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Physical Review A

Precision requirements for observing macroscopic quantum effects

Tian Wang, Roohollah Ghobadi, Sadegh Raeisi, Christoph Simon

Published Dec 27, 2013• 40 citations
Publisher

Abstract

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 counterexample involving macroscopic coherent states and Kerr or higher-order nonlinearities, we find that while measurements with coarse outcomes can be sufficient, the phase control precision of the necessary nonlinear operations has to increase with the size of the system. This suggests a refined conjecture that either the outcome precision or the control precision of the measurements has to increase with system size.

DOI
10.1103/physreva.88.062114

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Recent advances in quantum technologies enabled us to make large quantum states \nand pushed towards examining quantum theory at the macroscopic level. However observation \nof quantum e ects at a macroscopic level still remains a demanding task. In this \nthesis we try to address one of the challenges and propose and explore some new solutions. \nOne of the obstacles for observation of macroscopic quantum e ects is the sensitivity \nto the measurement resolution. For many di erent cases, it has been observed that the \nprecision requirement for measuring quantum e ects increases with the system size. We \nformalize this as a conjecture that for observation of macroscopic quantum e ects, either \nthe outcome precision or the control precision of the measurements has to increase with \nsystem size. This indicates that the complexity of macroscopic quantum measurement \nincreases with the system size and sheds some lights on the quantum-to-classical transition \nat the macroscopic level. \nWe also introduce a technique to go around the sensitivity problem for observation \nof micro-macro entanglement. We propose that using a unitary deampli cation process, \none can bring the system back to the microscopic level where the measurements are less \ndemanding and quantum e ects are easier to verify. As the unitary processes do not change \nthe entanglement, this serves as a veri cation tool for micro-macro entanglement. \nWe also explored the connection between quantum e ects and thermodynamics of \nmacroscopic quantum systems for two speci c cases. For one, we investigated the e ect of \nentanglement in composite bosons and Bose-Einstein condensation. We showed that as the \nstate of the composite boson approaches a maximally entangled state, the condensation \nrate also approaches one. \nThe other case we considered was heat-bath algorithmic cooling. We found the cooling \nlimit of this class of thermodynamic transformations and showed that it decreases \nexponentially with the number of qubits. \nWe also developed an entropic version of Mermin's inequality. Here the idea is to \ndevelop a tool to reveal the entanglement in many-body quantum systems based on the \nentropy of the measurement outcomes. We introduce a new inequality that holds for locally \nrealistic models, yet can be violated with quantum measurements. One of the nice features \nof this inequality is that it can be violated maximally with quantum measurements. This \nresembles the GHZ paradox but for entropies of the measurement outcomes.

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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 counterexample involving macroscopic coherent states and Kerr or higher-order nonlinearities, we find that while measurements with coarse outcomes can be sufficient, the phase control precision of the necessary nonlinear operations has to increase with the size of the system. This suggests a refined conjecture that either the outcome precision or the control precision of the measurements has to increase with system size.
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.
Entangled coherent states, which can in principle be created using strong Kerr non-linearities, allow the violation of Bell inequalities for very coarse-grained measurements. This seems to contradict a recent conjecture that observing quantum effects in macroscopic systems generally requires very precise measurements. However, here we show that both the creation of the required states and the required measurements rely on being able to control the phase of the necessary Kerr-nonlinearity based unitary operations with extreme precision. This lends support to the idea that there is a general principle that makes macroscopic quantum effects difficult to observe, even in the absence of decoherence.
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.
The possibility to observe quantum features at the macroscopic level stands out as one of the most challenging yet fascinating open questions in modern quantum physics. The difficulties inherent in such a quest are manifold. First, the unavoidable interaction with the surrounding environment lies deeply at the roots of the loss of coherence and corruption of quantum correlations in a quantum state, being more severe as the size of the system being studied grows. Second, one faces the debated problem of achieving a measurement-precision that is sufficient to observe quantum effects at such macro-scales. Recent studies have shown that, depending on the Hamiltonian models, classicality may emerge from the coarse-graininess of measurements performed over a quantum system.
Recent advances in quantum technologies enabled us to make large quantum states \nand pushed towards examining quantum theory at the macroscopic level. However observation \nof quantum e ects at a macroscopic level still remains a demanding task. In this \nthesis we try to address one of the challenges and propose and explore some new solutions. \nOne of the obstacles for observation of macroscopic quantum e ects is the sensitivity \nto the measurement resolution. For many di erent cases, it has been observed that the \nprecision requirement for measuring quantum e ects increases with the system size. We \nformalize this as a conjecture that for observation of macroscopic quantum e ects, either \nthe outcome precision or the control precision of the measurements has to increase with \nsystem size. This indicates that the complexity of macroscopic quantum measurement \nincreases with the system size and sheds some lights on the quantum-to-classical transition \nat the macroscopic level. \nWe also introduce a technique to go around the sensitivity problem for observation \nof micro-macro entanglement. We propose that using a unitary deampli cation process, \none can bring the system back to the microscopic level where the measurements are less \ndemanding and quantum e ects are easier to verify. As the unitary processes do not change \nthe entanglement, this serves as a veri cation tool for micro-macro entanglement. \nWe also explored the connection between quantum e ects and thermodynamics of \nmacroscopic quantum systems for two speci c cases. For one, we investigated the e ect of \nentanglement in composite bosons and Bose-Einstein condensation. We showed that as the \nstate of the composite boson approaches a maximally entangled state, the condensation \nrate also approaches one. \nThe other case we considered was heat-bath algorithmic cooling. We found the cooling \nlimit of this class of thermodynamic transformations and showed that it decreases \nexponentially with the number of qubits. \nWe also developed an entropic version of Mermin's inequality. Here the idea is to \ndevelop a tool to reveal the entanglement in many-body quantum systems based on the \nentropy of the measurement outcomes. We introduce a new inequality that holds for locally \nrealistic models, yet can be violated with quantum measurements. One of the nice features \nof this inequality is that it can be violated maximally with quantum measurements. This \nresembles the GHZ paradox but for entropies of the measurement outcomes.