We propose a scheme for the observation of micro-macro entanglement in photon number based on amplifying and deamplifying a single-photon entangled state in combination with homodyne quantum state tomography. The created micro-macro entangled state, which exists between the amplification and deamplification steps, is a superposition of two components with mean photon numbers that differ by approximately a factor of three. We show that for reasonable values of photon loss it should be possible to detect micro-macro photon-number entanglement where the macrosystem has a mean number of one hundred photons or more.
We propose a scheme for the observation of micro-macro entanglement in photon number based on amplifying and deamplifying a single-photon entangled state in combination with homodyne quantum state tomography. The created micro-macro entangled state, which exists between the amplification and deamplification steps, is a superposition of two components with mean photon numbers that differ by approximately a factor of three. We show that for reasonable values of photon loss it should be possible to detect micro-macro photon-number entanglement where the macrosystem has a mean number of one hundred photons or more.
In this paper, using Wigner function (WF) method in phase space, we re-investigate micro–macro entanglement of a single-photon entangled state after one-sided amplification and de-amplification proposed by Simon’s group, and discuss the effects of the amplification and the loss. For the input–output process, we first build the relation between the input WF and the output WF. Next, the analytical expression of the output WF is derived related to the factors of the amplification and the loss. Finally, based on the above results, using the trace rule we also obtain the exact expressions of the detected probability and concurrence to quantify micro–macro entanglement, and analyze numerically the results. The results show that it is possible to detect micro–macro photon-number entanglement for reasonable values of photon loss.
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.
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.
In this work we present the realization of multiphoton quantum states, obtained by optical parametric amplification, and we investigate their perspectives and possible applications. The multiphoton quantum states are generated by a quantum-injected optical parametric amplifier (QI-OPA) seeded by a single-photon belonging to an EPR entangled pair. The entanglement between the micro-macroscopic photon system is experimentally demonstrated, and the possible applications of the macro-qubits states are presented and discussed.
We discuss the conclusions that can be drawn on a recent experimental micro-macro entanglement test [De Martini, Sciarrino, and Vitelli, Phys. Rev. Lett. 100, 253601 (2008)]. The system under investigation is generated through optical parametric amplification of one photon belonging to an entangled pair. The adopted entanglement criterion makes it possible to infer the presence of entanglement before losses that occur on the macrostate under a specific assumption. In particular, an a priori knowledge of the system that generates the micro-macro pair is necessary to exclude a class of separable states that can reproduce the obtained experimental results. Finally, we discuss the feasibility of a micro-macro ``genuine'' entanglement test on the analyzed system by considering different strategies, which show that in principle a fraction $\ensuremath{\varepsilon}$, proportional to the number of photons that survive the lossy process, of the original entanglement persists in any loss regime.
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.