Polarization states of four-dimensional systems based on biphotons

Bogdanov, Yu. I.; Moreva, E. V.; Maslennikov, Gleb; Galeev, R. F.; Straupe, S. S.; Kulik, S. P.

doi:10.1103/physreva.73.063810

Cited by 54 publications

(68 citation statements)

References 35 publications

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“…Measurement block: We implement PaW or GPPT as in Fig.1. In PaW superobserver mode the final state is checked by quantum state tomography [27][28][29], realised by registering the coincidence rate for 16 different projections achieved through half and quarter wave plates and a fixed analyzer (V).…”

Section: Methodsmentioning

confidence: 99%

“…For temporal stability, the interferometer is placed into a closed box. The output state is reconstructed using ququart state tomography [27][28][29] (the two-photon polarization state lives in a four-dimensional Hilbert space), where the projective measurements are realized with polarization filters consisting of a sequence of quarter-and half-wave plates and a polarization prism which transmits vertical polarization (Fig.4). The fidelity between the tomographically reconstructed state and the theoretical state |Ψ is reported in Fig.…”

Section: Methodsmentioning

confidence: 99%

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Time from quantum entanglement: An experimental illustration

et al. 2014

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In the last years several theoretical papers discussed if time can be an emergent propertiy deriving from quantum correlations. Here, to provide an insight into how this phenomenon can occur, we present an experiment that illustrates Page and Wootters' mechanism of "static" time, and Gambini et al. subsequent refinements. A static, entangled state between a clock system and the rest of the universe is perceived as evolving by internal observers that test the correlations between the two subsystems. We implement this mechanism using an entangled state of the polarization of two photons, one of which is used as a clock to gauge the evolution of the second: an "internal" observer that becomes correlated with the clock photon sees the other system evolve, while an "external" observer that only observes global properties of the two photons can prove it is static."Quid est ergo tempus? si nemo ex me quaerat, scio; si quaerenti explicare velim, nescio." [1] The "problem of time" [2][3][4][5][6] in essence stems from the fact that a canonical quantization of general relativity yields the Wheeler-De Witt equation [7,8] predicting a static state of the universe, contrary to obvious everyday evidence. A solution was proposed by Page and Wootters [9, 10]: thanks to quantum entanglement, a static system may describe an evolving "universe" from the point of view of the internal observers. Energy-entanglement between a "clock" system and the rest of the universe can yield a stationary state for an (hypothetical) external observer that is able to test the entanglement vs. abstract coordinate time. The same state will be, instead, evolving for internal observers that test the correlations between the clock and the rest [9][10][11][12][13][14]. Thus, time would be an emergent property of subsystems of the universe deriving from their entangled nature: an extremely elegant but controversial idea [2,15]. Here we want to demystify it by showing experimentally that it can be naturally embedded into (small) subsystems of the universe, where Page and Wootters' mechanism (and Gambini et al. subsequent refinements [12,16]) can be easily studied. We show how a static, entangled state of two photons can be seen as evolving by an observer that uses one of the two photons as a clock to gauge the time-evolution of the other photon. However, an external observer can show that the global entangled state does not evolve.Even though it revolutionizes our ideas on time, Page and Wootters' (PaW) mechanism is quite simple [9-11]: they provide a static entangled state |Ψ whose subsystems evolve according to the Schrödinger equation for an observer that uses one of the subsystems as a clock system C to gauge the time evolution of the rest R. While the division into subsystems is largely arbitrary, the PaW model assumes the possibility of neglecting interaction among them writing the Hamiltonian of the global system as H = H c ⊗ 1 1 r + 1 1 c ⊗ H r , where H c , H r are the local terms associated with C and R, respectively and Uc(t) = e −iHct/ are the ...

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Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Time from quantum entanglement: An experimental illustration

et al. 2014

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“…Let us start by defining the basis states that form the biphoton ququart [14,15]. For the frequency-nondegenerate two-photon polarization state of SPDC, it is not difficult to realize that the two-photon polarization state must belong to the four-dimensional Hilbert space and that the four orthonormal basis states can be written as,…”

Section: Two-photon Ququartmentioning

confidence: 99%

“…In this paper, we investigate realistic and experimentally realizable two-ququart and multi-ququart entangling schemes in which the single ququart state is based on frequency-nondegenerate two-photon polarization state of spontaneous parametric down-conversion (SPDC) [14,15]. The SPDC process generates a coherent superposition of the vacuum, the two-photon amplitude, the four-photon amplitude, etc [22].…”

Section: Introductionmentioning

confidence: 99%

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Scalable scheme for entangling multiple ququarts using linear optical elements

Baek

Kim

2007

Physics Letters A

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We report a scalable linear optical scheme for generating entangled states of multiple ququarts in which the individual single-ququart state is prepared with the biphoton polarization state of frequency-nondegenerate spontaneous parametric down-conversion. The output state is calculated with the full consideration of the higher order effect (double-pair events) of spontaneous parametric down-conversion. Scalability to multiple-ququart entanglement is demonstrated with examples: linear optical entanglement of three and four individual biphoton ququarts.

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Nonlinear Interactions and Non-classical Light

Strekalov

Leuchs

2019

Springer Series in Optical Sciences

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Polarization states of four-dimensional systems based on biphotons

Cited by 54 publications

References 35 publications

Time from quantum entanglement: An experimental illustration

Time from quantum entanglement: An experimental illustration

Scalable scheme for entangling multiple ququarts using linear optical elements

Nonlinear Interactions and Non-classical Light

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