Sensitive observables of quantum mechanics

Capasso, Vincenzo; Fortunato, Donato; Selleri, F.

doi:10.1007/bf00669912

Cited by 124 publications

(40 citation statements)

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“…[111,112,113] where it was shown that for every pure entangled state of two quantum systems is possible to find pairs of observables whose correlations violate some specific Bell inequality. For example, the two photons maximally polarisation -entangled state |ψ = |H |H +|V |V √ 2…”

Section: Quantum States Violating Bell Inequalitiesmentioning

confidence: 99%

“…iv) Single atom entangled with single photon [381]. Where atomic, hyperfine levels of a trapped 111 Cd + ion, and photonic, polarisation, degrees of freedom are probabilistically entangled following a spontaneous emission of a photon from an atomic excited state. A value S = 2.203 ± 0.028 was observed.…”

Section: Test Of Local Realism With Other Physical Systems Than Photonsmentioning

confidence: 99%

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Research on hidden variable theories: A review of recent progresses

2005

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Quantum Mechanics (QM) is one of the pillars of modern physics: an impressive amount of experiments have confirmed this theory and many technological applications are based on it. Nevertheless, at one century since its development, various aspects concerning its very foundations still remain to be clarified. Among them, the transition from a microscopic probabilistic world into a macroscopic deterministic one and quantum non-locality. A possible way out from these problems would be if QM represents a statistical approximation of an unknown deterministic theory.This review is addressed to present the most recent progresses on the studies related to Hidden Variable Theories (HVT), both from an experimental and a theoretical point of view, giving a larger emphasis to results with a direct experimental application.More in details, the first part of the review is a historical introduction to this problem. The Einstein-Podolsky-Rosen argument and the first discussions about HVT are introduced, describing the fundamental Bell's proposal for a general experimental test of every Local HVT and the first attempts to realise it.The second part of the review is devoted to elucidate the recent progresses toward a conclusive Bell inequalities experiment obtained with entangled photons and other physical systems.Finally, the last sections are targeted to shortly discuss Non-Local HVT.1

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Section: Quantum States Violating Bell Inequalitiesmentioning

confidence: 99%

Section: Test Of Local Realism With Other Physical Systems Than Photonsmentioning

confidence: 99%

Research on hidden variable theories: A review of recent progresses

2005

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“…However, only for pure states the entanglement always 4 results in a violation of the Bell inequality. In contrast, some mixed entangled two-qubit states (as we will see, most of them) do not violate the Bell inequality, 5 though they may still exhibit nonlocality in other ways.…”

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confidence: 99%

Bell-inequality violation versus entanglement in the presence of local decoherence

Kofman

Korotkov

2008

Phys. Rev. A

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We analyze the effect of local decoherence of two qubits on their entanglement and the Bell inequality violation. Decoherence is described by Kraus operators, which take into account dephasing and energy relaxation at an arbitrary temperature. We show that in the experiments with superconducting phase qubits the survival time for entanglement should be much longer than for the Bell inequality violation.PACS numbers: 03.65. Ud; 03.65.Yz; 85.25.Cp Entanglement of separated systems is a genuine quantum effect and an essential resource in quantum information processing.1 Experimentally, a convincing evidence of a two-qubit entanglement is a violation of the Bell inequality 2 in its Clauser-Horne-Shimony-Holt 3 (CHSH) form. However, only for pure states the entanglement always 4 results in a violation of the Bell inequality. In contrast, some mixed entangled two-qubit states (as we will see, most of them) do not violate the Bell inequality, 5 though they may still exhibit nonlocality in other ways. 6Distinction between entanglement and Bell-inequality violation, in its relevance to experiments with superconducting phase qubits, 7 is the subject of our paper. The two-qubit entanglement is usually characterized by the concurrence 8 C or by the entanglement of formation, 9 which is a monotonous function 8 of C. Nonentangled states have C = 0, while C = 1 corresponds to maximally entangled states. There is a straightforward way 8 to calculate C for any two-qubit density matrix ρ. The Bell inequality in the CHSH form 3 is |S| ≤ 2, whereand E( a, b) is the correlator of results (±1) for measurement of two qubits (pseudospins) along directions a and b. This inequality should be satisfied by any local hidden-variable theory, while in quantum mechanics it is violated up to |S| = 2 √ 2 for maximally entangled (e.g., spin-zero) states. Mixed states produce smaller violation (if any), and there is a straightforward way 10 to calculate the maximum value S + of |S| for any two-qubit density matrix.For states with a given concurrence C, there is an exact bound 11 for S + : 2 √ 2C ≤ S + ≤ 2 √ 1 + C 2 (we consider only S + > 2), so that the Bell inequality violation is guaranteed if C > 1/ √ 2. For any pure state the upper bound is reached: S + = 2 √ 1 + C 2 , so that non-zero entanglement always leads to S + > 2. The distinction between entanglement and Bell inequality violation has been well studied for so-called Werner states 5 which have the form ρ = f ρ s + (1 − f )ρ mix , where ρ s denotes the maximally entangled (singlet) state, and ρ mix = 1/4 is the density matrix of the completely mixed state. The Werner state is entangled for 5 f > 1/3, while it violates the Bell inequality only when 10 f > 1/ √ 2. The Werner states, however, are not relevant to most of experiments (including those with superconducting phase qubits 7 ), in which an initially pure state becomes mixed due to decoherence (Werner states are produced due to so-called depolarizing channel 1 ). Recently a number of authors have analyzed effects of qubit decohe...

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“…It has been shown in Capasso et al (1973) that essentially the left-hand side of (1.2) is a sensitive observable, since all state vectors of the first type always satisfy the inequality (1.2).…”

Section: Introductionmentioning

confidence: 98%

“…The distinction between these two types of state vectors has received increasing attention in recent years (D'Espagnat, 1965;Jammer, 1974;Jauch, A concept useful to the experimental distinction between the two types of vectors is that of sensitive observables, which are defined as those observables whose expectation value over a statistical ensemble of Nidentical pairs of systems S + T is different according to whether the N pairs are described by a mixture of state vectors of the first type, or by a state vector of the second type (Capasso et al, 1973).…”

Section: Introductionmentioning

confidence: 99%