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Hybrid non-locality test in a microscopic-macroscopic system

Nicolò Spagnolo, Chiara Vitelli, Mauro Paternostro, F. De Martini, Fabio Sciarrino

Published Dec 16, 2010• 2 citations
OpenAlex

Abstract

We investigate the feasibility of a non-locality test in a bipartite system composed of a single-photon and a multi-photon field that embodies the paradigm of a microscopic-macroscopic entangled state. We run an intrinsically hybrid test requiring polarization measurements on the microscopic part of the state and phase-space ones on the macroscopic counterpart. Our analysis shows that, under ideal conditions, maximal violation of a Bell-CHSH inequality is achievable regardless of the number of photons in the macroscopic part of the state. The difficulty in observing non-locality when losses and detection inefficiency are included can be overcome using a hybrid entanglement witness that allows to efficiently correct for losses in the few photon regime.

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We investigate the feasibility of a non-locality test in a bipartite system composed of a single-photon and a multi-photon field that embodies the paradigm of a microscopic-macroscopic entangled state. We run an intrinsically hybrid test requiring polarization measurements on the microscopic part of the state and phase-space ones on the macroscopic counterpart. Our analysis shows that, under ideal conditions, maximal violation of a Bell-CHSH inequality is achievable regardless of the number of photons in the macroscopic part of the state. The difficulty in observing non-locality when losses and detection inefficiency are included can be overcome using a hybrid entanglement witness that allows to efficiently correct for losses in the few photon regime.
We propose a hybrid approach to the experimental assessment of the genuine quantum features of a general system consisting of microscopic and macroscopic parts. We infer entanglement by combining dichotomic measurements on a bidimensional system and phase-space inference through the Wigner distribution associated with the macroscopic component of the state. As a benchmark, we investigate the feasibility of our proposal in a bipartite-entangled state composed of a single-photon and a multiphoton field. Our analysis shows that, under ideal conditions, maximal violation of a Clauser-Horne-Shimony-Holt-based inequality is achievable regardless of the number of photons in the macroscopic part of the state. The difficulty in observing entanglement when losses and detection inefficiency are included can be overcome by using a hybrid entanglement witness that allows efficient correction for losses in the few-photon regime.
Abstract Optical hybrid entanglement can be created between two qubits, one encoded in a single photon and another one in coherent states with opposite phases. It opens the path to a variety of quantum technologies, such as heterogeneous quantum networks, merging continuous- and discrete-variable encoding, and enabling the transport and interconversion of information. However, reliable characterization of the non-local nature of this quantum state is limited so far to full quantum state tomography. Here, we perform a thorough study of Clauser–Horne–Shimony–Holt Bell inequality tests, enabling practical verification of quantum nonlocality for optical hybrid entanglement. We show that a practical violation of this inequality is possible with simple photon number on/off measurements if detection efficiencies stay above 82%. Another approach, based on photon-number parity measurements, requires 94% efficiency but works well in the limit of higher photon populations. Both tests use no postselection of the measurement outcomes and they are free of the fair-sampling hypothesis. Our proposal paves the way to performing loophole-free tests using feasible experimental tasks such as coherent state interference and photon counting.
A Bell test is performed on a Micro‐Macroscopic photon system obtained by parametric amplification of a spin‐1 entangled photon state. The optical parametric amplification leads to the creation of a Micro‐Macroscopic entangled system consisting of N≃3.5×104. The performed Bell’s inequality non locality test involves the adoption of a positive operator valued measurement (POVM) strategy for a sharper identification of the amplified states. This is obtained through a local filtering technique and the experimental data are found to violate the Bell’s inequality albeit with a loophole similar to the detection efficiency one in photon counting experiments.
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.
We show that a Bell inequality test using an optical hybrid state between a polarized single photon and a coherent field can be highly robust against detection inefficiency. The Bell violation occurs until the efficiency becomes as low as 67% even though its degree becomes small as the detection efficiency degrades. We consider on/off and photon number parity measurements, respectively, for the Bell test and they result in the similar conditions. If the detection efficiency is higher than 98.68%, parity measurements give larger Bell violations close to Cirel'son's bound, while on/off measurements give larger but moderate violations for realistic values of detector efficiency. Experimental realization of our proposal seems feasible in the near future for the implementation of a loophole-free Bell inequality test.
The categorization of quantum states for composite systems as either separable or entangled, or alternatively as Bell local or Bell non-local states based on local hidden variable theory is outlined, focusing on simple bipartite systems. The significance of states demonstrating Bell non-locality for settling the long standing controversy between the Copenhagen interpretation of the quantum measurement process involving “collapse of the wave-function” and the alternative interpretation based on pre-existing hidden variables is emphasized. Although experiments demonstrating violations of Bell locality in microscopic systems have now been carried out, there is current interest in finding Bell non-locality in quantum systems on a macroscopic scale, since this is a regime where a classical hidden variable theory might still apply. Progress towards finding macroscopic quantum states that violate Bell inequalities is reviewed. A new test for Bell non-locality that applies when the sub-system measured quantities are spin components with large outcomes is described, and applied to four mode systems of identical massive bosons in Bose-Einstein condensates.