Related papers: $T\bar{T}$ Deformation and the Complexity=Volume C…
This work is originally a Cambridge Part III essay paper. Quantum complexity arises as an alternative measure to the Fubini metric between two quantum states. Given two states and a set of allowed gates, it is defined as the least complex…
We study a quantum theory based on two assumptions: In the intrinsic frame of reference of an isolated, macroscopic system, (i) the system has no global motion and is not entangled with any other system, (ii) time evolution of statevectors…
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…
State conversion generalizes query complexity to the problem of converting between two input-dependent quantum states by making queries to the input. We characterize the complexity of this problem by introducing a natural…
It was recently shown that the theory obtained by deforming a general two dimensional conformal theory by the irrelevant operator $T\bar T$ is solvable. In the context of holography, a large class of such theories can be obtained by…
Within framework of the quantum calculus, we represent the partition function and the mass exponent of a multifractal, as well as the average of random variables distributed over self-similar set, on the basis of the deformed expansion in…
The concept of quantum complexity has far-reaching implications spanning theoretical computer science, quantum many-body physics, and high energy physics. The quantum complexity of a unitary transformation or quantum state is defined as the…
We describe a deformation of the observable algebra of quantum gravity in which the loop algebra is extended to framed loops. This allows an alternative nonperturbative quantization which is suitable for describing a phase of quantum…
We explore the holographic duality between string theory in backgrounds that interpolate between asymptotically linear dilaton spacetime in the UV and $AdS_3$ in the IR, and single-trace $T\bar T$ deformed CFT. In particular, we explain how…
The ER=EPR conjecture states that quantum entanglement between boundary degrees of freedom leads to the emergence of bulk spacetime itself. Although this has been tested extensively in String Theory for asymptotically anti-de Sitter…
Based on the complexity equals action (CA) and complexity equals volume (CV) conjectures, we investigate the holographic complexity of a slowly accelerating Kerr-AdS black hole in the bulk Einstein gravity theory which is dual to…
The paper has heuristic character. The conceptual frame, based on the assumption of quantum uncertainty only, has been formerly introduced in two papers [S. Tosto, Il Nuovo Cimento B, vol. 111, n.2, 1996 and S. Tosto, Il Nuovo Cimento D,…
Complex numbers are widely used in both classical and quantum physics, and are indispensable components for describing quantum systems and their dynamical behavior. Recently, the resource theory of imaginarity has been introduced, allowing…
Important characteristics of the loop approach to quantum gravity are a specific choice of the algebra A of observables and of a representation of A on a measure space over the space of generalized connections. This representation is…
We present a conjecture for the exact expression of finite volume expectation values in excited states in integrable quantum field theories, which is an extension of an earlier conjecture to the case of general diagonal factorized…
A argument is described for how deformed or doubly special relativity may arise in the semiclassical limit of a quantum theory of gravity. We consider a generic quantum theory of gravity coupled to matter, from which we use only the…
Duality transformations within the quantum mechanics of a finite number of degrees of freedom can be regarded as the dependence of the notion of a quantum, i.e., an elementary excitation of the vacuum, on the observer on classical phase…
We study the holographic complexity conjectures for rotating black holes, uncovering a relationship between the complexity of formation and the thermodynamic volume of the black hole. We suggest that it is the thermodynamic volume and not…
We initiate a study of the complexity of quantum field theories (QFTs) by proposing a measure of information contained in a QFT and its observables. We show that from minimal assertions, one is naturally led to measure complexity by two…
The present work is a natural continuation of the previous paper arXiv:0911.5597. In this work, within the scope of the Generalized Uncertainty Principle, a model of the high energy deformation for a particular case of Einstein's equations…