arXiv subjects

Mario Ziman

Publications and source records attributed to Mario Ziman.

At least 55 records · Page 3Linked to original sources

arXiv2007

Optimality of private quantum channels

We addressed the question of optimality of private quantum channels. We have shown that the Shannon entropy of the classical key necessary to securely transfer the quantum information is lower bounded by the entropy exchange of the private quantum channel $\cal E$ and von Neumann entropy of the ciphertext state $\varrho^{(0)}$. Based on these bounds we have shown that decomposition of private quantum channels into orthogonal unitaries (if exists) is optimizing the entropy. For non-ancillary single qubit PQC we have derived the optimal entropy for arbitrary set of plaintexts. In particular, we have shown that except when the (closure of the) set of plaintexts contains all states, one bit key is sufficient. We characterized and analyzed all the possible single qubit private quantum channels for arbitrary set of plaintexts. For the set of plaintexts consisting of all qubit states we have characterized all possible approximate private quantum channels and we have derived the relation between the security parameter and the corresponding minimal entropy.

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arXiv2007

Entanglement measures: state ordering vs local operations

A set of all states of a bi-partite quantum system can be divided into subsets each of which contains states with the same degree of entanglement. In this paper we address a question whether local operations (without classical communication) affect the entanglement-induced state ordering. We show that arbitrary unilocal channel (i.e., a channel that acts on one sub-system of a bi-partite system only) might change the ordering for an arbitrary nontrivial measure of entanglement. A slightly weaker result holds for the maximally entangled states. In particular, the maximally entangled states might not remain the most entangled ones at the output of a unilocal noise channel.

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arXiv2007

Unambiguous coherent state identification: Searching a quantum database

We consider an unambiguous identification of an unknown coherent state with one of two unknown coherent reference states. Specifically, we consider two modes of an electromagnetic field prepared in unknown coherent states alpha_1 and alpha_2, respectively. The third mode is prepared either in the state alpha_1 or in the state alpha_2. The task is to identify (unambiguously) which of the two modes are in the same state. We present a scheme consisting of three beamsplitters capable to perform this task. Although we don't prove the optimality, we show that the performance of the proposed setup is better than the generalization of the optimal measurement known for a finite-dimensional case. We show that a single beamsplitter is capable to perform an unambiguous quantum state comparison for coherent states optimally. Finally we propose an experimental setup consisting of 2N-1 beamsplitters for unambiguous identification among N unknown coherent states. This setup can be considered as a search in a quantum database. The elements of the database are unknown coherent states encoded in different modes of an electromagnetic field. The task is to specify the two modes that are excited in the same, though unknown, coherent state.

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arXiv2006

Universality and optimality of programmable quantum processors

We analyze and compare the optimality of approximate and probabilistic universal programmable quantum processors. We define several characteristics how to quantify the optimality and we study in detail performance of three types of programmable quantum processors based on (1) the C-NOT gate, (2) the SWAP operation, and (3) the model of the quantum information distributor - the QID processor. We show under which conditions the measurement assisted QID processor is optimal. We also investigate optimality of the so-called U-processors and we also compare the optimal approximative implementation of U(1) qubit rotations with the known probabilistic implementation as introduced by Vidal, Masanes and Cirac [ {\em Phys. Rev. Lett.} {\bf 88}, 047905 (2002)].

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arXiv2006

Quantum process tomography: the role of initial correlations

We address the problem of quantum process tomography with the preparators producing states correlated with the environmental degrees of freedom that play role in the system-environment interactions. We discuss the physical situations, in which the dynamics is described by nonlinear, or noncompletely positive transformations. In particular, we show that arbitrary mapping $\varrho_{\rm in}\to\varrho_{\rm out}$ can be realized by using appropriate set of preparators and applying the unitary operation SWAP. The experimental ``realization'' of perfect NOT operation is presented. We address the problem of the verification of the compatibility of the preparator devices with the estimating process. The evolution map describing the dynamics in arbitrary time interval is known not to be completely positive, but still linear. The tomography and general properties of these maps are discussed.

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arXiv2006

Entanglement, purity and energy: Two qubits vs Two modes

We study the relationship between the entanglement, mixedness and energy of two-qubit and two-mode Gaussian quantum states. We parametrize the set of allowed states of these two fundamentally different physical systems using measures of entanglement, mixedness and energy that allow us to compare and contrast the two systems using a phase diagram. This phase diagram enables one to clearly identify not only the physically allowed states, but the set of states connected under an arbitrary quantum operation. We pay particular attention to the maximally entangled mixed states (MEMS) of each system. Following this we investigate how efficiently one may transfer entanglement from two-mode to two-qubit states.

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arXiv2006

Notes on optimality of direct characterisation of quantum dynamics

We argue that the claimed optimality of a new process tomography method suggested in [quant-ph/0601033] and [quant-ph/0601034] is based on not completely fair comparison that does not take into account the available information in an equal way. We also argue that the method is not a new process tomography scheme, but rather represents an interesting modification of ancilla assisted process tomography method. In our opinion these modifications require deeper understanding and further investigation.

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arXiv2005

Approximate programmable quantum processors

A quantum processor is a programmable quantum circuit in which both the data and the program, which specifies the operation that is carried out on the data, are quantum states. We study the situation in which we want to use such a processor to approximate a set of unitary operators to a specified level of precision. We measure how well an operation is performed by the process fidelity between the desired operation and the operation produced by the processor. We show how to find the program for a given processor that produces the best approximation of a particular unitary operation. We also place bounds on the dimension of the program space that is necessary to approximate a set of unitary operators to a specified level of precision.

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arXiv2005

Entanglement-induced state ordering under local operations

We analyze how entanglement between two components of a bipartite system behaves under the action of local channels of the form $\cE\otimes\cI$. We show that a set of maximally entangled states is by the action of $\cE\otimes\cI$ transformed into the set of states that exhibit the same degree of entanglement. Moreover, this degree represents an upper bound on entanglement that is available at the output of the channel irrespective what is the input state of the composite system. We show that within this bound the the entanglement-induced state ordering is ``relative'' and can be changed by the action of local channels. That is, two states $\varrho_1^{(in)}$ and $\varrho_2^{(in)}$ such that the entanglement $E[\varrho_1^{(in)}]$ of the first state is larger than the entanglement $E[\varrho_2^{(in)}]$ of the second state are transformed into states $\varrho_1^{(out)}$ and $\varrho_2^{(out)}$ such that $E[\varrho_2^{(out)}] > E[\varrho_1^{(out)}]$.

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arXiv2005

Towards quantum-based privacy and voting

The privacy of communicating participants is often of paramount importance, but in some situations it is an essential condition. A typical example is a fair (secret) voting. We analyze in detail communication privacy based on quantum resources, and we propose new quantum protocols. Possible generalizations that would lead to voting schemes are discussed.

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arXiv2005

Concurrence vs. purity: Influence of local channels on Bell states of two qubits

We analyze how a maximally entangled state of two-qubits (e.g., the singlet $ψ_s$) is affected by action of local channels described by completely positive maps $\cE$ . We analyze the concurrence and the purity of states $\varrho_\cE=\cE\otimes\cI[ψ_s]$.Using the concurrence-{\it vs}-purity phase diagram we characterize local channels $\cE$ by their action on the singlet state $ψ_s$. We specify a region of the concurrence-{\it vs.}-purity diagram that is achievable from the singlet state via the action of unital channels. We show that even most general (including non-unital) local channels acting just on a single qubit of the original singlet state cannot generate the maximally entangled mixed states (MEMS). We study in detail various time evolutions of the original singlet state induced by local Markovian semigroups. We show that the decoherence process is represented in the concurrence-{\it vs.}-purity diagram by a line that forms the lower bound of the achievable region for unital maps. On the other hand, the depolarization process is represented by a line that forms the upper bound of the region of maps induced by unital maps.

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arXiv2005

Limits and restrictions of private quantum channel

We study private quantum channels on a single qubit, which encrypt given set of plaintext states $P$. Specifically, we determine all achievable states $ρ^{(0)}$ (average output of encryption) and for each particular set $P$ we determine the entropy of the key necessary and sufficient to encrypt this set. It turns out that single bit of key is sufficient when the set $P$ is two dimensional. However, the necessary and sufficient entropy of the key in case of three dimensional $P$ varies continuously between 1 and 2 bits depending on the state $ρ^{(0)}$. Finally, we derive private quantum channels achieving these bounds. We show that the impossibility of universal NOT operation on qubit can be derived from the fact that one bit of key is not sufficient to encrypt qubit.

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arXiv2005

All (qubit) decoherences: Complete characterization and physical implementation

We investigate decoherence channels that are modelled as a sequence of collisions of a quantum system (e.g., a qubit) with particles (e.g., qubits) of the environment. We show that collisions induce decoherence when a bi-partite interaction between the system qubit and an environment (reservoir) qubit is described by the controlled-U unitary transformation (gate). We characterize decoherence channels and in the case of a qubit we specify the most general decoherence channel and derive a corresponding master equation. Finally, we analyze entanglement that is generated during the process of decoherence between the system and its environment.

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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.

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arXiv2004

Process reconstruction from incomplete and/or inconsistent data

We analyze how an action of a qubit channel (map) can be estimated from the measured data that are incomplete or even inconsistent. That is, we consider situations when measurement statistics is insufficient to determine consistent probability distributions. As a consequence either the estimation (reconstruction) of the channel completely fails or it results in an unphysical channel (i.e., the corresponding map is not completely positive). We present a regularization procedure that allows us to derive physically reasonable estimates (approximations) of quantum channels. We illustrate our procedure on specific examples and we show that the procedure can be also used for a derivation of optimal approximations of operations that are forbidden by the laws of quantum mechanics (e.g., the universal NOT gate).

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arXiv2004

Realization of POVMs using measurement-assisted programmable quantum processors

We study possible realizations of generalized quantum measurements on measurement-assisted programmable quantum processors. We focus our attention on the realization of von Neumann measurements and informationally complete POVMs. It is known that two unitary transformations implementable by the same programmable processor require mutually {\it orthogonal} states. It turns out that the situation with von Neumann measurements is different. Specifically, in order to realize two such measurements one does not have to use orthogonal program states. On the other hand, the number of the implementable von Neumann measurements is still limited. As an example of a programmable processor we use the so-called quantum information distributor.

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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.

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arXiv2004

Reconstruction of superoperators from incomplete measurements

We present strategies how to reconstruct (estimate) properties of a quantum channel described by the map E based on incomplete measurements. In a particular case of a qubit channel a complete reconstruction of the map E can be performed via complete tomography of four output states E[rho_j ] that originate from a set of four linearly independent test states j (j = 1, 2, 3, 4) at the input of the channel. We study the situation when less than four linearly independent states are transmitted via the channel and measured at the output. We present strategies how to reconstruct the channel when just one, two or three states are transmitted via the channel. In particular, we show that if just one state is transmitted via the channel then the best reconstruction can be achieved when this state is a total mixture described by the density operator rho = I/2. To improve the reconstruction procedure one has to send via the channel more states. The best strategy is to complement the total mixture with pure states that are mutually orthogonal in the sense of the Bloch-sphere representation. We show that unitary transformations (channels) can be uniquely reconstructed (determined) based on the information of how three properly chosen input states are transformed under the action of the channel.

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