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Testing sequential quantum measurements: how can maximal knowledge be extracted?

Nagali E, Felicetti S, de Assis PL, D'Ambrosio V, Filip R, Sciarrino F - Sci Rep (2012)

Bottom Line: In this framework partial measurements can be carried out in order to extract only a portion of the information encoded in a quantum system, at the cost of inducing a limited amount of disturbance.Here we analyze experimentally the dynamics of sequential partial measurements carried out on a quantum system, focusing on the trade-off between the maximal information extractable and the disturbance.In particular we implement two sequential measurements observing that, by exploiting an adaptive strategy, is possible to find an optimal trade-off between the two quantities.

View Article: PubMed Central - PubMed

Affiliation: Dipartimento di Fisica, Sapienza Università di Roma, Roma 00185, Italy.

ABSTRACT
The extraction of information from a quantum system unavoidably implies a modification of the measured system itself. In this framework partial measurements can be carried out in order to extract only a portion of the information encoded in a quantum system, at the cost of inducing a limited amount of disturbance. Here we analyze experimentally the dynamics of sequential partial measurements carried out on a quantum system, focusing on the trade-off between the maximal information extractable and the disturbance. In particular we implement two sequential measurements observing that, by exploiting an adaptive strategy, is possible to find an optimal trade-off between the two quantities.

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Theoretical expectations (red dashed line) compared to experimental data (black squares) for concurrence as function of the knowledge for the single measurement case.Continuous line reports theoretical expectations rescaled to experimental imperfections as the parameters of the PBS (tH = rV = 0.992, rH = tV = 0.008) and the concurrence of the initial state (Cin = (0.95 ± 0.01)).
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f3: Theoretical expectations (red dashed line) compared to experimental data (black squares) for concurrence as function of the knowledge for the single measurement case.Continuous line reports theoretical expectations rescaled to experimental imperfections as the parameters of the PBS (tH = rV = 0.992, rH = tV = 0.008) and the concurrence of the initial state (Cin = (0.95 ± 0.01)).

Mentions: In order to control the interaction between the qubit B and the meter, we exploit a Sagnac interferometer with a polarizing beam splitter (PBS), that interfaces the polarization to the transmitted and reflected spatial modes2930313233: Fig. 2-b. We note that such interfacing between the two degrees of freedom could be achieved also in a Mach-Zehnder34, however the Sagnac interferometer provides a higher stability and thus is more suitable for experimental purposes. The interferometer, here and after denoted as the measurement kit MK, has been aligned in a non-degenerate configuration, where the two internal modes are spatially separated and propagate clockwise (mode a) and anticlockwise (mode b). Such configuration allows an independent manipulation of the polarization on a and b by two half-waveplates rotated at angles θa and θb, respectively, providing a controlled modification of the coupling strength ψ associated to the information extraction. Indeed ψ is fixed by the waveplates in the interferometer by the relation . The latter relations have been expressed in terms of the physical angle θb as in order to perform a projective measurement on the meter qubit in the basis /±〉M, corresponding to the output modes of the interferometer, the two waveplates of the Sagnac have a fixed shift relation, equal to θb = θa + π/4. The projective measurement on the meter qubit corresponds to the selection of one of the output modes 0 and 1 of the PBS. According to definition in (i), in the single measurement case the knowledge K has been measured as , where p(i, j) is the probability that an input photon with polarization j emerges on the mode corresponding to the outcome i. On the other hand the concurrence of the state ρAB after the measurement process acting on qubit B has been estimated from the density matrix reconstructed via quantum state tomography27. In order to estimate probabilities p(i, j) and the elements of the density matrix, we have recorded the coincidence counts between the single photon detector DA and detectors D0 and D1 on the output modes of the first measurement kit, measuring around 600 events per second. Experimental results are reported in Fig. 3, and compared to theoretical expectations evaluated taking into account imperfections due to the PBS and to the source of entangled states. We observe that the single measurement process saturates the optimal trade-off between information extracted and disturbance, allowed by quantum mechanics22.


Testing sequential quantum measurements: how can maximal knowledge be extracted?

Nagali E, Felicetti S, de Assis PL, D'Ambrosio V, Filip R, Sciarrino F - Sci Rep (2012)

Theoretical expectations (red dashed line) compared to experimental data (black squares) for concurrence as function of the knowledge for the single measurement case.Continuous line reports theoretical expectations rescaled to experimental imperfections as the parameters of the PBS (tH = rV = 0.992, rH = tV = 0.008) and the concurrence of the initial state (Cin = (0.95 ± 0.01)).
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3379168&req=5

f3: Theoretical expectations (red dashed line) compared to experimental data (black squares) for concurrence as function of the knowledge for the single measurement case.Continuous line reports theoretical expectations rescaled to experimental imperfections as the parameters of the PBS (tH = rV = 0.992, rH = tV = 0.008) and the concurrence of the initial state (Cin = (0.95 ± 0.01)).
Mentions: In order to control the interaction between the qubit B and the meter, we exploit a Sagnac interferometer with a polarizing beam splitter (PBS), that interfaces the polarization to the transmitted and reflected spatial modes2930313233: Fig. 2-b. We note that such interfacing between the two degrees of freedom could be achieved also in a Mach-Zehnder34, however the Sagnac interferometer provides a higher stability and thus is more suitable for experimental purposes. The interferometer, here and after denoted as the measurement kit MK, has been aligned in a non-degenerate configuration, where the two internal modes are spatially separated and propagate clockwise (mode a) and anticlockwise (mode b). Such configuration allows an independent manipulation of the polarization on a and b by two half-waveplates rotated at angles θa and θb, respectively, providing a controlled modification of the coupling strength ψ associated to the information extraction. Indeed ψ is fixed by the waveplates in the interferometer by the relation . The latter relations have been expressed in terms of the physical angle θb as in order to perform a projective measurement on the meter qubit in the basis /±〉M, corresponding to the output modes of the interferometer, the two waveplates of the Sagnac have a fixed shift relation, equal to θb = θa + π/4. The projective measurement on the meter qubit corresponds to the selection of one of the output modes 0 and 1 of the PBS. According to definition in (i), in the single measurement case the knowledge K has been measured as , where p(i, j) is the probability that an input photon with polarization j emerges on the mode corresponding to the outcome i. On the other hand the concurrence of the state ρAB after the measurement process acting on qubit B has been estimated from the density matrix reconstructed via quantum state tomography27. In order to estimate probabilities p(i, j) and the elements of the density matrix, we have recorded the coincidence counts between the single photon detector DA and detectors D0 and D1 on the output modes of the first measurement kit, measuring around 600 events per second. Experimental results are reported in Fig. 3, and compared to theoretical expectations evaluated taking into account imperfections due to the PBS and to the source of entangled states. We observe that the single measurement process saturates the optimal trade-off between information extracted and disturbance, allowed by quantum mechanics22.

Bottom Line: In this framework partial measurements can be carried out in order to extract only a portion of the information encoded in a quantum system, at the cost of inducing a limited amount of disturbance.Here we analyze experimentally the dynamics of sequential partial measurements carried out on a quantum system, focusing on the trade-off between the maximal information extractable and the disturbance.In particular we implement two sequential measurements observing that, by exploiting an adaptive strategy, is possible to find an optimal trade-off between the two quantities.

View Article: PubMed Central - PubMed

Affiliation: Dipartimento di Fisica, Sapienza Università di Roma, Roma 00185, Italy.

ABSTRACT
The extraction of information from a quantum system unavoidably implies a modification of the measured system itself. In this framework partial measurements can be carried out in order to extract only a portion of the information encoded in a quantum system, at the cost of inducing a limited amount of disturbance. Here we analyze experimentally the dynamics of sequential partial measurements carried out on a quantum system, focusing on the trade-off between the maximal information extractable and the disturbance. In particular we implement two sequential measurements observing that, by exploiting an adaptive strategy, is possible to find an optimal trade-off between the two quantities.

Show MeSH