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Experimental violation and reformulation of the Heisenberg's error-disturbance uncertainty relation.

Baek SY, Kaneda F, Ozawa M, Edamatsu K - Sci Rep (2013)

Bottom Line: However, Ozawa in 1988 showed a model of position measurement that breaks Heisenberg's relation and in 2003 revealed an alternative relation for error and disturbance to be proven universally valid.Here, we report an experimental test of Ozawa's relation for a single-photon polarization qubit, exploiting a more general class of quantum measurements than the class of projective measurements.The test is carried out by linear optical devices and realizes an indirect measurement model that breaks Heisenberg's relation throughout the range of our experimental parameter and yet validates Ozawa's relation.

View Article: PubMed Central - PubMed

Affiliation: Research Institute of Electrical Communication, Tohoku University, Sendai 980-8577, Japan.

ABSTRACT
The uncertainty principle formulated by Heisenberg in 1927 describes a trade-off between the error of a measurement of one observable and the disturbance caused on another complementary observable such that their product should be no less than the limit set by Planck's constant. However, Ozawa in 1988 showed a model of position measurement that breaks Heisenberg's relation and in 2003 revealed an alternative relation for error and disturbance to be proven universally valid. Here, we report an experimental test of Ozawa's relation for a single-photon polarization qubit, exploiting a more general class of quantum measurements than the class of projective measurements. The test is carried out by linear optical devices and realizes an indirect measurement model that breaks Heisenberg's relation throughout the range of our experimental parameter and yet validates Ozawa's relation.

No MeSH data available.


Experimental setup to test the error-disturbance relation.ND (neutral density filter), Pol. (vertical polarizer), and WP (wave plates) prepare the initial polarization qubit /ψ〉. Pol. or HWP is inserted to prepare Z/ψ〉, (Z + I)/ψ〉, X/ψ〉, and (X + I)/ψ〉. VBS(t,r) is realized by using a pair of HWPs and a PBS. A HWP at an angle of 22.5° and a PBS are used to carry out the projective measurement of X.
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f3: Experimental setup to test the error-disturbance relation.ND (neutral density filter), Pol. (vertical polarizer), and WP (wave plates) prepare the initial polarization qubit /ψ〉. Pol. or HWP is inserted to prepare Z/ψ〉, (Z + I)/ψ〉, X/ψ〉, and (X + I)/ψ〉. VBS(t,r) is realized by using a pair of HWPs and a PBS. A HWP at an angle of 22.5° and a PBS are used to carry out the projective measurement of X.

Mentions: In our experiment, both the system and the probe are qubits, called the signal qubit and the probe qubit. Let X, Y, and Z be the Pauli matrices; /0〉 and /1〉 denote the eigenstates of Z with eigenvalues +1 and −1, respectively. The measurement is carried out by an interaction U between the signal qubit and the probe qubit initialized in the state /ξ〉 = /0′〉; we use the prime symbol for probe observables and probe states, when a distinction is necessary. We take the meter observable M in the probe as M = Z′. The measurement operators Mm = 〈m′/U/0′〉 with m = 0, 1 describe the measurement as In this paper, we employ a general form of measurement given as where 0 ≤ θ ≤ π/4 (See Supplementary Information). The measurement strength s of this measurement is quantified by s = cos 2θ = cos2θ − sin2θ, varying from unity at the full-strength measurement (θ = 0) to zero at the weakest measurement (θ = π/4). The positive operator valued measure (POVM) elements corresponding to the outcomes λ0 = 1, λ1 = −1 are A theoretically simple procedure (quantum circuit) to realize the generalized measurement given in (7) and (8) is shown in Fig. 2 (a). In our experiment, as described later, to realize this measurement we employ a different procedure shown in Fig. 2 (b) that is optically implemented as in Fig. 3. Note that both circuits provide the same measurement operators defined in (7) and (8) for the probe input state /0′〉, although the explicit interactions are different (See Supplementary Information). This optical implementation was previously introduced by Baek, Cheong, and Kim26. The same measurement was proposed by Lund and Wiseman23 for testing Ozawa's relation using the “weak-measurement technique.”


Experimental violation and reformulation of the Heisenberg's error-disturbance uncertainty relation.

Baek SY, Kaneda F, Ozawa M, Edamatsu K - Sci Rep (2013)

Experimental setup to test the error-disturbance relation.ND (neutral density filter), Pol. (vertical polarizer), and WP (wave plates) prepare the initial polarization qubit /ψ〉. Pol. or HWP is inserted to prepare Z/ψ〉, (Z + I)/ψ〉, X/ψ〉, and (X + I)/ψ〉. VBS(t,r) is realized by using a pair of HWPs and a PBS. A HWP at an angle of 22.5° and a PBS are used to carry out the projective measurement of X.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3713528&req=5

f3: Experimental setup to test the error-disturbance relation.ND (neutral density filter), Pol. (vertical polarizer), and WP (wave plates) prepare the initial polarization qubit /ψ〉. Pol. or HWP is inserted to prepare Z/ψ〉, (Z + I)/ψ〉, X/ψ〉, and (X + I)/ψ〉. VBS(t,r) is realized by using a pair of HWPs and a PBS. A HWP at an angle of 22.5° and a PBS are used to carry out the projective measurement of X.
Mentions: In our experiment, both the system and the probe are qubits, called the signal qubit and the probe qubit. Let X, Y, and Z be the Pauli matrices; /0〉 and /1〉 denote the eigenstates of Z with eigenvalues +1 and −1, respectively. The measurement is carried out by an interaction U between the signal qubit and the probe qubit initialized in the state /ξ〉 = /0′〉; we use the prime symbol for probe observables and probe states, when a distinction is necessary. We take the meter observable M in the probe as M = Z′. The measurement operators Mm = 〈m′/U/0′〉 with m = 0, 1 describe the measurement as In this paper, we employ a general form of measurement given as where 0 ≤ θ ≤ π/4 (See Supplementary Information). The measurement strength s of this measurement is quantified by s = cos 2θ = cos2θ − sin2θ, varying from unity at the full-strength measurement (θ = 0) to zero at the weakest measurement (θ = π/4). The positive operator valued measure (POVM) elements corresponding to the outcomes λ0 = 1, λ1 = −1 are A theoretically simple procedure (quantum circuit) to realize the generalized measurement given in (7) and (8) is shown in Fig. 2 (a). In our experiment, as described later, to realize this measurement we employ a different procedure shown in Fig. 2 (b) that is optically implemented as in Fig. 3. Note that both circuits provide the same measurement operators defined in (7) and (8) for the probe input state /0′〉, although the explicit interactions are different (See Supplementary Information). This optical implementation was previously introduced by Baek, Cheong, and Kim26. The same measurement was proposed by Lund and Wiseman23 for testing Ozawa's relation using the “weak-measurement technique.”

Bottom Line: However, Ozawa in 1988 showed a model of position measurement that breaks Heisenberg's relation and in 2003 revealed an alternative relation for error and disturbance to be proven universally valid.Here, we report an experimental test of Ozawa's relation for a single-photon polarization qubit, exploiting a more general class of quantum measurements than the class of projective measurements.The test is carried out by linear optical devices and realizes an indirect measurement model that breaks Heisenberg's relation throughout the range of our experimental parameter and yet validates Ozawa's relation.

View Article: PubMed Central - PubMed

Affiliation: Research Institute of Electrical Communication, Tohoku University, Sendai 980-8577, Japan.

ABSTRACT
The uncertainty principle formulated by Heisenberg in 1927 describes a trade-off between the error of a measurement of one observable and the disturbance caused on another complementary observable such that their product should be no less than the limit set by Planck's constant. However, Ozawa in 1988 showed a model of position measurement that breaks Heisenberg's relation and in 2003 revealed an alternative relation for error and disturbance to be proven universally valid. Here, we report an experimental test of Ozawa's relation for a single-photon polarization qubit, exploiting a more general class of quantum measurements than the class of projective measurements. The test is carried out by linear optical devices and realizes an indirect measurement model that breaks Heisenberg's relation throughout the range of our experimental parameter and yet validates Ozawa's relation.

No MeSH data available.