arXiv subjects

P. Horodecki

Publications and source records attributed to P. Horodecki.

At least 19 recordsLinked to original sources

arXiv2022

Optimal Quantum Control of Charging Quantum Batteries

Quantum control allows us to address the problem of engineering quantum dynamics for special purposes. While recently the field of quantum batteries has attracted much attention, optimization of their charging has not benefited from the quantum control methods. Here we fill this gap by using an optimization method. We apply for the first time this convergent iterative method for the control of the population of a bipartite quantum system in two cases, starting with a qubit-qubit case. The quantum charger-battery system is considered here, where the energy is pumped into the charger by an external classical electromagnetic field. Secondly, we systematically develop the original formulation of the method for two harmonic oscillators in the Gaussian regime. In both cases, the charger is considered to be an open dissipative system. Our optimization takes into account experimentally viable problem of turning-on and off of the charging external field. Optimising the shape of the pulse significantly boosts both the power and efficiency of the charging process in comparison to the sinusoidal drive. The harmonic oscillator setting of quantum batteries is of a particular interest, as the optimal driving pulse remains so independently of the temperature of environment.

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arXiv2016

Generic appearance of objective results in quantum measurements

Measurement is of central interest in quantum mechanics as it provides the link between the quantum world and the world of everyday experience. One of the features of the latter is its robust, objective character, contrasting the delicate nature of quantum systems. Here we analyze in a completely model-independent way the celebrated von Neumann measurement process, using recent techniques of information flow, studied in open quantum systems. We show the generic appearance of objective results in quantum measurements, provided we macroscopically coarse-grain the measuring apparatus and wait long enough. To study genericity, we employ the widely-used Gaussian Unitary Ensemble of random matrices and the Hoeffding inequality. We derive generic objectivization timescales, given solely by the interaction strength and the systems' dimensions. Our results are manifestly universal and are a generic property of von Neumann measurements.

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arXiv2015

Bound on Bell Inequalities by Fraction of Determinism and Reverse Triangle Inequality

It is an established fact that entanglement is a resource. Sharing an entangled state leads to non-local correlations and to violations of Bell inequalities. Such non-local correlations illustrate the advantage of quantum resources over classical resources. Here, we study quantitatively Bell inequalities with $2\times n$ inputs. As found in [N. Gisin et al., Int. J. Q. Inf. 5, 525 (2007)] quantum mechanical correlations cannot reach the algebraic bound for such inequalities. In this paper, we uncover the heart of this effect which we call the {\it fraction of determinism}. We show that any quantum statistics with two parties and $2 \times n$ inputs exhibits nonzero fraction of determinism, and we supply a quantitative bound for it. We then apply it to provide an explicit {\it universal upper bound} for Bell inequalities with $2\times n$ inputs. As our main mathematical tool we introduce and prove a {\it reverse triangle inequality}, stating in a quantitative way that if some states are far away from a given state, then their mixture is also. The inequality is crucial in deriving the lower bound for the fraction of determinism, but is also of interest on its own.

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arXiv2014

Quantum metrology: Heisenberg limit with bound entanglement

Quantum metrology allows for a huge boost in the precision of parameters estimation. However, it seems to be extremely sensitive on the noise. Bound entangled states are states with large amount of noise what makes them unusable for almost all quantum informational tasks. Here we provide a counterintuitive example of a family of bound entangled states which can be used in quantum enhanced metrology. We show that these states give advantage as big as maximally entangled states and asymptotically reach the Heisenberg limit. Moreover, entanglement of the applied states is very weak which is reflected by its so called unlockability poperty. Finally, we find instances where behaviour of Quantum Fisher Information reports presence of bound entanglement while a well-known class of strong correlation Bell inequality does not. The question rises of whether (and if so, then to what degree) violation of local realism is required for the sub-shot noise precision in quantum metrology.

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arXiv2014

Information Content of Systems as a Physical Principle

To explain conceptual gap between classical/quantum and other, hypothetical descriptions of world, several principles has been proposed. So far, all these principles have not explicitly included the uncertainty relation. Here we introduce an information content principle (ICP) which represents the new - constrained uncertainty principle. The principle, by taking into account the encoding/decoding properties of single physical system, is capable of separation both classicality and quanta from a number of potential physical theories including hidden variable theories. The ICP, which is satisfied by both classical and quantum theory, states that the amount of non-redundant information which may be extracted from a given system is bounded by a perfectly decodable information content of the system. We show that ICP allows to discriminate theories which do not allow for correlations stronger than Tsirelson's bound. We show also how to apply the principle to composite systems, ruling out some theories despite their elementary constituents behave quantumly.

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arXiv2014

Tensor product extension of entanglement witnesses and their connection with measurement device independent entanglement

We provide a new extension of entanglement witnesses for $\mathbb{C}^{d_{1}}\otimes\mathbb{C}^{d_{2}}$ systems. Our construction preserves the properties of indecomposability and spanning property of entanglement witnesses. We show how our concept of extended entanglement witnesses is connected with the idea of measurement device independent entanglement witnesses.

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arXiv2014

Intrinsic asymmetry with respect to adversary: new feature of Bell inequalities

It is known that the local bound of a Bell inequality is sensitive to the knowledge of the external observer about the settings statistics. Here we ask how that sensitivity depends on the structure of that knowledge. It turns out that in some cases it may happen that the local bound is much more sensitive to adversary's knowledge about settings of one party than the other. Remarkably, there are Bell inequalities which are highly asymmetric with respect to the adversary's knowledge about local settings. This property may be viewed as a hidden intrinsic asymmetry of Bell inequalities. Potential implications of the revealed asymmetry effect are also discussed.

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arXiv2014

Objectivity in the Photonic Environment Through State Information Broadcasting

Recently, the emergence of classical objectivity as a property of a quantum state has been explicitly derived for a small object embedded in a photonic environment in terms of a spectrum broadcast form---a specific classically correlated state, redundantly encoding information about the preferred states of the object in the environment. However, the environment was in a pure state and the fundamental problem was how generic and robust is the conclusion. Here we prove that despite of the initial environmental noise the emergence of the broadcast structure still holds, leading to the perceived objectivity of the state of the object. We also show how this leads to a quantum Darwinism-type condition, reflecting classicality of proliferated information in terms of a limit behavior of the mutual information. Quite surprisingly, we find ,,singular points'' of the decoherence, which can be used to faithfully broadcast a specific classical message through the noisy environment.

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arXiv2013

Quantum origins of objectivity

In spite of all of its successes, quantum mechanics leaves us with a central problem: How does Nature create a "foot-bridge" from fragile quanta to the objective world of everyday experience? Here we identify within quantum mechanics a fundamental process leading to the perceived objectivity and called state information broadcasting. This is the trick that Nature uses instead of a simple cloning. We uncover it basing on minimal assumptions, without referring to any dynamical details or a concrete model. More specifically, we show how a crucial for quantum mechanics notion of non-disturbance due to Bohr and a natural definition of objectivity lead to a canonical structure of a quantum system-environment state, reflecting objective information records about the system stored in the environment.

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arXiv2013

Universal scheme for violation of local realism from quantum advantage in one-way communication complexity

We consider relations between communication complexity problems and detecting correlations (violating local realism) with no local hidden variable model. We show first universal equivalence between characteristics of protocols used in that type of problems and non-signaling correlations. We construct non linear bipartite Bell type inequalities and strong nonlocality test with binary observables by providing general method of Bell inequalities construction and showing that existence of gap between quantum and classical complexity leads to violation of these inequalities. We obtain, first to our knowledge, explicit Bell inequality with binary observables and exponential violation.

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arXiv2013

Objectivity Through State Broadcasting: The Origins Of Quantum Darwinism

Quantum mechanics is one of the most successful theories, correctly predicting huge class of physical phenomena. Ironically, in spite of all its successes, there is a notorious problem: how does Nature create a ''bridge'' from fragile quanta to the robust, objective world of everyday experience? It is now commonly accepted that the most promising approach is the Decoherence Theory, based on the system-environment paradigm. To explain the observed redundancy and objectivity of information in the classical realm, Zurek proposed to divide the environment into independent fractions and argued that each of them carries a nearly complete classical information about the system. This Quantum Darwinism model has nevertheless some serious drawbacks: i) the entropic information redundancy is motivated by a priori purely classical reasoning; ii) there is no answer to the basic question: what physical process makes the transition from quantum description to classical objectivity possible? Here we prove that the necessary and sufficient condition for objective existence of a state is the spectrum broadcasting process, which, in particular, implies Quantum Darwinism. We first show it in general, using multiple environments paradigm, a suitable definition of objectivity, and Bohr's notion of non-disturbance, and then on the emblematic example for Decoherence Theory: a dielectric sphere illuminated by photons. We also apply Perron-Frobenius Theorem to show a faithful, ''decoherence-free'' form of broadcasting. We suggest that the spectrum broadcasting might be one of the foundational properties of Nature, which opens a ''window'' for life processes.

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arXiv2012

Quantifying Contextuality

Contextuality is central to both the foundations of quantum theory and to the novel information processing tasks. Although it was recognized before Bell's nonlocality, despite some recent proposals, it still faces a fundamental problem: how to quantify its presence? In this work, we provide a framework for quantifying contextuality. We conduct two complementary approaches: (i) bottom-up approach, where we introduce a communication game, which grasps the phenomenon of contextuality in a quantitative manner; (ii) top-down approach, where we just postulate two measures - relative entropy of contextuality and contextuality cost, analogous to existent measures of non-locality (a special case of contextuality). We then match the two approaches, by showing that the measure emerging from communication scenario turns out to be equal to the relative entropy of contextuality. We give analytical formulas for the proposed measures for some contextual systems. Furthermore we explore properties of these measures such as monotonicity or additivity.

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arXiv2012

Quantum-correlation breaking channels, broadcasting scenarios, and finite Markov chains

One of the classical results concerning quantum channels is the characterization of entanglement-breaking channels [M. Horodecki et al., Rev. Math. Phys 15, 629 (2003)]. We address the question whether there exists a similar characterization on the level of quantum correlations which may go beyond entanglement. The answer is fully affirmative in the case of breaking quantum correlations down to the, so called, CQ (Classical-Quantum) type, and the corresponding channels turn out to be measurement maps, while it is no longer true in the CC (Classical-Classical) case. The study of the latter reveals an unexpected link between quantum state and local correlation broadcasting and finite Markov chains. We present a possibility of broadcasting via non von Neumann measurements, which relies on the Perron-Frobenius Theorem. Surprisingly, this is not the typical generalized C-NOT gate scenario, appearing naturally in this context.

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arXiv2011

Experimental generation of complex noisy photonic entanglement

We present an experimental scheme based on spontaneous parametric down-conversion to produce multiple photon pairs in maximally entangled polarization states using an arrangement of two type-I nonlinear crystals. By introducing correlated polarization noise in the paths of the generated photons we prepare mixed entangled states whose properties illustrate fundamental results obtained recently in quantum information theory, in particular those concerning bound entanglement and privacy.

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arXiv2011

No-broadcasting of non-signalling boxes via operations which transform local boxes into local ones

We deal with families of probability distributions satisfying non-signalling condition, called non-signalling boxes and consider class of operations that transform local boxes into local ones (the one that admit LHV model). We prove that any operation from this class can not broadcast a nonlocal box in 2x2 case. We consider a function called anti-Robustness which can not decrease under these operations. The proof reduces to showing that anti-Robustness would decrease after broadcasting.

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arXiv2011

Schemes of transmission of classical information via quantum channels with many senders: discrete and continuous variables cases

Superadditivity effects in the classical capacity of discrete multi-access channels (MACs) and continuous variable (CV) Gaussian MACs are analysed. New examples of the manifestation of superadditivity in the discrete case are provided including, in particular, a channel which is fully symmetric with respect to all senders. Furthermore, we consider a class of channels for which {\it input entanglement across more than two copies of the channels is necessary} to saturate the asymptotic rate of transmission from one of the senders to the receiver. The 5-input entanglement of Shor error correction codewords surpass the capacity attainable by using arbitrary two-input entanglement for these channels. In the CV case, we consider the properties of the two channels (a beam-splitter channel and a "non-demolition" XP gate channel) analyzed in [Czekaj {\it et al.}, Phys. Rev. A {\bf 82}, 020302 (R) (2010)] in greater detail and also consider the sensitivity of capacity superadditivity effects to thermal noise. We observe that the estimates of amount of two-mode squeezing required to achieve capacity superadditivity are more optimistic than previously reported.

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arXiv2011

Directed percolation effects emerging from superadditivity of quantum networks

Entanglement indcued non--additivity of classical communication capacity in networks consisting of quantum channels is considered. Communication lattices consisiting of butterfly-type entanglement breaking channels augmented, with some probability, by identity channels are analyzed. The capacity superadditivity in the network is manifested in directed correlated bond percolation which we consider in two flavours: simply directed and randomly oriented. The obtained percolation properties show that high capacity information transfer sets in much faster in the regime of superadditive communication capacity than otherwise possible. As a byproduct, this sheds light on a new type of entanglement based quantum capacity percolation phenomenon.

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arXiv2010

Sudden death of effective entanglement

Sudden death of entanglement is a well-known effect resulting from the finite volume of separable states. We study the case when the observer has a limited measurement capability and analyse the effective entanglement, i.e. entanglement minimized over the output data. We show that in the well defined system of two quantum dots monitored by single electron transistors, one may observe a sudden death of effective entanglement when real, physical entanglement is still alive. For certain measurement setups, this occurs even for initial states for which sudden death of physical entanglement is not possible at all. The principles of the analysis may be applied to other analogous scenarios, such as etimation of the parameters arising from quantum process tomography.

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