Papers by Zbigniew Puchała
Open Systems & Information Dynamics
We study the problem of accessibility in a set of classical and quantum channels admitting a grou... more We study the problem of accessibility in a set of classical and quantum channels admitting a group structure. Group properties of the set of channels, and the structure of the closure of the analyzed group [Formula: see text] plays a pivotal role in this regard. The set of all convex combinations of the group elements contains a subset of channels that are accessible by a dynamical semigroup. We demonstrate that accessible channels are determined by probability vectors of weights of a convex combination of the group elements, which depend neither on the dimension of the space on which the channels act, nor on the specific representation of the group. Investigating geometric properties of the set [Formula: see text] of accessible maps we show that this set is nonconvex, but it enjoys the star-shape property with respect to the uniform mixture of all elements of the group. We demonstrate that the set [Formula: see text] covers a positive volume in the polytope of all convex combinatio...
Scientific Reports
The project "Near-term quantum computers: Challenges, optimal implementations and applications" u... more The project "Near-term quantum computers: Challenges, optimal implementations and applications" under Grant Number POIR.04.04.00-00-17C1/18-00, is carried out within the Team-Net programme of the Foundation for Polish Science co-financed by the European Union under the European Regional Development Fund. " The original Article has been corrected.
Scientific Reports
The project "Near-term quantum computers Challenges, optimal implementations and applications" un... more The project "Near-term quantum computers Challenges, optimal implementations and applications" under Grant Number POIR.04.04.00-00-17C1/18-00, is carried out within the Team-Net programme of the Foundation for Polish Science co-financed by the European Union under the European Regional Development Fund. " The original Article has been corrected.
IEEE Transactions on Information Theory, 2022
We introduce and analyse the problem of encoding classical information into different resources o... more We introduce and analyse the problem of encoding classical information into different resources of a quantum state. More precisely, we consider a general class of communication scenarios characterised by encoding operations that commute with a unique resource destroying map and leave free states invariant. Our motivating example is given by encoding information into coherences of a quantum system with respect to a fixed basis (with unitaries diagonal in that basis as encodings and the decoherence channel as a resource destroying map), but the generality of the framework allows us to explore applications ranging from super-dense coding to thermodynamics. For any state, we find that the number of messages that can be encoded into it using such operations in a one-shot scenario is upper-bounded in terms of the information spectrum relative entropy between the given state and its version with erased resources. Furthermore, if the resource destroying map is a twirling channel over some unitary group, we find matching one-shot lower-bounds as well. In the asymptotic setting where we encode into many copies of the resource state, our bounds yield an operational interpretation of resource monotones such as the relative entropy of coherence and its corresponding relative entropy variance.
Implementation of generalized quantum measurements is often experimentally demanding, as it requi... more Implementation of generalized quantum measurements is often experimentally demanding, as it requires performing a projective measurement on a system of interest extended by the ancilla. We report an alternative scheme for implementing generalized measurements that uses solely: (a) classical randomness and post-processing, (b) projective measurements on a relevant quantum system and (c) postselection on non-observing certain outcomes. The method implements arbitrary quantum measurement in d dimensional system with success probability 1/d. It is optimal in the sense that for any dimensionn d there exist measurements for which the success probability cannot be higher. We apply our results to bound the relative power of projective and generalised measurements for unambiguous state discrimination. Finally, we test our scheme experimentally on IBM quantum processor. Interestingly, due to noise involved in the implementation of entangling gates, the quality with which our scheme implements...
Physical Review A, 2018
Detecting quantumness of correlations (especially entanglement) is a very hard task even in the s... more Detecting quantumness of correlations (especially entanglement) is a very hard task even in the simplest case i.e. two-partite quantum systems. Here we provide an analysis whether there exists a relation between two most popular types of entanglement identifiers: the first one based on positive maps and not directly applicable in laboratory and the second one-geometric entanglement identifier which is based on specific Hermiticity-preserving maps. We show a profound relation between those two types of entanglement criteria. Hereunder we have proposed a general framework of nonlinear functional entanglement identifiers which allows us to construct new experimentally friendly entanglement criteria.
We study the entanglement of a pure state of a composite quantum system consisting of several sub... more We study the entanglement of a pure state of a composite quantum system consisting of several subsystems with d levels each. It can be described by the Rényi-Ingarden-Urbanik entropy S q of a decomposition of the state in a product basis, minimized over all local unitary transformations. In the case q = 0, this quantity becomes a function of the rank of the tensor representing the state, while in the limit q → ∞, the entropy becomes related to the overlap with the closest separable state and the geometric measure of entanglement. For any bipartite system, the entropy S 1 coincides with the standard entanglement entropy. We analyze the distribution of the minimal entropy for random states of three-and four-qubit systems. In the former case, the distribution of the three-tangle is studied and some of its moments are evaluated, while in the latter case, we analyze the distribution of the hyperdeterminant. The behavior of the maximum overlap of a three-qudit system with the closest separable state is also investigated in the asymptotic limit.
Physical Review A, 2021
We characterise a class of environmental noises that decrease coherent properties of quantum chan... more We characterise a class of environmental noises that decrease coherent properties of quantum channels by introducing and analysing the properties of dephasing superchannels. These are defined as superchannels that affect only non-classical properties of a quantum channel E , i.e., they leave invariant the transition probabilities induced by E in the distinguished basis. We prove that such superchannels ΞC form a particular subclass of Schur-product supermaps that act on the Jamio lkowski state J(E) of a channel E via a Schur product, J ′ = J • C. We also find physical realizations of general ΞC through a pre-and post-processing employing dephasing channels with memory, and show that memory plays a non-trivial role for quantum systems of dimension d > 2. Moreover, we prove that coherence generating power of a general quantum channel is a monotone under dephasing superchannels. Finally, we analyse the effect dephasing noise can have on a quantum channel E by investigating the number of distinguishable channels that E can be mapped to by a family of dephasing superchannels. More precisely, we upper bound this number in terms of hypothesis testing channel divergence between E and its fully dephased version, and also relate it to the robustness of coherence of E .
Quantum Information Processing, 2020
The main goal of this work is to provide an insight into the problem of discrimination of positiv... more The main goal of this work is to provide an insight into the problem of discrimination of positive operator-valued measures with rank-one effects. It is our intention to study multiple-shot discrimination of such measurements, that is the case when we are able to use to unknown measurement a given number of times. Furthermore, we are interested in comparing two possible discrimination schemes: the parallel and adaptive ones. To this end, we construct a pair of symmetric informationally complete positive operator-valued measures which can be perfectly discriminated in a two-shot adaptive scheme but cannot be distinguished in the parallel scheme. On top of this, we provide an explicit algorithm which allows us to find this adaptive scheme.
Entropy, 2021
In this work, we study two different approaches to defining the entropy of a quantum channel. One... more In this work, we study two different approaches to defining the entropy of a quantum channel. One of these is based on the von Neumann entropy of the corresponding Choi–Jamiołkowski state. The second one is based on the relative entropy of the output of the extended channel relative to the output of the extended completely depolarizing channel. This entropy then needs to be optimized over all possible input states. Our results first show that the former entropy provides an upper bound on the latter. Next, we show that for unital qubit channels, this bound is saturated. Finally, we conjecture and provide numerical intuitions that the bound can also be saturated for random channels as their dimension tends to infinity.
New Journal of Physics, 2018
View the article online for updates and enhancements. Recent citations Coherence-generating power... more View the article online for updates and enhancements. Recent citations Coherence-generating power of quantum dephasing processes Georgios Styliaris et al
Physical Review A, 2018
In this work we study the problem of single-shot discrimination of von Neumann measurements, whic... more In this work we study the problem of single-shot discrimination of von Neumann measurements, which we associate with measure-and-prepare channels. There are two possible approaches to this problem. The first one is simple and does not utilize entanglement. We focus only on the discrimination of classical probability distributions, which are outputs of the channels. We find necessary and sufficient criterion for perfect discrimination in this case. A more advanced approach requires the usage of entanglement. We quantify the distance between two measurements in terms of the diamond norm (called sometimes the completely bounded trace norm). We provide an exact expression for the optimal probability of correct distinction and relate it to the discrimination of unitary channels. We also state a necessary and sufficient condition for perfect discrimination and a semidefinite program which checks this condition. Our main result, however, is a cone program which calculates the distance between the measurements and hence provides an upper bound on the probability of their correct distinction. As a by-product, the program finds a strategy (input state) which achieves this bound. Finally, we provide a full description for the cases of Fourier matrices and mirror isometries.
Physical Review A, 2019
We report an alternative scheme for implementing generalized quantum measurements that does not r... more We report an alternative scheme for implementing generalized quantum measurements that does not require the usage of auxiliary system. Our method utilizes solely: (a) classical randomness and post-processing, (b) projective measurements on a relevant quantum system and (c) postselection on non-observing certain outcomes. The scheme implements arbitrary quantum measurement in dimension d with the optimal success probability 1/d. We apply our results to bound the relative power of projective and generalised measurements for unambiguous state discrimination. Finally, we test our scheme experimentally on IBM's quantum processor. Interestingly, due to noise involved in the implementation of entangling gates, the quality with which our scheme implements generalized qubit measurements outperforms the standard construction using the auxiliary system.
Quantum Information Processing, 2018
Quantum key distribution protocols constitute an important part of quantum cryptography, where th... more Quantum key distribution protocols constitute an important part of quantum cryptography, where the security of sensitive information arises from the laws of physics. In this paper, we introduce a family of key distribution protocols which generalize the PBC00 protcol. We compare its key with the well-known protocols such as BB84, PBC00 and generation rate to the well-known protocols such as BB84, PBC0 and R04. We also state the security analysis of these protocols based on the entanglement distillation and CSS codes techniques.
Journal of Physics A: Mathematical and Theoretical, 2019
We investigate an original family of quantum distinguishability problems, where the goal is to pe... more We investigate an original family of quantum distinguishability problems, where the goal is to perfectly distinguish between M quantum states that become identical under a completely decohering map. Similarly, we study distinguishability of M quantum channels that cannot be distinguished when one is restricted to decohered input and output states. The studied problems arise naturally in the presence of a superselection rule, allow one to quantify the amount of information that can be encoded in phase degrees of freedom (coherences), and are related to time-energy uncertainty relation. We present a collection of results on both necessary and sufficient conditions for the existence of M perfectly distinguishable states (channels) that are classically indistinguishable.
Physics Letters A, 2019
We adopt the perspective of similarity equivalence, in gate set tomography called the gauge, to a... more We adopt the perspective of similarity equivalence, in gate set tomography called the gauge, to analyze various properties of quantum operations belonging to a semigroup, Φ = e Lt , and therefore given through the Lindblad operator. We first observe that the non unital part of the channel decouples from the time evolution. Focusing on unital operations we restrict our attention to the single-qubit case, showing that the semigroup embedded inside the tetrahedron of Pauli channels is bounded by the surface composed of product probability vectors and includes the identity map together with the maximally depolarizing channel. Consequently, every member of the Pauli semigroup is unitarily equivalent to a unistochastic map, describing a coupling with one-qubit environment initially in the maximally mixed state, determined by a unitary matrix of order four.
Journal of Mathematical Physics, 2018
In this work we analyze properties of generic quantum channels in the case of large system size. ... more In this work we analyze properties of generic quantum channels in the case of large system size. We use random matrix theory and free probability to show that the distance between two independent random channels converges to a constant value as the dimension of the system grows larger. As a measure of the distance we use the diamond norm. In the case of a flat Hilbert-Schmidt distribution on quantum channels, we obtain that the distance converges to 1 2 + 2 π , giving also an estimate for the maximum success probability for distinguishing the channels. We also consider the problem of distinguishing two random unitary rotations.
Quantum Information Processing, 2018
The entropic uncertainty relations are a very active field of scientific inquiry. Their applicati... more The entropic uncertainty relations are a very active field of scientific inquiry. Their applications include quantum cryptography and studies of quantum phenomena such as correlations and non-locality. In this work we find entanglement-dependent entropic uncertainty relations in terms of the Tsallis entropies for states with a fixed amount of entanglement. Our main result is stated as Theorem 1. Taking the special case of von Neumann entropy and utilizing the concavity of conditional von Neumann entropies, we extend our result to mixed states. Finally we provide a lower bound on the amount of extractable key in a quantum cryptographic scenario.
Journal of Physics A: Mathematical and Theoretical, 2018
Majorization uncertainty relations are generalized for an arbitrary mixed quantum state ρ of a fi... more Majorization uncertainty relations are generalized for an arbitrary mixed quantum state ρ of a finite size N. In particular, a lower bound for the sum of two entropies characterizing probability distributions corresponding to measurements with respect to arbitrary two orthogonal bases is derived in terms of the spectrum of ρ and the entries of a unitary matrix U relating both bases. The obtained results can also be formulated for two measurements performed on a single subsystem of a bipartite system described by a pure state, and consequently expressed as uncertainty relation for the sum of conditional entropies.
Quantum Information Processing, 2018
In this paper, we show that all nodes can be found optimally for almost all random Erdős-Rényi G(... more In this paper, we show that all nodes can be found optimally for almost all random Erdős-Rényi G(n, p) graphs using continuous-time quantum spatial search procedure. This works for both adjacency and Laplacian matrices, though under different conditions. The first one requires p = ω(log 8 (n)/n), while the second requires p ≥ (1+ε) log(n)/n, where ε > 0. The proof was made by analyzing the convergence of eigenvectors corresponding to outlying eigenvalues in the • ∞ norm. At the same time for p < (1 − ε) log(n)/n, the property does not hold for any matrix, due to the connectivity issues. Hence, our derivation concerning Laplacian matrix is tight.
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Papers by Zbigniew Puchała