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Peter Stelmachovic

Publications and source records attributed to Peter Stelmachovic.

8 recordsLinked to original sources
arXiv2006

Local control of remote entanglement

We address the problem of the generation of entanglement. We focus on the control of entanglement shared by two non-interacting parties $A$ and $C$ via interaction with a third party $B$. We show that, for certain physical models, it is possible to have an asymptotically complete control of the entanglement shared by $A$ and $C$ by changing parameters of the Hamiltonian local at site $B$. We present an example where different models (propositions) of physical situation, that lead to different descriptions of the system $B$, result into different amount entanglement produced. In the end we discuss limits of the procedure.

quant-ph↗
arXiv2006

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 multi-partite quantum states. We assume that the individual channels $Λ_j$ affect single-particle states so, that for an arbitrary input $ρ_j$, the distance $D_j (Λ_j [ ρ_j ], ρ_j)$ between the input $ρ_j$ and the output $Λ_j [ ρ_j ]$ of the channel is less than $ε$. Given this assumption we show that for an arbitrary {\em separable} two-partite state $ρ_{12}$ the distance between the input $ρ_{12}$ and the output $Λ_1\otimesΛ_2[ρ_{12} ]$ fulfills the bound $D_{12} (Λ_1 \otimes Λ_2 [ ρ_{12} ], ρ_{12}) \leq \sqrt{2+ 2 \sqrt{(1-1/d_1)(1-1/d_2)}} ε$ where $d_1$ and $d_2$ are dimensions of first and second quantum system respectively. On the contrary, entangled states are transformed in such a way, that the bound on the action of the local channels is $D_{12} (Λ_1 \otimes Λ_2 [ ρ_{12} ], ρ_{12}) \leq 2 \sqrt{2 - 1/d} \: ε$, 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 into two different bounds which in turn can be exploited for a discrimination between the two sets of states. We generalize our results to multi-partite channels.

quant-ph↗
arXiv2005

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 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 un-physical operations. In particular, we analyze the optimal approximation of the universal NOT gate as well as a physical approximation of a quantum nonlinear polarization rotation.

quant-ph↗
arXiv2004

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 is completely positive and simultaneously has a semigroup property. We analyze a 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 a process of an exponential decay and a process of decoherence can be derived from a collision-like model in which particular collisions are described by SWAP and controlled-NOT interactions, respectively.

quant-ph↗
arXiv2002

Quantum theory: kinematics, linearity and no-signaling condition

We show that the linearity of an evolution of Quantum Mechanics follows from the definition of kinematics. The same result is obtained for an arbitrary theory with the state space that includes mixtures of different preparations. Next, we formulate the non-signaling theorem and show that the theorem poses no additional restriction on Quantum Mechanics provided the kinematics is given. We also discuss validity of the postulate for the case of more general theories.

quant-ph↗
arXiv2002

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.

quant-ph↗
arXiv2001

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 whole 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 address the question: ``Under what conditions are the two states states, $\varrho$ and $σ$, 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 divided into two parts A and B, by unitary operations acting only on the systems A and B, separately.

quant-ph↗