Can one certify the preparation of a coherent, many-body quantum state? This is a fundamental question in the field of quantum mechanics. A group of researchers, Florian Fröwis, Maarten van den Nest, and Wolfgang Dür, have made significant progress in addressing this question with their research article titled “Certifiability Criterion for Large-Scale Quantum Systems.”
Within the realm of quantum systems, there is always a presence of noise and decoherence, which can hinder the accurate measurement and preparation of quantum states. The researchers propose a novel criterion to assess the fragility of large-scale quantum states based on the distinguishability of orthogonal states, even in the presence of small amounts of noise. States that fail to meet this criterion are termed “asymptotically incertifiable.”
What is the Certifiability Criterion for Large-Scale Quantum Systems?
The certifiability criterion for large-scale quantum systems introduced by Fröwis, van den Nest, and Dür enables the assessment of the fragility of quantum states. It determines the capability to certify the preparation of a coherent, many-body quantum state by conducting measurements with bounded accuracy, despite the presence of noise and decoherence.
This criterion examines the distinguishability of orthogonal states after the action of small amounts of noise. If a quantum state fails to meet the criterion, it is deemed asymptotically incertifiable. In other words, it becomes impossible to certify the preparation of such states with high accuracy due to the influence of noise and decoherence.
What are Asymptotically Incertifiable States?
Asymptotically incertifiable states are quantum states that cannot be certified with high accuracy due to the effects of noise and decoherence. The certifiability criterion introduced by Fröwis, van den Nest, and Dür identifies these states by measuring the distinguishability of orthogonal states after the application of small amounts of noise.
Interestingly, their research demonstrates that if a coherent quantum state is asymptotically incertifiable, there exists an incoherent mixture that is experimentally indistinguishable from the initial state. This mixture has an entropy of at least log 2, implying a high level of uncertainty and disorder in the quantum system.
Are Greenberger-Horne-Zeilinger States Asymptotically Incertifiable?
Yes, Greenberger-Horne-Zeilinger (GHZ) states are examples of quantum states that are asymptotically incertifiable. GHZ states represent an entangled quantum state involving multiple particles, where the state of each particle is correlated with the others.
The research article by Fröwis, van den Nest, and Dür establishes that GHZ states fail to meet the certifiability criterion and cannot be certified accurately. This means that the preparation of GHZ states is significantly hindered by the presence of noise and decoherence, making their certification challenging.
Are Macroscopic Superposition States Asymptotically Incertifiable?
Macroscopic superposition states, which are quantum states that exhibit superposition at a macroscopic scale, are indeed asymptotically incertifiable. These states involve the simultaneous existence of two or more distinct macroscopic states.
The research article provides a general proof that any so-called macroscopic superposition state fails to satisfy the certifiability criterion. This implies that the accurate certification of macroscopic superpositions is not possible due to the impact of noise and decoherence.
Quantum States Indistinguishable from Highly Incoherent Mixtures
The researchers also present examples of quantum states that are experimentally indistinguishable from highly incoherent mixtures. These states exhibit an almost-linear entropy in the number of qubits, showcasing a high level of disorder and randomness.
Such quantum states pose a unique challenge for certification since they can be easily mistaken for highly incoherent mixtures. The certifiability criterion helps identify these states, allowing researchers to differentiate between genuinely coherent quantum states and those that mimic incoherent mixtures.
Certifiability of Unique Ground States of Local Gapped Hamiltonians
The research article concludes by demonstrating that all unique ground states of local gapped Hamiltonians, regardless of the dimension, are certifiable. Ground states of local gapped Hamiltonians refer to stable states with low energy in quantum systems that satisfy locality conditions.
By establishing the certifiability of these ground states, the research provides valuable insights into the robustness and reliability of quantum systems. It validates the ability to accurately prepare and measure ground states in the presence of noise and decoherence, enhancing our understanding of large-scale quantum systems.
This research article by Fröwis, van den Nest, and Dür offers significant contributions to the field of quantum mechanics. By introducing the certifiability criterion for large-scale quantum systems, they enable the assessment of quantum state preparation in the presence of noise and decoherence. The identification of asymptotically incertifiable states and the certification of unique ground states of local gapped Hamiltonians further enhance our understanding of the complexities of quantum systems.
To further explore the intersection of quantum mechanics and computer science, you may find the article “From Cbits To Qbits: Teaching Computer Scientists Quantum Mechanics” intriguing. It offers insights into teaching computer scientists about the fundamental principles of quantum mechanics, bridging the gap between classical and quantum computing.
Source: Certifiability criterion for large-scale quantum systems
Further reading: From Cbits To Qbits: Teaching Computer Scientists Quantum Mechanics
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