Related papers: Quantum Kolmogorov Complexity and Bounded Quantum …
We consider memoryless quantum communication protocols, where the two parties do not possess any memory besides their classical input and they take turns performing unitary operations on a pure quantum state that they exchange between them.…
We compare the classical Kolmogorov and quantum probability models. We show that the gap between these model is not so huge as it was commonly believed. The main structures of quantum theory (interference of probabilities, Born's rule,…
Quantum direct coding or Schumacher compression generalised the ideas of Shannon theory, gave an operational meaning to the von Neumann entropy and established the term qubit. But remembering that information processing is carried out by…
The purpose of this thesis is to give a formal definition of quantum Kolmogorov complexity (QC), and rigorous mathematical proofs of its basic properties. The definition used here is similar to that by Berthiaume, van Dam, and Laplante. It…
We consider the communication complexity of the binary inner product function in a variation of the two-party scenario where the parties have an a priori supply of particles in an entangled quantum state. We prove linear lower bounds for…
A fundamental task in modern cryptography is the joint computation of a function which has two inputs, one from Alice and one from Bob, such that neither of the two can learn more about the other's input than what is implied by the value of…
We propose a protocol for Alice to implement a multiqubit quantum operation from the restricted sets on distant qubits possessed by Bob, and then we investigate the communication complexity of the task in different communication scenarios.…
In Coles-Piani's recent remarkable version of the entropic uncertainty principle, the entropic sum is controlled by the first and second maximum overlaps between the two projective measurements. We generalize the entropic uncertainty…
The uncertainty principle is an important principle in quantum theory. Based on this principle, it is impossible to predict the measurement outcomes of two incompatible observables, simultaneously. Uncertainty principle basically is…
We show that classical and quantum Kolmogorov complexity of binary strings agree up to an additive constant. Both complexities are defined as the minimal length of any (classical resp. quantum) computer program that outputs the…
Since the seminal work of Paturi and Simon \cite[FOCS'84 & JCSS'86]{PS86}, the unbounded-error classical communication complexity of a Boolean function has been studied based on the arrangement of points and hyperplanes. Recently,…
We suggest implementation of quantum teleportation protocol of unknown qubit beyond Bell states formalism. Hybrid entangled state composed of coherent components that belong to Alice and dual-rail single photon at Bob disposal is used.…
Memory is the fundamental form of temporal complexity: when present but uncontrollable, it manifests as non-Markovian noise; conversely, if controllable, memory can be a powerful resource for information processing. Memory effects arise…
We consider the problem of the classical simulation of quantum measurements in the scenario of communication complexity. Regev and Toner (2007) have presented a 2-bit protocol which simulates one particular correlation function arising from…
Entropic uncertainty relations are universal quantifiers of fundamental uncertainties of quantum measurements and are widely discussed in the quantum metrology literature. Quantum memory is a phenomenon related to the specific type of…
Understanding temporal processes and their correlations in time is of paramount importance for the development of near-term technologies that operate under realistic conditions. Capturing the complete multi-time statistics defining a…
Consider two parties: Alice and Bob and suppose that Bob is given a qubit system in a quantum state $\phi$, unknown to him. Alice knows $\phi$ and she is supposed to convince Bob that she knows $\phi$ sending some test message. Is it…
Suppose Alice and Bob have access to two separated regions, respectively, of a system of electrons moving in the presence of a regular one-dimensional lattice of binding atoms. We consider the problem of communicating as much quantum…
Quantum resources may provide advantage over their classical counterparts. Theoretically, in certain tasks, this advantage can be very high. In this work, we construct such a task based on a game, mediated by Referee and played between…
Cumulative memory -- the sum of space used per step over the duration of a computation -- is a fine-grained measure of time-space complexity that was introduced to analyze cryptographic applications like password hashing. It is a more…