the lack of universal saturation in multipath duality relations for pure states.