What is the most significant problem that we face in practical quantum mechanics? Isn’t it accuracy of the measurements?
Heisenberg’s uncertainty principle redefined the field of metrology in 1927. According to uncertainty principle, the accuracy of values measured for a pair of physical quantities of a system is limited. That is, if the precision of the measurement of one of the quantities is high, then the accuracy of the measurement of the other physical quantity becomes small. Such pair of variables are called complementary or conjugate variables and the principle is also called complementarity.
What if I say that we can make measurements with more accuracy than that predicted by this celebrated principle? Probably, you will be thinking, “But, this principle is one of the underpinnings of quantum mechanics”. Well, we are not going to shake this foundation at all. We will use another quantum mechanical principle, Quantum Steering , to overcome this limitation.
Quantum steering is a non-classical correlation stronger than entanglement. The term was coined by Erwin Schrödinger in 1935. The phenomenon can be explained as follows.
Consider a system consisting of two particles. A measurement on the first particle allows us to make the prediction about the measurement on the second particle more precise even if the particles are far apart.
This phenomenon was actually first recognised and acknowledged by Albert Einstein, Boris Podolsky and Nathan Rosen in 1935. Evidently, this phenomenon violates the uncertainty principle. Therefore, they have seen this as a paradox doubting the validity of quantum mechanics, the most successful theory as of now. So, it is also known as Einstein-Podolsky-Rosen (EPR) paradox.
Quantum steering is a powerful resource in quantum information theory and quantum metrology. Let us see how this phenomenon is going to help in quantum metrology.
In an article published in Nature Communications, the researchers Benjamin Yadin, Matteo Fadel and Manuel Gessner revealed that they have formulated the EPR paradox in the framework of quantum metrology. They have formulated a steering condition in terms of Quantum Fisher Information (QFI). QFI is a tool for quantifying the accuracy in measurement of quantum parameters. Here, the complementary variables taken are phase shift (theta) and its generating Hamiltonian H . Information theoretic tools from quantum metrology were used in the formalism. They have illustrated their result with the help of two sample systems. One of them is a system composed of (N+1) qubits ( a qubit is a two state quantum mechanical system which can be defined with the principles of quantum mechanics). Among these (N+1) qubits, one is a single control qubit and the remaining N qubits are in a specific state namely, Greenberger-Horne-Zeilinger(GHZ) state. The other sample system taken here is an N-particle system over which (N/2) spin excitations are symmetrically distributed(a twin Fock state).
In 2018, the researchers measured quantum steering between two clouds containing hundreds of cold atoms each. This gave them the idea to formulate mathematically the EPR paradox to be used in metrology which is published through this paper. This discovery might pave the way for setting up sensing applications in quantum technology.
In a nutshell, the main result of the research is that the quantum steering can be used in quantum sensing applications to measure more accurately.
References :
Spooky Quantum Steering at a Distance for More Precise Measurements | SciTechDaily
Yadin, B., Fadel, M., & Gessner, M. (2021, April 23). Metrological complementarity reveals the Einstein-Podolsky-Rosen paradox. Nature Communications. doi:10.1038/s41467-021-22353-3
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