Related papers: Comparing quantum complexity and quantum fidelity
Characterizing complexity and criticality in quantum systems requires diagnostics that are both computationally tractable and physically insightful. We apply a measure of quantum state complexity for n-qubit systems, defined as the…
Quantum fidelity is one of the most important measures of similarity between mixed quantum states. However, the usual formulation is cumbersome and hard to understand when encountering the first time. This work shows in a novel, elegant…
One of the most widespread methods to determine if a quantum state is entangled, or to quantify its entanglement dimensionality, is by measuring its fidelity with respect to a pure state. In this Letter we find a large class of states whose…
Characterizing entanglement in all but the simplest case of a two qubit pure state is a hard problem, even understanding the relevant experimental quantities that are related to entanglement is difficult. It may not be necessary, however,…
Recently developed quantum algorithms suggest that quantum computers can solve certain problems and perform certain tasks more efficiently than conventional computers. Among other reasons, this is due to the possibility of creating…
Computational complexity is a new quantum information concept that may play an important role in holography and in understanding the physics of the black hole interior. We consider quantum computational complexity for $n$ qubits using…
The computational complexity of a quantum state quantifies how hard it is to make. `Complexity geometry', first proposed by Nielsen, is an approach to defining computational complexity using the tools of differential geometry. Here we…
Quantum machine learning (QML) holds promise for accelerating pattern recognition, optimization, and data analysis, but the conditions under which it can truly outperform classical approaches remain unclear. Existing research often…
This paper defines a complexity between states in quantum field theory by introducing a Finsler structure based on ladder operators (the generalization of creation and annihilation operators). Two simple models are shown as examples to…
Beyond computer science, quantum complexity theory can potentially revolutionize multiple branches of physics, ranging from quantum many-body systems to quantum field theory. In this paper, we investigate the relationship between the sample…
A quantum system can be described and characterized by at least two different concepts, namely, its physical and informational properties. Here, we explicitly connect these two concepts, by equating the time-energy cost which is the product…
Quantum fidelity is a central tool in quantum information, quantifying how much two quantum states are similar. Here we propose a limit formula for the quantum fidelity between a mixed state and a pure state. As an example of an…
It is shown that the fidelity, a basic notion of quantum information science, may be used to characterize quantum phase transitions, regardless of what type of internal order is present in quantum many-body states. If the fidelity of two…
Applications of quantum technology often require fidelities to quantify performance. These provide a fundamental yardstick for the comparison of two quantum states. While this is straightforward in the case of pure states, it is much more…
We define predictive states and predictive complexity for quantum systems composed of distinct subsystems. This complexity is a generalization of entanglement entropy. It is inspired by the statistical or forecasting complexity of…
Although the foundations of quantum and classical physics are much different, it is often difficult to pinpoint which features of a particular system are intrinsically "quantum". Perhapse, the most clear-cut distinction between "classical"…
Assessing the quality of an ensemble of noisy entangled states is a central task in quantum information processing. Usually this is done by measuring and hence destroying multiple copies, from which state tomography or fidelity estimation…
While we have intuitive notions of structure and complexity, the formalization of this intuition is non-trivial. The statistical complexity is a popular candidate. It is based on the idea that the complexity of a process can be quantified…
Entanglement is the key resource for quantum technologies and is at the root of exciting many-body phenomena. However, quantifying the entanglement between two parts of a real-world quantum system is challenging when it interacts with its…
Quantum computational complexity estimates the difficulty of constructing quantum states from elementary operations, a problem of prime importance for quantum computation. Surprisingly, this quantity can also serve to study a completely…