We construct a dynamical map which is not positive divisible and does present information backflow either (as measured by trace norm quantifiers). It formulated for qutrit system undergoing noninvertible dynamics. This provides an evidence that the two definitions of quantum Markovianity based on absence divisibility are nonequivalent general maps.

We show that the quantum SAT problem is QMA1-complete when restricted to interactions between a three-dimensional particle and a five-dimensional particle. The best previously known result is for particles of dimensions 4 and 9. The main novel ingredient of our proof is a certain Hamiltonian construction named the Triangle Hamiltonian. It allows to verify the application of a 2-qubit CNOT gate ...

Abstract The existence of GHZ contradictions in many-qutrit systems was a long-standing theoretical question until it’s (affirmative) resolution in 2013. To enable experimental tests, we derive Mermin inequalities from concurrent observable sets identified in those proofs. These employ a weighted sum of observables, called M, in which every term has the chosen GHZ state as an eigenstate with ei...

It is well known that quantum entanglement plays very important roles in quantum information theory. One of the main tasks in quantum information theory is to find out how many different ways multipartite pure states can be entangled. It has been shown that entangled qudits are less affected by noise than entangled qubits [1, 2]. In quantum cryptography it is more secure against evesdropping at...

The choice of the best set of universal ternary gates for quantum circuits is an open problem. We create exact minimum cost ternary reversible gates with quantum multiplexers using the method of iterative deepening depth-first search (IDDFS) [25]. Such search is better for small problems than evolutionary algorithms or other search methods. Several new gates that are provably exact minimum cost...

Quantum Entanglement It has been shown that entanglement is not necessary for ancilla-assisted quantum process tomography. Surprisingly, by presenting two examples of two-qutrit entangled states, it found Cheng-Jie Zhang and co-workers in article number 2100550 there also exist some states which are useless Moreover, experimental verification performed on the IBM platform ibmq_athens.

It is shown that the E6(6) symmetric entropy formula describing black holes and black strings in D = 5 is intimately tied to the geometry of the generalized quadrangle GQ(2, 4) with automorphism group the Weyl group W (E6). The 27 charges correspond to the points and the 45 terms in the entropy formula to the lines of GQ(2, 4). Different truncations with 15, 11 and 9 charges are represented by ...

Classical communication through quantum channels may be enhanced by sharing entanglement. Superdense coding allows the encoding, and transmission, of up to two classical bits of information in a single qubit. In this paper, the maximum classical channel capacity for states that are not maximally entangled is derived. Particular schemes are then shown to attain this capacity, firstly for pairs o...