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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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(a) Scheme of the two-slits experiment with the interference fringes (on the right), whose visibility depends on the information extracted on the path followed by the single photon. (b) Circuital scheme of the sequential measurements scenario. The qubit B is coupled with the ancillary qubit /0〉M. The measurement result affects the next sequential one by adapting the measurement basis through a rotation Ri in the next measurement process (MK2). (c) Scheme for the implementation of two sequential measurements strategy on single photon states. An individual photon passing through the whole measurement apparatus is detected only in one of the four output ports, which indicates which combination of results for MK1 and MK2 is obtained.
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f1: (a) Scheme of the two-slits experiment with the interference fringes (on the right), whose visibility depends on the information extracted on the path followed by the single photon. (b) Circuital scheme of the sequential measurements scenario. The qubit B is coupled with the ancillary qubit /0〉M. The measurement result affects the next sequential one by adapting the measurement basis through a rotation Ri in the next measurement process (MK2). (c) Scheme for the implementation of two sequential measurements strategy on single photon states. An individual photon passing through the whole measurement apparatus is detected only in one of the four output ports, which indicates which combination of results for MK1 and MK2 is obtained.

Mentions: The measurement process represents one of the most distinctive aspects of quantum mechanics with respect to classical physics12. The main result of quantum measurement theory is the unavoidable disturbance of the quantum state by the measuring process, as epitomized by the early Heisenberg x-ray microscope thought experiment3. The duality between the information available on an unknown quantum system and the disturbance induced by a measurement process is of utmost relevance when investigating the quantum world456 and lies at the basis of the security of quantum cryptographic protocols7. In this framework, a partial measurement approach can be adopted to extract only a limited amount of information from the quantum system at the cost of limited induced disturbance89101112. Such partial measurement technique allows to perform consecutive observations (i.e. sequential measurements) on the same quantum system in order to investigate its properties without destroying it131415161718192021. In such context a question arises whether it is possible to extract an optimal amount of information from sequential measurements, compared to the degree of disturbance induced on the system. The aim of this paper is to investigate experimentally the trade-off between information gained and disturbance induced by partial sequential measurements on a quantum system22. Conceptually our experiment is similar to a double-slit experiment Fig. 1-a where the which-way information is acquired via successive measurements on the same particle. In particular we implement two sequential measurements performed on the same quantum system and observe that the optimal trade-off that characterizes the single measurement can be retrieved by adopting a proper adaptive strategy. Such result, observed for N = 2 sequential measurements, can be extended for any value of N.


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)

(a) Scheme of the two-slits experiment with the interference fringes (on the right), whose visibility depends on the information extracted on the path followed by the single photon. (b) Circuital scheme of the sequential measurements scenario. The qubit B is coupled with the ancillary qubit /0〉M. The measurement result affects the next sequential one by adapting the measurement basis through a rotation Ri in the next measurement process (MK2). (c) Scheme for the implementation of two sequential measurements strategy on single photon states. An individual photon passing through the whole measurement apparatus is detected only in one of the four output ports, which indicates which combination of results for MK1 and MK2 is obtained.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f1: (a) Scheme of the two-slits experiment with the interference fringes (on the right), whose visibility depends on the information extracted on the path followed by the single photon. (b) Circuital scheme of the sequential measurements scenario. The qubit B is coupled with the ancillary qubit /0〉M. The measurement result affects the next sequential one by adapting the measurement basis through a rotation Ri in the next measurement process (MK2). (c) Scheme for the implementation of two sequential measurements strategy on single photon states. An individual photon passing through the whole measurement apparatus is detected only in one of the four output ports, which indicates which combination of results for MK1 and MK2 is obtained.
Mentions: The measurement process represents one of the most distinctive aspects of quantum mechanics with respect to classical physics12. The main result of quantum measurement theory is the unavoidable disturbance of the quantum state by the measuring process, as epitomized by the early Heisenberg x-ray microscope thought experiment3. The duality between the information available on an unknown quantum system and the disturbance induced by a measurement process is of utmost relevance when investigating the quantum world456 and lies at the basis of the security of quantum cryptographic protocols7. In this framework, a partial measurement approach can be adopted to extract only a limited amount of information from the quantum system at the cost of limited induced disturbance89101112. Such partial measurement technique allows to perform consecutive observations (i.e. sequential measurements) on the same quantum system in order to investigate its properties without destroying it131415161718192021. In such context a question arises whether it is possible to extract an optimal amount of information from sequential measurements, compared to the degree of disturbance induced on the system. The aim of this paper is to investigate experimentally the trade-off between information gained and disturbance induced by partial sequential measurements on a quantum system22. Conceptually our experiment is similar to a double-slit experiment Fig. 1-a where the which-way information is acquired via successive measurements on the same particle. In particular we implement two sequential measurements performed on the same quantum system and observe that the optimal trade-off that characterizes the single measurement can be retrieved by adopting a proper adaptive strategy. Such result, observed for N = 2 sequential measurements, can be extended for any value of N.

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