arXiv subjects
Publications and source records attributed to Mikolaj Czechlewski.
We consider violation of CHSH inequality for states before and after entanglement swapping. We present a pair of initial states which do not violate CHSH inequality however the final state violates CHSH inequality for some results of Bell measurements performed in order to swap entanglement.
We present an entanglement purification protocol for a mixture of a pure entangled state and a pure product state, which are orthogonal to each other. The protocol is combination of bisection method and one-way hashing protocol. We give recursive formula for the rate of the protocol for different states, i.e. the number of maximally entangled two-qubit pairs obtained with the protocol per a single copy of the initial state. We also calculate numerically the rate for some states.
The two observables are complementary if they cannot be measured simultaneously, however they become maximally complementary if their eigenstates are mutually unbiased. Only then the measurement of one observable gives no information about the other observable. The spin projection operators onto three mutually orthogonal directions are maximally complementary only for the spin 1/2. For the higher spin numbers they are no longer unbiased. In this work we examine the properties of spin 1 Mutually Unbiased Bases (MUBs) and look for the physical meaning of the corresponding operators. We show that if the computational basis is chosen to be the eigenbasis of the spin projection operator onto some direction z, the states of the other MUBs have to be squeezed. Then, we introduce the analogs of momentum and position operators and interpret what information about the spin vector the observer gains while measuring them. Finally, we study the generation and the measurement of MUBs states by introducing the Fourier like transform through spin squeezing. The higher spin numbers are also considered.
We discuss properties of probabilistic coding of two qubits to one qutrit and generalize the scheme to higher dimensions. We show that the protocol preservers entanglement between qubits to be encoded and environment and can be also applied to mixed states. We present the protocol which enables encoding of n qudits to one qudit of dimension smaller than the Hilbert space of the original system and then probabilistically but error-free decode any subset of k qudits. We give a formula for the probability of successful decoding.