Observing quantum effects such as superpositions and entanglement in macroscopic systems requires not only a system that is well protected against environmental decoherence, but also sufficient measurement precision. Motivated by recent experiments, we study the effects of coarse-graining in photon number measurements on the observability of micro-macro entanglement that is created by greatly amplifying one photon from an entangled pair. We compare the results obtained for a unitary quantum cloner, which generates micro-macro entanglement, and for a measure-and-prepare cloner, which produces a separable micro-macro state. We show that the distance between the probability distributions of results for the two cloners approaches zero for a fixed moderate amount of coarse-graining. Proving the presence of micro-macro entanglement therefore becomes progressively harder as the system size increases.
Observing quantum effects such as superpositions and entanglement in macroscopic systems requires not only a system that is well protected against environmental decoherence, but also sufficient measurement precision. Motivated by recent experiments, we study the effects of coarse-graining in photon number measurements on the observability of micro-macro entanglement that is created by greatly amplifying one photon from an entangled pair. We compare the results obtained for a unitary quantum cloner, which generates micro-macro entanglement, and for a measure-and-prepare cloner, which produces a separable micro-macro state. We show that the distance between the probability distributions of results for the two cloners approaches zero for a fixed moderate amount of coarse-graining. Proving the presence of micro-macro entanglement therefore becomes progressively harder as the system size increases.
Observing quantum effects such as superpositions and entanglement in macroscopic systems requires not only a system that is well protected against environmental decoherence, but also sufficient measurement precision. Motivated by recent experiments, we study the effects of coarse graining in photon number measurements on the observability of micro-macro entanglement that is created by greatly amplifying one photon from an entangled pair. We compare the results obtained for a unitary quantum cloner, which generates micro-macro entanglement, and for a measure-and-prepare cloner, which produces a separable micro-macro state. We show that the distance between the probability distributions of results for the two cloners approaches zero for a fixed moderate amount of coarse graining. Proving the presence of micro-macro entanglement therefore becomes progressively harder as the system size increases.
In recent years two fundamental aspects of quantum mechanics have attracted a great deal of interest, namely the investigation on the irreducible nonlocal properties of Nature implied by quantum entanglement and the physical realization of the 'Schroedinger Cat'. In the present work a macro - state consisting of about 3.5 x 10^4 photons in a quantum superposition and entangled with a far apart single - photon state is generated. Then, the non-separability of the overall micro-macro system is demonstrated and the corresponding Bell's inequalities are found to be violated. Precisely, an entangled photon pair is created by a nonlinear optical process, then one photon of the pair is injected into an optical parametric amplifier operating for any input polarization state, i.e. into a phase-covariant cloning machine. Such transformation establishes a connection between the single photon and the multi particle fields. We then demonstrate the non-separability of the bipartite system by adopting a local filtering technique within a positive operator valued measurement.
Macro-micro entanglement originates from the Schrodinger's Cat paradox. The paradox has been attracting the interest of the physicists since it was proposed. Schrodinger's Cat paradox is a thought experiment that entangles a cat with some decay atoms, in which the entanglement between the macroscopic object and the microscopic atoms is established. Mac-micro entanglement relates to some important problems in quantum physics. It is more likely to interact with the surroundings for the quantum system as its size increases, which is the reason why we hardly observe the macroscopic superposition state. Can the superposition state theory of quantum physics be used in macro domain? Is there a limitation to the scale for the objects in the superposition states? These questions need studying and verifying in experiment. In addition, the preparation of the macro-micro entanglement state provides a new possibility to study the decoherence model. Macro-micro entanglement can be realized in many physical systems, such as atomic ensembles, superconducting circuits, electro-mechanical and opto-mechanical systems. Here in this paper we will introduce the development of macro-micro entanglement in optical system. The initial approach to creating the macro-micro entanglement in the context of optical system is quantum cloning by simulating the emission. Then the quantum-injected optical parametric amplification is used to amplify single photon to a macroscopic level. Afterwards, the displacement in phase space is proposed to create the macro-micro entanglement. Since the photon number of the macro-micro entanglement with the optical parametric amplification approach can be about 104, the studies towards the detection of this type of entanglement with human eyes have been extensively conducted. But it is realized that the coarse-grained measurements, such as those with the human eye, generally cannot judge whether macro-micro entanglement exists, and hence cannot be used to prove the considered type of micro-macro entanglement. A way of overcoming this difficulty is to invert the amplification process, bringing the macro system back to the micro level. The entanglement can then be verified by using single-photon detectors. Because local operation and classical communication cannot create entanglement, the de-amplification process will not increase the entanglement and the presence of the entanglement in the end shows that entanglement is present between the amplification and de-amplification process. Inspired by this thought, two groups create and verify mac-micro entanglement between one photon and 108 photons. What they used to amplify the micro states is the displacement operation in phase space, which can be realized by combining a single photon state and a coherent state with a highly asymmetric beam splitter. Because the entanglement is a precondition for a secure quantum key distribution, and the macro-micro entanglement has more photons than the traditional micro entanglement, we will discuss the possibility whether the macro-micro entanglement can be used in quantum key distribution and improve the distance of the quantum key distribution. We point out that the mac-micro entanglement and the binary reverse reconciliation continuous variable quantum key distribution protocol are the same in physics essence. We will introduce a quantum key distribution scheme with two phase entangled coherent states. Although the security proof of the scheme is not complete, it still provides us with the possibility to use the macro-micro entanglement in quantum key distribution.
It has recently been conjectured that detecting quantum effects such as superposition or entanglement for macroscopic systems always requires high measurement precision. Analyzing an apparent counter-example involving macroscopic coherent states and Kerr non-linearities, we find that while measurements with coarse outcomes can be sufficient, the phase control precision of the necessary non-linear operations has to increase with the size of the system. This suggests a refined conjecture that either the {\it outcome precision} or the {\it control precision} of the measurements has to increase with system size.
The experimental verification of quantum features, such as entanglement, at large scales is extremely challenging because of environment-induced decoherence. Indeed, measurement techniques for demonstrating the quantumness of multiparticle systems in the presence of losses are difficult to define and, if not sufficiently accurate, they provide wrong conclusions. We present a Bell test where one photon of an entangled pair is amplified and then detected by threshold detectors, whose signals undergo postselection. The amplification is performed by a classical machine, which produces a fully separable micro-macro state. However, by adopting such a technique, one can surprisingly observe a violation of the CHSH inequality. This is due to the fact that ignoring the detection loophole, opened by the postselection and the system losses, can lead to misinterpretations, such as claiming the micro-macro entanglement in a setup where evidently there is not. By using threshold detectors and postselection, one can only infer the entanglement of the initial pair of photons, so micro-micro entanglement, as it is further confirmed by the violation of a non-separability criterion for bipartite systems. How to detect photonic micro-macro entanglement in the presence of losses with currently available technology remains an open question.
Glorious victories have been achieved when quantum theory (QT) is applied to microscopic systems. However, although there might be good reasons for us to believe that QT applies at the macroscopic level as well, to give a definite answer ”yes” there is still a long journey. If it does apply, a direct result is that it predicts highly counter-intuitive macroscopic quantum superpositions and entanglements, which we never experience in our daily lives. In this thesis we assume that QT applies to the macroscopic level, and try to find out why we never really observe macroscopic quantum effects. The thesis contains two projects, aiming at two reasons for the above problem. In the first project (Chapter 3 and 4), we show that the required resolution to observe macroscopic quantum effects increases with the size of the system, when both outcome precision and control precision are taken into account. This means that for really large quantum effects we need a very good measuring resolution to observe them, while what we usually do are coarse-grained measurements, whose resolutions are much lower. In the second project (Chapter 5), we try to deal with decoherence, another obstacle preventing us from observing macroscopic quantum effects. We propose to create and detect strong entanglement of micro-macro and macro-macro beams of photons with very weak cross Kerr nonlinearities that are obtainable by current technology. We analyze the entanglement under environmental decoherence with various methods, and show that strong entanglement can still be created and detected under decoherence. We hope that the above results will help to push the boundary of the realm of QT towards the macroscopic level.