Peter Štelmachovič

Dynamics of open quantum systems initially entangled with environment: Beyond the Kraus representation

We present a general analysis of the role of initial correlations between the open system and an environment on quantum dynamics of the open system.

Thermalizing Quantum Machines: Dissipation and Entanglement

We study the relaxation of a quantum system towards the thermal equilibrium using tools developed within the context of quantum information theory. We consider a model in which the system is a qubit, and reaches equilibrium after several successive two-qubit interactions (thermalizing machines) with qubits of a reservoir. We characterize completely the family of thermalizing machines. The model shows a tight link between dissipation, fluctuations, and the maximal entanglement that can be generated by the machines. The interplay of quantum and classical information processes that give rise to practical irreversibility is discussed.

Description of Quantum Dynamics of Open Systems Based on Collision-Like Models

Master equations in the Lindblad form describe evolution of open quantum systems that are completely positive and simultaneously have a semigroup property. We analyze the possibility to derive this type of master equations from an intrinsically discrete dynamics that is modelled as a sequence of collisions between a given quantum system (a qubit) with particles that form the environment. In order to illustrate our approach we analyze in detail how the process of an exponential decay and the process of decoherence can be derived from a collision-like model in which particular collisions are described by SWAP and controlled-NOT interactions, respectively.

Process reconstruction: From unphysical to physical maps via maximum likelihood

We show that the method of maximum likelihood (MML) provides us with an efficient scheme for the reconstruction of quantum channels from incomplete measurement data. By construction this scheme always results in estimations of channels that are completely positive. Using this property we use the MML for a derivation of physical approximations of unphysical operations. In particular, we analyze the optimal approximation of the universal NOT gate as well as the physical approximation of a quantum nonlinear polarization rotation.

Saturation of Coffman–Kundu–Wootters inequalities via quantum homogenization

We study how entanglement between an open system and a reservoir is established. The system is considered to be a qubit, while the reservoir is modelled as a collection of qubits. The system and the reservoir qubits interact via a sequence of partial-swap operations. This processes is called quantum homogenization since at the output the system as well as all reservoir qubits are in states that are, in a limit sense, equal to the original state of the reservoir qubits. We show that in this process the Coffman–Kundu–Wootters inequalities are saturated. This means that no intrinsic multi-partite entanglement is created.

On the Local Unitary Equivalence of States of Multi-partite Systems

Two pure states of a multi-partite system are alway are related by a unitary transformation acting on the Hilbert space of the hole system. This transformation involves multi-partite transformations. On the other hand some quantum information protocols such as the quantum teleportation and quantum dense coding are based on equivalence of some classes of states of bi-partite systems under the action of local (one-particle) unitary operations. In this paper we adress the question: Under what conditions are the two states states, Q and a, of a multi-partite system locally unitary equivalent? We present a set of conditions which have to be satisfied in order that the two states are locally unitary equivalent. In addition, we study whether it is possible to prepare a state of a multi-qudit system. Which is devided into two parts A and B, by unitary operations acting only on the systems A and B, separately.

Bounds on action of local quantum channels

We derive an upper bound on the action of a direct product of two quantum maps (channels) acting on bi-partite quantum states. We assume that the individual channelsj affect single-particle states so that for an arbitrary input ρj , the distance Dj (� j (ρj ) ,ρ j ) between the input ρj and the outputj (ρj ) of the channel is less than � . Given this assumption we show that for an arbitrary separable two-partite state ρ12, the distance between the input ρ12 and the output � 1 ⊗ � 2(ρ12) fulfils the bound D12(� 1 ⊗ � 2(ρ12) ,ρ 12) � 2+2 √ (1 − 1/d 1)(1 − 1/d2 )� where d1 and d2 are the dimensions of the first and second quantum system respectively. In contrast, entangled states are transformed in such a way that the bound on the action of the local channels is D12(� 1 ⊗ � 2(ρ12) ,ρ 12) 2 √ 2 − 1/d � , where d is the dimension of the smaller of the two quantum systems passing through the channels. Our results show that the fundamental distinction between the set of separable and the set of entangled states results in two different bounds which in turn can be exploited for discrimination between the two sets of states. We generalize our results to multi-partite channels.

Quantum safe with classical key: physics of open systems from the point view of information theory

We design a universal quantum homogenizer, which is a quantum machine that takes as an input a system qubit initially in the state ? and a set of N reservoir qubits initially prepared in the same state ?. In the homogenizer the system qubit sequentially interacts with the reservoir qubits via the partial swap transformation. The homogenizer realizes, in the limit sense, the transformation such that at the output each qubit is in an arbitratily small neighbourhood of the state ? irrespective of the initial states of the system and the reservoir qubits. This means that the system qubit undergoes an evolution that has a fixed point, which is the reservoir state ?. We also study approximate homogenization when the reservoir is composed of a finite set of identically prepared qubits. The homogenizer allows us to understand various aspects of the dynamics of open systems interacting with environments in non-equilibrium states. In particular, the reversibility vs or irreversibility of the dynamics of the open system is directly linked to specific (classical) information about the order in which the reservoir qubits interacted with the system qubit. This aspect of the homogenizer leads to a model of a quantum safe with a classical combination.We analyze in detail how entanglement between the reservoir and the system is created during the process of quantum homogenization. We show that the information about the initial state of the system qubit is stored in the entanglement between the homogenized qubits.