We have experimentally demonstrated the interferometric complementarity, which relates the distinguishability D quantifying the amount of which-way (WW) information to the fringe visibility V characterizing the wave feature of a quantum entity, in a bulk ensemble by Nuclear Magnetic Resonance (NMR) techniques. We primarily concern on the intermediate cases: partial fringe visibility and incomplete WW information. We define D by an alternative formalism and investigate the relation between D and entanglement. By measuring D and V independently, it turns out that the duality relation D 2 + V 2 = 1 holds for pure quantum states of the markers.We have experimentally demonstrated the interferometric complementarity, which relates the distinguishability D quantifying the amount of which-way (WW) information to the fringe visibility V characterizing the wave feature of a quantum entity, in a bulk ensemble by Nuclear Magnetic Resonance (NMR) techniques. We primarily concern on the intermediate cases: partial fringe visibility and incomplete WW information. We define D by an alternative formalism and investigate the relation between D and entanglement. By measuring D and V independently, it turns out that the duality relation D 2 + V 2 = 1 holds for pure quantum states of the markers.

Jan 31, 200218 citations

Experimental demonstration of the interferometric complementarity of one- and two-particle interference in a bulk Nuclear Magnetic Resonance ensemble

Xinhua Peng, Zhu, Xiwen, Maili Liu +1 more

We analyze an interferometric complementarity between one- and two-particle interference in the general case: $V_{i}^{2}+V_{12}^{2}\leq 1$ $(i=1$ , $2)$ , and further examine the relation among one-particle interference visibility $V_{i}$ , two-particle interference visibility $V_{12}$ and the predication $P_{i}$ of the path of a single particle. An equality $V_{i}^{2}+V_{12}^{2}+P_{i}^{2}=1$ $(i=1$ , $2)$ is achieved for any pure two-particle source, which implies the condition of the complementarity relation to reach the upper bound and its relation to another interferometric complementarity between path information and interference visibility of a single particle. Meanwhile, the relationships of the complementarities and the entanglement $E$ of the composite system are also investigated. Using nuclear magnetic resonance techniques, the two-particle interferometric complementarity was experimentally tested with the ensemble-averaged spin states, including two extreme cases and an intermediate case.We analyze an interferometric complementarity between one- and two-particle interference in the general case: $V_{i}^{2}+V_{12}^{2}\leq 1$ $(i=1$, $2)$, and further examine the relation among one-particle interference visibility $V_{i}$, two-particle interference visibility $V_{12}$ and the predication $P_{i}$ of the path of a single particle. An equality $V_{i}^{2}+V_{12}^{2}+P_{i}^{2}=1$ $(i=1$, $2)$ is achieved for any pure two-particle source, which implies the condition of the complementarity relation to reach the upper bound and its relation to another interferometric complementarity between path information and interference visibility of a single particle. Meanwhile, the relationships of the complementarities and the entanglement $E$ of the composite system are also investigated. Using nuclear magnetic resonance techniques, the two-particle interferometric complementarity was experimentally tested with the ensemble-averaged spin states, including two extreme cases and an intermediate case.

arXiv:quant-ph/0208081Aug 13, 20020 citations

Experimental Test of Complementarity by Nuclear Magnetic Resonance Techniques

Xiwen Zhu, Ximing Fang, Xinhua Peng +3 more

We have tested complementarity for the ensemble-averaged spin states of nuclei $^{13}$ C in the molecule of $^{13}$ CHCl $_{3}$ by the use of the spin states of another nuclei $^{1}$ H as the path marker. It turns out that the wave-particle duality holds when one merely measures the probability density of quantum states, and that the wave- and particle-like behavior is simultaneously observed with the help of measuring populations and coherence in a single nuclear magnetic resonance(NMR) experiment. Effects of path-marking schemes and causes of the appearance and disappearance of the wave behavior are analysed.We have tested complementarity for the ensemble-averaged spin states of nuclei $^{13}$C in the molecule of $^{13}$CHCl$_{3}$ by the use of the spin states of another nuclei $^{1}$H as the path marker. It turns out that the wave-particle duality holds when one merely measures the probability density of quantum states, and that the wave- and particle-like behavior is simultaneously observed with the help of measuring populations and coherence in a single nuclear magnetic resonance(NMR) experiment. Effects of path-marking schemes and causes of the appearance and disappearance of the wave behavior are analysed.

arXiv:quant-ph/0011094Nov 22, 20000 citations

Quantification of complementarity in multiqubit systems

Xinhua Peng, Xiwen Zhu, Dieter Suter +3 more

Complementarity was originally introduced as a qualitative concept for the discussion of properties of quantum mechanical objects that are classically incompatible. More recently, complementarity has become a quantitative relation between classically incompatible properties, such as the visibility of interference fringes and ``which-way'' information, but also between purely quantum mechanical properties, such as measures of entanglement. We discuss different complementarity relations for systems of two-, three-, or $n$ qubits. Using nuclear magnetic resonance techniques, we have experimentally verified some of these complementarity relations in a two-qubit system.Complementarity was originally introduced as a qualitative concept for the discussion of properties of quantum mechanical objects that are classically incompatible. More recently, complementarity has become a quantitative relation between classically incompatible properties, such as the visibility of interference fringes and ``which-way'' information, but also between purely quantum mechanical properties, such as measures of entanglement. We discuss different complementarity relations for systems of two-, three-, or $n$ qubits. Using nuclear magnetic resonance techniques, we have experimentally verified some of these complementarity relations in a two-qubit system.

arXiv:quant-ph/0507183Physical Review ANov 16, 200556 citations

Fringe Visibility and Which-Way Information in an Atom Interferometer

Stephan Dürr, T. Nonn, Gerhard Rempe

We experimentally investigate the reduction of the fringe visibility in an atom interferometer due to the storage of which-way information. We focus on the case of incomplete which-way information and use the distinguishability $D$ to quantify how much information is stored. For a given value of $D$ , the fringe visibility $V$ is limited by the duality relation ${D}^{2}{+V}^{2}\ensuremath{\le}1$. We have measured $D$ and $V$ independently. Combining the results, we find good agreement with the duality relation.We experimentally investigate the reduction of the fringe visibility in an atom interferometer due to the storage of which-way information. We focus on the case of incomplete which-way information and use the distinguishability $D$ to quantify how much information is stored. For a given value of $D$, the fringe visibility $V$ is limited by the duality relation ${D}^{2}{+V}^{2}\ensuremath{\le}1$. We have measured $D$ and $V$ independently. Combining the results, we find good agreement with the duality relation.

Physical Review LettersDec 28, 1998204 citations

Experimental testing of complementarity for ensemble-averaged spin states

Xiwen Zhu, Ximing Fang, Xinhua Peng +3 more

We tested wave-particle duality with the ensemble-averaged spin states of 13 C nuclei in 13 CHCl 3 using the spin states of 1 H nuclei as the path marker. It turns out that wave-particle duality holds when one merely measures the probability density of quantum states, and that wave- and particle-like behaviour is simultaneously observed when measuring populations and coherences in a single nuclear magnetic resonance experiment. The effects of path-marking schemes and the causes of the appearance and disappearance of wave behaviour are analysed.We tested wave-particle duality with the ensemble-averaged spin states of 13 C nuclei in 13 CHCl 3 using the spin states of 1 H nuclei as the path marker. It turns out that wave-particle duality holds when one merely measures the probability density of quantum states, and that wave- and particle-like behaviour is simultaneously observed when measuring populations and coherences in a single nuclear magnetic resonance experiment. The effects of path-marking schemes and the causes of the appearance and disappearance of wave behaviour are analysed.

Journal of Physics B Atomic Molecular and Optical PhysicsNov 13, 200110 citations

We analyze an interferometric complementarity between one- and two-particle interference in the general case:

V_{i}^{2}+V_{12}^{2}\leq 1

(i=1

2)

, and further examine the relation among one-particle interference visibility

V_{i}

, two-particle interference visibility

V_{12}

and the predication

P_{i}

of the path of a single particle. An equality

V_{i}^{2}+V_{12}^{2}+P_{i}^{2}=1

(i=1

2)

is achieved for any pure two-particle source, which implies the condition of the complementarity relation to reach the upper bound and its relation to another interferometric complementarity between path information and interference visibility of a single particle. Meanwhile, the relationships of the complementarities and the entanglement

E

of the composite system are also investigated. Using nuclear magnetic resonance techniques, the two-particle interferometric complementarity was experimentally tested with the ensemble-averaged spin states, including two extreme cases and an intermediate case.

We have tested complementarity for the ensemble-averaged spin states of nuclei

^{13}

C in the molecule of

^{13}

CHCl

_{3}

by the use of the spin states of another nuclei

^{1}

H as the path marker. It turns out that the wave-particle duality holds when one merely measures the probability density of quantum states, and that the wave- and particle-like behavior is simultaneously observed with the help of measuring populations and coherence in a single nuclear magnetic resonance(NMR) experiment. Effects of path-marking schemes and causes of the appearance and disappearance of the wave behavior are analysed.

n

qubits. Using nuclear magnetic resonance techniques, we have experimentally verified some of these complementarity relations in a two-qubit system.

D

to quantify how much information is stored. For a given value of

D

, the fringe visibility

V

is limited by the duality relation ${D}^{2}{+V}^{2}\ensuremath{\le}1$. We have measured

D

and

V

independently. Combining the results, we find good agreement with the duality relation.