arXiv subjects

Jakub Czartowski

Publications and source records attributed to Jakub Czartowski.

33 records · Page 2Linked to original sources

arXiv2024

Quantum Random Access Codes Implementation for Resource Allocation and Coexistence with Classical Telecommunication

In a world where Quantum Networks are rapidly becoming a reality, the development of the Quantum Internet is gaining increasing interest. Nevertheless, modern quantum networks are still in the early stages of development and have limited capacity to distribute resources among different users -- a constraint that needs to be taken into account. In this work we aim to investigate these constraints, using a novel setup for implementing Quantum Random Access Codes (QRACs), communication protocols known for their quantum advantage over their classical counterparts and semi-device-independent self-testing applications. Our QRAC states, made for the first time using weak coherent pulses instead of entangled single photons, allow us to experimentally test our encoding and decoding strategy from the resource allocation perspective. Moreover, by emulating a coexistent classical communication, we test the resilience of our implementation in presence of noise. The achieved results represent a significant milestone both for theoretical studies of quantum resource allocation and for the implementation of quantum infrastructures capable of coexisting with regular telecommunication networks.

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arXiv2024

Entanglement generation from athermality

We investigate the thermodynamic constraints on the pivotal task of entanglement generation using out-of-equilibrium states through a model-independent framework with minimal assumptions. We establish a necessary and sufficient condition for a thermal process to generate bipartite qubit entanglement, starting from an initially separable state. Consequently, we identify the set of system states that cannot be entangled, when no external work is invested. In the regime of infinite temperature, we analytically construct this set; while for finite temperature, we provide a simple criterion to verify whether any given initial state is or is not entanglable. Furthermore, we provide an explicit construction of the future thermal cone of entanglement - the set of entangled states that a given separable state can thermodynamically evolve to. We offer a detailed discussion on the properties of this cone, focusing on the interplay between entanglement and its volumetric properties. We conclude with several key remarks on the generation of entanglement beyond two-qubit systems, and discuss its dynamics in the presence of dissipation.

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arXiv2023

Thermal recall: Memory-assisted Markovian thermal processes

We develop a resource-theoretic framework that allows one to bridge the gap between two approaches to quantum thermodynamics based on Markovian thermal processes (which model memoryless dynamics) and thermal operations (which model arbitrarily non-Markovian dynamics). Our approach is built on the notion of memory-assisted Markovian thermal processes, where memoryless thermodynamic processes are promoted to non-Markovianity by explicitly modelling ancillary memory systems initialised in thermal equilibrium states. Within this setting, we propose a family of protocols composed of sequences of elementary two-level thermalisations that approximate all transitions between energy-incoherent states accessible via thermal operations. We prove that, as the size of the memory increases, these approximations become arbitrarily good for all transitions in the infinite temperature limit, and for a subset of transitions in the finite temperature regime. Furthermore, we present solid numerical evidence for the convergence of our protocol to any transition at finite temperatures. We also explain how our framework can be used to quantify the role played by memory effects in thermodynamic protocols such as work extraction. Finally, our results show that elementary control over two energy levels at a given time is sufficient to generate all energy-incoherent transitions accessible via thermal operations if one allows for ancillary thermal systems.

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arXiv2023

Iso-entangled bases and joint measurements

While entanglement between distant parties has been extensively studied, entangled measurements have received relatively little attention despite their significance in understanding non-locality and their central role in quantum computation and networks. We present a systematic study of entangled measurements, providing a complete classification of all equivalence classes of iso-entangled bases for projective joint measurements on 2 qubits. The application of this classification to the triangular network reveals that the Elegant Joint Measurement, along with white noise, is the only measurement resulting in output permutation invariant probability distributions when the nodes are connected by Werner states. The paper concludes with a discussion of partial results in higher dimensions.

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arXiv2022

Geometric structure of thermal cones

The second law of thermodynamics imposes a fundamental asymmetry in the flow of events. The so-called thermodynamic arrow of time introduces an ordering that divides the system's state space into past, future and incomparable regions. In this work, we analyse the structure of the resulting thermal cones, i.e., sets of states that a given state can thermodynamically evolve to (the future thermal cone) or evolve from (the past thermal cone). Specifically, for a $d$-dimensional classical state of a system interacting with a heat bath, we find explicit construction of the past thermal cone and the incomparable region. Moreover, we provide a detailed analysis of their behaviour based on thermodynamic monotones given by the volumes of thermal cones. Results obtained apply also to other majorisation-based resource theories (such as that of entanglement and coherence), since the partial ordering describing allowed state transformations is then the opposite of the thermodynamic order in the infinite temperature limit. Finally, we also generalise the construction of thermal cones to account for probabilistic transformations.

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arXiv2022

Resource theory of Absolute Negativity

A crucial goal of quantum information is to find new ways to exploit the properties of quantum devices as resources. One of the prominent properties of quantum devices of particular interest is their negativity in quasi-probability representations, intensively studied in foundational and practical investigations. In this article, we introduce the concept of Absolute Negativity to characterise the negativity of sets of quantum devices in a basis-independent way. Moreover, we provide a resource theory for our relational notion of Absolute Negativity, which applies to sets of quantum state-measurement pairs. Additionally, we determine a complete hierarchy of upper bounds for resource measures, which allows for estimating the resources of a set of devices. We demonstrate operational interpretations of our resource theory for communication and output-estimation advantages over state-measurement pairs with a classical probability representation. Furthermore, we illustrate the newly introduced concepts with an exhaustive analysis of a simple case of four qubit state-measurement pairs. Finally, we outline possible generalisations, applications and open questions.

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arXiv2021

Confident entanglement detection via separable numerical range

We investigate the joint (separable) numerical range of multiple measurements, i.e., the regions of expectation values accessible with (separable) quantum states for given observables. This not only enables efficient entanglement detection, but also sheds light on the geometry of the set of quantum states. More precisely, in an experiment, if the confidence region for the obtained data and the separable numerical range are disjoint, entanglement is reliably detected. Generically, the success of such an experiment is more likely the smaller the separable numerical range is compared to the standard numerical range of the observables measured. We quantify this relation using the ratio between these two volumes and show that it cannot be arbitrarily small, giving analytical bounds for any number of particles, local dimensions as well as number of measurements. Moreover, we explicitly compute the volume of separable and standard numerical range for two locally traceless two-qubit product observables, which are of particular interest as they are easier to measure in practice. Furthermore, we consider typical volume ratios for generic observables and extreme instances.

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arXiv2021

Perfect quantum-state synchronization

We investigate the most general mechanisms that lead to perfect synchronization of the quantum states of all subsystems of an open quantum system starting from an arbitrary initial state. We provide a necessary and sufficient condition for such "quantum-state synchronization", prove tight lower bounds on the dimension of the environment's Hilbert space in two main classes of quantum-state synchronizers, and give an analytical solution for their construction. The functioning of the found quantum-state synchronizer of two qubits is demonstrated experimentally on an IBM quantum computer and we show that the remaining asynchronicity is a sensitive measure of the quantum computer's imperfection.

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arXiv2021

Entanglement in highly symmetric multipartite quantum states

We present a construction of genuinely entangled multipartite quantum states based on the group theory. Analyzed states resemble the Dicke states, whereas the interactions occur only between specific subsystems related by the action of the selected group. The states constructed by this technique exhibit desired symmetry properties and form a natural resource for less-symmetric quantum informational tasks. We propose quantum circuits efficiently generating such states, which in general have smaller complexity than the circuits necessary to create fully symmetric entangled states.

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arXiv2021

Bipartite quantum measurements with optimal single-sided distinguishability

We analyse orthogonal bases in a composite $N\times N$ Hilbert space describing a bipartite quantum system and look for a basis with optimal single-sided mutual state distinguishability. This condition implies that in each subsystem the $N^2$ reduced states form a regular simplex of a maximal edge length, defined with respect to the trace distance. In the case $N=2$ of a two-qubit system our solution coincides with the elegant joint measurement introduced by Gisin. We derive explicit expressions of an analogous constellation for $N=3$ and provide a general construction of $N^2$ states forming such an optimal basis in ${\cal H}_N \otimes {\cal H}_N$. Our construction is valid for all dimensions for which a symmetric informationally complete (SIC) generalized measurement is known. Furthermore, we show that the one-party measurement that distinguishes the states of an optimal basis of the composite system leads to a local quantum state tomography with a linear reconstruction formula. Finally, we test the introduced tomographical scheme on a complete set of three mutually unbiased bases for a single qubit using two different IBM machines.

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arXiv2021

Optimal allocation of quantum resources

The optimal allocation of resources is a crucial task for their efficient use in a wide range of practical applications in science and engineering. This paper investigates the optimal allocation of resources in multipartite quantum systems. In particular, we show the relevance of proportional fairness and optimal reliability criteria for the application of quantum resources. Moreover, we present optimal allocation solutions for an arbitrary number of qudits using measurement incompatibility as an exemplary resource theory. Besides, we study the criterion of optimal equitability and demonstrate its relevance to scenarios involving several resource theories such as nonlocality vs local contextuality. Finally, we highlight the potential impact of our results for quantum networks and other multi-party quantum information processing, in particular to the future Quantum Internet.

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arXiv2020

Separability gap and large deviation entanglement criterion

For a given Hamiltonian $H$ on a multipartite quantum system, one is interested in finding the energy $E_0$ of its ground state. In the separability approximation, arising as a natural consequence of measurement in a separable basis, one looks for the minimal expectation value $λ_{\rm min}^{\otimes}$ of $H$ among all product states. For several concrete model Hamiltonians, we investigate the difference $λ_{\rm min}^{\otimes}-E_0$, called separability gap, which vanishes if the ground state has a product structure. In the generic case of a random Hermitian matrix of the Gaussian orthogonal ensemble, we find explicit bounds for the size of the gap which depend on the number of subsystems and hold with probability one. This implies an effective entanglement criterion applicable for any multipartite quantum system: If an expectation value of a typical observable among a given state is sufficiently distant from the average value, the state is almost surely entangled.

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arXiv2019

Iso-entangled mutually unbiased bases, symmetric quantum measurements and mixed-state designs

Discrete structures in Hilbert space play a crucial role in finding optimal schemes for quantum measurements. We solve the problem whether a complete set of five iso-entangled mutually unbiased bases exists in dimension four, providing an explicit analytical construction. The reduced density matrices of these $20$ pure states forming this generalized quantum measurement form a regular dodecahedron inscribed in a sphere of radius $\sqrt{3/20}$ located inside the Bloch ball of radius $1/2$. Such a set forms a mixed-state $2$-design --- a discrete set of quantum states with the property that the mean value of any quadratic function of density matrices is equal to the integral over the entire set of mixed states with respect to the flat Hilbert-Schmidt measure. We establish necessary and sufficient conditions mixed-state designs need to satisfy and present general methods to construct them. Furthermore, it is shown that partial traces of a projective design in a composite Hilbert space form a mixed-state design, while decoherence of elements of a projective design yields a design in the classical probability simplex. We identify a distinguished two-qubit orthogonal basis such that four reduced states are evenly distributed inside the Bloch ball and form a mixed-state $2$-design.

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arXiv2019

Trade--off relations for operation entropy of complementary quantum channels

The entropy of a quantum operation, defined as the von Neumann entropy of the corresponding Choi-Jamiołkowski state, characterizes the coupling of the principal system with the environment. For any quantum channel $Φ$ acting on a state of size $N$ one defines the complementary channel $\tilde Φ$, which sends the input state into the state of the environment after the operation. Making use of subadditivity of entropy we show that for any dimension $N$ the sum of both entropies, $S(Φ)+ S(\tilde Φ)$, is bounded from below. This result characterizes the trade-off between the information on the initial quantum state accessible to the principal system and the information leaking to the environment. For one qubit maps, $N=2$, we describe the interpolating family of depolarising maps, for which the sum of both entropies gives the lower boundary of the region allowed in the space spanned by both entropies.

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arXiv2018

Entanglement properties of multipartite informationally complete quantum measurements

We analyze tight informationally complete measurements for arbitrarily large multipartite systems and study their configurations of entanglement. We demonstrate that tight measurements cannot be exclusively composed neither of fully separable nor maximally entangled states. We establish an upper bound on the maximal number of fully separable states allowed by tight measurements and investigate the distinguished case, in which every measurement operator carries the same amount of entanglement. Furthermore, we introduce the notion of nested tight measurements, i.e. multipartite tight informationally complete measurements such that every reduction to a certain number of parties induces a lower dimensional tight measurement, proving that they exist for any number of parties and internal levels.

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