arXiv subjects

Tomasz Paterek

Publications and source records attributed to Tomasz Paterek.

At least 55 records · Page 3Linked to original sources

arXiv2018

Detecting non-decomposability of time evolution via extreme gain of correlations

Non-commutativity is one of the most elementary non-classical features of quantum observables. Here we propose a method to detect non-commutativity of interaction Hamiltonians of two probe objects coupled via a mediator. If these objects are open to their local environments, our method reveals non-decomposability of temporal evolution into a sequence of interactions between each probe and the mediator. The Hamiltonians or Lindblad operators can remain unknown throughout the assessment, we only require knowledge of the dimension of the mediator. Furthermore, no operations on the mediator are necessary. Technically, under the assumption of decomposable evolution, we derive upper bounds on correlations between the probes and then demonstrate that these bounds can be violated with correlation dynamics generated by non-commuting Hamiltonians, e.g., Jaynes-Cummings coupling. An intuitive explanation is provided in terms of multiple exchanges of a virtual particle which lead to the excessive accumulation of correlations. A plethora of correlation quantifiers are helpful in our method, e.g., quantum entanglement, discord, mutual information, and even classical correlation. Finally, we discuss exemplary applications of the method in quantum information: the distribution of correlations and witnessing dimension of an object.

quant-ph↗

arXiv2018

Higher dimensional entanglement without correlations

It has been demonstrated both theoretically and experimentally that genuine multipartite entanglement between qubits can exist even in the absence of multipartite correlations. Here we provide first examples of this effect in higher dimensional systems -- qudits. We construct states in which genuine $N$-partite entanglement between qudits is supported only by correlations involving strictly less than $N$ particles. The construction differs in several aspects from the ones for qubits. The states introduced here are a natural test-bed for candidate quantifiers of genuinely multipartite quantum correlations.

quant-ph↗

arXiv2018

Paradoxical consequences of multipath coherence: perfect interaction-free measurements

Quantum coherence can be used to infer the presence of a detector without triggering it. Here we point out that, according to quantum mechanics, such interaction-free measurements cannot be perfect, i.e., in a single-shot experiment one has strictly positive probability to activate the detector. We formalize the extent to which such measurements are forbidden by deriving a trade-off relation between the probability of activation and the probability of an inconclusive interaction-free measurement. Our description of interaction-free measurements is theory independent and allows derivations of similar relations in models generalizing quantum mechanics. We provide the trade-off for the density cube formalism, which extends the quantum model by permitting coherence between more than two paths. The trade-off obtained hints at the possibility of perfect interaction-free measurements and indeed we construct their explicit examples. Such measurements open up a paradoxical possibility where we can learn by means of interference about the presence of an object in a given location without ever detecting a probing particle in that location. We therefore propose that absence of perfect interaction-free measurement is a natural postulate expected to hold in all physical theories. As shown, it holds in quantum mechanics and excludes the models with multipath coherence.

quant-ph↗

arXiv2018

Entanglement gain in measurements with unknown results

We characterise non-selective global projective measurements capable of increasing quantum entanglement between two particles. We show that non-selective global projective measurements are capable of increasing entanglement between two particles, in particular, entanglement of any pure non-maximally entangled state can be improved in this way (but not of any mixed state) and we provide detailed analysis for two qubits. It is then shown that Markovian open system dynamics can only approximate such measurements, but this approximation converges exponentially fast as illustrated using Araki-Zurek model. We conclude with numerical evidence that macroscopic bodies in a random pure state do not gain entanglement in a random non-selective global measurement.

quant-ph↗

arXiv2017

Revealing non-classicality of inaccessible objects

Some physical objects are hardly accessible to direct experimentation. It is then desirable to infer their properties based solely on the interactions they have with systems over which we have control. In this spirit, here we introduce schemes for assessing the non-classicality of the inaccessible objects as characterised by quantum discord. We consider two probes individually interacting with the inaccessible object, but not with each other. The schemes are based on monitoring entanglement dynamics between the probes. Our method is robust and experimentally friendly as it allows the probes and the object to be open systems, makes no assumptions about the initial state, dimensionality of involved Hilbert spaces and details of the probe-object Hamiltonian. We apply our scheme to a membrane-in-the-middle optomechanical system, to detect system-environment correlations in open system dynamics as well as non-classicality of the environment, and we foresee potential benefits for the inference of the non-classical nature of gravity.

quant-ph↗

arXiv2017

Genuine $N$-partite entanglement without $N$-partite correlation functions

A genuinely $N$-partite entangled state may display vanishing $N$-partite correlations measured for arbitrary local observables. In such states the genuine entanglement is noticeable solely in correlations between subsets of particles. A straightforward way to obtain such states for odd $N$ is to design an `anti-state' in which all correlations between an odd number of observers are exactly opposite. Evenly mixing a state with its anti-state then produces a mixed state with no $N$-partite correlations, with many of them genuinely multiparty entangled. Intriguingly, all known examples of `entanglement without correlations' involve an \emph{odd} number of particles. Here we further develop the idea of anti-states, thereby shedding light on the different properties of even and odd particle systems. We conjecture that there is no anti-state to any pure even-$N$-party entangled state making the simple construction scheme unfeasable. However, as we prove by construction, higher-rank examples of `entanglement without correlations' for arbitrary even $N$ indeed exist. These classes of states exhibit genuine entanglement and even violate an $N$-partite Bell inequality, clearly demonstrating the non-classical features of these states as well as showing their applicability for quantum communication complexity tasks.

quant-ph↗

arXiv2017

Divisible quantum dynamics satisfies temporal Tsirelson's bound

We give strong evidence that divisibility of qubit quantum processes implies temporal Tsirelson's bound. We also give strong evidence that the classical bound of the temporal Bell's inequality holds for dynamics that can be described by entanglement-breaking channels---a more general class of dynamics than that allowed by classical physics.

quant-ph↗

arXiv2016

Correlations between outcomes of random measurements

We recently showed that multipartite correlations between outcomes of random observables detect quantum entanglement in all pure and some mixed states. In this followup article we further develop this approach, derive a maximal amount of such correlations, and show that they are not monotonous under local operations and classical communication. Nevertheless, we demonstrate their usefulness in entanglement detection with a single random observable per party. Finally we study convex-roof extension of the correlations and provide a closed-form necessary and sufficient condition for entanglement in rank-2 mixed states and a witness in general.

quant-ph↗

arXiv2015

Quantum entanglement from random measurements

We show that the expectation value of squared correlations measured along random local directions is an identifier of quantum entanglement in pure states which can be directly experimentally assessed if two copies of the state were available. Entanglement can therefore be detected by parties who do not share a common reference frame and whose local reference frames, such as polarisers or Stern-Gerlach magnets, remain unknown. Furthermore, we also show that in every experimental run access to only one qubit from the macroscopic reference is sufficient to identify entanglement, violate a Bell inequality, and in fact observe all phenomena observable with macroscopic references. Finally, we provide a state-independent entanglement witness solely in terms of random correlations and emphasise how data gathered for a single random measurement setting per party reliably detects entanglement. This is only possible due to utilised randomness and should find practical applications in experimental confirmation of multi-photon entanglement or space experiments.

quant-ph↗

arXiv2015

Excessive distribution of quantum entanglement

We classify protocols of entanglement distribution as excessive and non-excessive ones. In a non-excessive protocol, the gain of entanglement is bounded by the amount of entanglement being communicated between the remote parties, while excessive protocols violate such bound. We first present examples of excessive protocols that achieve a significant entanglement gain. Next we consider their use in noisy scenarios, showing that they improve entanglement achieved in other ways and for some situations excessive distribution is the only possibility of gaining entanglement.

quant-ph↗

arXiv2015

Non-classicality of temporal correlations

The results of space-like separated measurements are independent of distant measurement settings, a property one might call two-way no-signalling. In contrast, time-like separated measurements are only one-way no-signalling since the past is independent of the future but not vice-versa. For this reason temporal correlations that are formally identical to non-classical spatial correlations can still be modelled classically. We define non-classical temporal correlations as the ones which cannot be simulated by propagating in time a classical information content of a quantum system. We first show that temporal correlations between results of any projective quantum measurements on a qubit can be simulated classically. Then we present a sequence of POVM measurements on a single $m$-level quantum system that cannot be explained by propagating in time $m$-level classical system and using classical computers with unlimited memory.

quant-ph↗

arXiv2015

Genuine Multipartite Entanglement without Multipartite Correlations

Non-classical correlations between measurement results make entanglement the essence of quantum physics and the main resource for quantum information applications. Surprisingly, there are $n$-particle states which do not exhibit $n$-partite correlations at all but still are genuinely $n$-partite entangled. We introduce a general construction principle for such states, implement them in a multiphoton experiment and analyze their properties in detail. Remarkably, even without $n$-partite correlations, these states do violate Bell inequalities showing that there is no classical, i.e., local realistic model describing their properties.

quant-ph↗

arXiv2014

Werner gap in presence of simple coloured noise

A `Werner gap' is the range of relevant parameters characterising a quantum state for which it is both entangled and admits local hidden variable model. Werner showed that the gap becomes maximal for entanglement mixed with white noise if subsystems have infinitely many levels. Here we study pure entangled states mixed with simple coloured noise modelled as a single pure product state. We provide an explicit local hidden variable model for quantum correlations of some states of this family and give hints that likely there is a model for all quantum predictions. This demonstrates essentially maximal Werner gap already for two qubits. Additionally to fundamental interest the study has implications for quantum computation and communication.

quant-ph↗

arXiv2014

Genuinely multi-point temporal quantum correlations and universal measurement-based quantum computing

We introduce a constructive procedure that maps all spatial correlations of a broad class of states into temporal correlations between general quantum measurements. This allows us to present temporal phenomena analogous to genuinely multipartite nonlocal phenomena, such as Greenberger-Horne-Zeilinger correlations, which do not exist if only projective measurements on qubits are considered. The map is applied to certain lattice systems in order to replace one spatial dimension with a temporal one, without affecting measured correlations. We use this map to show how repeated application of a 1d-cluster-gate leads to universal one-way quantum computing when supplemented with the general measurements.

quant-ph↗

arXiv2014

Density cubes and higher-order interference theories

Can quantum theory be seen as a special case of a more general probabilistic theory, similarly as classical theory is a special case of the quantum one? We study here the class of generalized probabilistic theories defined by the order of interference they exhibit as proposed by Sorkin. A simple operational argument shows that the theories require higher-order tensors as a representation of physical states. For the third-order interference we derive an explicit theory of "density cubes" and show that quantum theory, i.e. theory of density matrices, is naturally embedded in it. We derive the genuine non-quantum class of states and non-trivial dynamics for the case of three-level system and show how one can construct the states of higher dimensions. Additionally to genuine third-order interference, the density cubes are shown to violate the Leggett-Garg inequality beyond the quantum Tsirelson bound for temporal correlations.

quant-ph↗

arXiv2013

Optimized state independent entanglement detection based on geometrical threshold criterion

Experimental procedures are presented for the rapid detection of entanglement of unknown arbitrary quantum states. The methods are based on the entanglement criterion using accessible correlations and the principle of correlation complementarity. Our first scheme essentially establishes the Schmidt decomposition for pure states, with few measurements only and without the need for shared reference frames. The second scheme employs a decision tree to speed up entanglement detection. We analyze the performance of the methods using numerical simulations and verify them experimentally for various states of two, three and four qubits.

quant-ph↗

arXiv2013

Entanglement witnesses with variable number of local measurements

We present a class of entanglement identifiers which has the following experimentally friendly feature: once the expectation value of the identifier exceeds some definite limit, we can conclude the state is entangled, even if not all measurements defining the identifier have been performed. These identifiers are in the form of sums of non-negative functions of correlations in a quantum state, mostly squares of correlations, and we illustrate their use and strengths on various examples.

quant-ph↗

arXiv2013

Quantum discord as resource for remote state preparation

Quantum entanglement is widely recognized as one of the key resources for the advantages of quantum information processing, including universal quantum computation, reduction of communication complexity or secret key distribution. However, computational models have been discovered, which consume very little or no entanglement and still can efficiently solve certain problems thought to be classically intractable. The existence of these models suggests that separable or weakly entangled states could be extremely useful tools for quantum information processing as they are much easier to prepare and control even in dissipative environments. It has been proposed that a requirement for useful quantum states is the generation of so-called quantum discord, a measure of non-classical correlations that includes entanglement as a subset. Although a link between quantum discord and few quantum information tasks has been studied, its role in computation speed-up is still open and its operational interpretation remains restricted to only few somewhat contrived situations. Here we show that quantum discord is the optimal resource for the remote quantum state preparation, a variant of the quantum teleportation protocol. Using photonic quantum systems, we explicitly show that the geometric measure of quantum discord is related to the fidelity of this task, which provides an operational meaning. Moreover, we demonstrate that separable states with non-zero quantum discord can outperform entangled states. Therefore, the role of quantum discord might provide fundamental insights for resource-efficient quantum information processing.

quant-ph↗