# Publications

**Authors: **Roman Krcmar, Andrej Gendiar, Peter Rapcan and Tomotoshi Nishino

**Year:** 2020

Thermodynamic properties of the four-dimensional cross-polytope model, the 16-cell model, which is an example of higher dimensional generalizations of the octahedron model, are studied on the square lattice. By means of the corner transfer matrix renormalization group (CTMRG) method, presence of the first-order phase transition is confirmed. The latent heat is estimated to be L 4=0.3172, which is larger than that of the octahedron model L 3=0.0516. The result suggests that the latent heat increases with the internal dimension n when the higher-dimensional series of the cross-polytope models is considered.

**Authors: **Michal Sedlák and Mário Ziman

**Year:** 2020

Probabilistic storage and retrieval (PSR) of unitary quantum dynamics is possible with exponentially small failure probability with respect to the number of systems used as a quantum memory [PRL 122, 170502 (2019)]. Here we study improvements due to a priori knowledge about the unitary transformation to be stored. In particular, we study N→1 PSR of qubit phase gates, i.e. qubit rotations a round Z axis with an unknown angle, and show that if we access the gate only N-times, the optimal probability of perfect retrieving of its single use is N/(N+1). We propose a quantum circuit realization for the optimal protocol and show that programmable phase gate [PRL 88, 047905 (2002)] can be turned into (2k−1)→1 optimal PSR of phase gates and requires only k CNOT gates, while having exponentially small failure probability in k.

**Authors: **Andrej Gendiar

**Year:** 2020

Magnetic properties of the transverse-field Ising model on curved (hyperbolic) lattices are studied by a tensor product variational formulation that we have generalized for this purpose. First, we identify the quantum phase transition for each hyperbolic lattice by calculating the magnetization. We study the entanglement entropy at the phase transition in order to analyze the correlations of various subsystems located at the center with the rest of the lattice. We confirm that the entanglement entropy satisfies the area law at the phase transition for fixed coordination number, i.e., it scales linearly with the increasing size of the subsystems. On the other hand, the entanglement entropy decreases as power-law with respect to the increasing coordination number.

**Authors: **Leevi Leppäjärvi and Michal Sedlák

**Year:** 2020

Studying sequential measurements is of the utmost importance to both the foundational aspects of quantum theory and the practical implementations of quantum technologies, with both of these applications being abstractly described by the concatenation of quantum instruments into a sequence of certain length. In general, the choice of instrument at any given step in the sequence can be conditionally chosen based on the classical results of all preceding instruments. For two instruments in a sequence we consider the conditional second instrument as an effective way of post-processing the first instrument into a new one. This is similar to how a measurement described by a positive operator-valued measure (POVM) can be post-processed into another by way of classical randomization of its outcomes using a stochastic matrix. In this work we study the post-processing relation of instruments and the partial order it induces on their equivalence classes. We characterize the greatest and the least element of this order, give examples of post-processings between different types of instruments and draw connections between post-processings of some of these instruments and their induced POVMs.

**Authors: **Sk Sazim, Michal Sedlak, Kratveer Singh and Arun Kumar Pati

**Year:** 2021

If two identical copies of a completely depolarizing channel are put into a superposition of their possible causal orders, they can transmit non-zero classical information. Here, we study how well we can transmit classical information with N depolarizing channels put in superposition of M causal orders via quantum SWITCH. We calculate Holevo quantity if the superposition uses only cyclic permutations of channels and find that it increases with M and it is independent of N. For a qubit it never reaches 1 if we are increasing M. On the other hand, the classical capacity decreases with the dimension d of the message system. Further, for N=3 and N=4 we studied superposition of all causal orders and uniformly superposed causal orders belonging to different cosets created by cyclic permutation subgroup.

**Authors: ** Natália S. Móller, Bruna Sahdo, Nelson Yokomizo

**Year:** 2020

We introduce a protocol for a quantum switch in the gravitational field of a spherical mass and determine the time interval required for its realization in the gravity of Earth. One of the agents that perform operations with indefinite order is a quantum system in a path superposition state. Entanglement between its proper time and position is explored as a resource for the implementation of the quantum switch. The realization of the proposed protocol would probe the physical regime described by quantum mechanics on curved spacetimes, which has not yet been explored experimentally.