arXiv subjects

Marcin Wieśniak

Publications and source records attributed to Marcin Wieśniak.

34 records · Page 2Linked to original sources

arXiv2018

Subadditivity of logarithm of violation of geometric Bell inequalities for qudits

Geometrical Bell Inequalities (GBIs) are the strongest known Bell inequalities for collections of qubits. However, their generalizations to other systems is not yet fully understood. We formulate GBIs for an arbitrary number $N$ of observers, each of which possesses a particle of an arbitrary dimension $d$. The whole $(d-1)$-parameter family of local observables with eigenbases unbiased to the computational basis is used, but it is immediate to use a discrete subset of them. We argue analytically for qutrits and numerically for other systems that the violations grows exponenetially with $N$. Within the studied range, the violation also grows with $d$. Interestingly, we observe that the logarithm of the violation ratio for ququats grows with $N$ slower than the doubled logarithm of the violation ratio for qubits, which implies a kind of subadditivity.

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arXiv2017

The entire history of a photon

Using the most basic mathematical tools, I present the full analysis of the experiment decribed in [A. Danan, D. Farfurnik, S. Bar-Ad, and L. Vaidman, {\em Phys. Rev. Lett.} {\bf 111}, 240402 (2013)]. First, I confirm that the data presented therein are in full agreement with the standard quantum mechanics. I then show other symptoms of presence of photons at all mirrors in the setup. I then analytically explain both the absence of peaks a Readers of [A. Danan, D. Farfurnik, S. Bar-Ad, and L. Vaidman, {\em Phys. Rev. Lett.} {\bf 111}, 240402 (2013)] are made to expect and presence of those not discussed in the Reference.

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arXiv2017

Clearer visibility Hong-Ou-Mandel effect with correlation function based on rates rather than intensities

We test ideas put forward e.g in arXiv:1508.02368, which suggest that using rates in quantum optics can lead to better indicators of non-classicality for states of quantum optical fields with undefined photon numbers. By rate we mean the ratio of registered photons in a given detector to the total number of detected photons in all detectors in the experiment. For the Hong-Ou-Mandel effect for parametric down conversion fields, we show that by using two detector correlation functions which are defined in terms of averages of products of measured rates, rather than usual intensities, one can observe non -- classical visibilities beyond $1/2$ for significantly higher pump rates. At such rates we already have a partially stimulated emission which leads to significant amplitudes for multiple pairs production, still the new approach allows to clearly see the non-classical dip.

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arXiv2016

Quadratic Entanglement Criteria for Qutrits

The problem of detecting non-classical correlations of states of many qudits is incomparably more involved than in a case of qubits. The reason is that for qubits we have a convenient description of the system by the means of the well-studied correlation tensor. Simply, the complete information about the state can be encoded in mean values of dichotomic measurements. WE demonstrate that for three-dimensional quantum subsystems we are able to formulate nonlinear entanglement criteria of the state with existing formalisms. We also point out where the idea for constructing these criteria fails for higher-dimensional systems, which poses well-defined open questions.

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arXiv2016

Geometrical Bell inequalities for arbitrarily many qudits with different outcome strategies

Greenberger-Horne-Zeilinger states are intuitively known to be the most non-classical ones. They lead to the most radically nonclassical behavior of three or more entangled quantum subsystems. However, in case of two-dimensional systems, it has been shown that GHZ states lead to more robustness of Bell nonclassicality in case of geometrical inequalities than in case of Mermin inequalities. We investigate various strategies of constructing geometrical Bell inequalities (BIs) for GHZ states for any dimensionality of subsystems.

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arXiv2016

Multipartite entanglement detection with minimal effort

Certifying entanglement of a multipartite state is generally considered as a demanding task. Since an $N$ qubit state is parametrized by $4^{N}-1$ real numbers, one might naively expect that the measurement effort of generic entanglement detection also scales exponentially with $N$. Here, we introduce a general scheme to construct efficient witnesses requiring a constant number of measurements independent of the number of qubits for states like, e.g., Greenberger-Horne-Zeilinger states, cluster states and Dicke states. For four qubits, we apply this novel method to experimental realizations of the aforementioned states and prove genuine four-partite entanglement with two measurement settings only.

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arXiv2015

Two Copies of the Einstein-Podolsky-Rosen State of Light Lead to Refutation of EPR Ideas

Bell's theorem applies to the normalizable approximations of the original Einstein-Podolsky-Rosen (EPR) state. The constructions of the proof require measurements difficult to perform, and dichotomic observables. By noticing the fact that the four mode squeezed vacuum state produced in type II down-conversion can be seen both as two copies of approximate EPR states, and also as a kind of polarization supersinglet, we show a straightforward way to test violations of the EPR concepts with direct use of their state. The observables involved are simply photon numbers at outputs of polarizing beam splitters. Suitable chained Bell inequalities are based on the geometric concept of distance. For a few settings they are potentially a new tool for quantum information applications, involving observables of a nondichotomic nature, and thus of higher informational capacity. In the limit of infinitely many settings we get a Greenberger-Horne-Zeilinger-type contradiction: EPR reasoning points to a correlation, while quantum prediction is an anticorrelation. Violations of the inequalities are fully resistant to multipair emissions in Bell experiments using parametric down-conversion sources.

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arXiv2014

True Multipartite Entanglement Hardy Test

Quantum mechanics allows systems to be entangled with each other, which results in stronger than classical correlations. Many methods of identifying entanglement have been proposed over years, most of which are based on violating some statistical inequalities. In this work we extend the idea due to Hardy, in which entanglement is not identified with use of statistical inequalities, but by simultaneous satisfaction of certain conditions. We show that the new variant of the Hardy paradox relying on marginal probabilities can be resolved only by true multipartite entangled states. Also, the state resolving this paradox for given local measurements is pure and unique in case of qubit collections.

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arXiv2014

Quantum Byzantine Agreement via Hardy correlations and entanglement swapping

We present a device-independent quantum scheme for the {\em Byzantine Generals} problem. The protocol is for three parties. Party $C$ is to send two identical one bit messages to parties $A$ and $B$. The receivers $A$ and $B$ may exchange two one bit messages informing the other party on the message received from $C$. A bit flipping error in one of the transmissions, does not allow the receiving parties to establish what was the message of $C$. Our quantum scheme has the feature that if the messages of the Byzantine protocol are readable (that is give an unambiguous bit value for any of the receivers), then any error by $C$ (cheating by one of the commanding general) is impossible. $A$ and $B$ do not have to exchange protocol messages to be sure of this.

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arXiv2013

N-particle nonclassicality without N-particle correlations

Most of known multipartite Bell inequalities involve correlation functions for all subsystems. They are useless for entangled states without such correlations. We give a method of derivation of families of Bell inequalities for N parties, which involve, e.g., only (N-1)-partite correlations, but still are able to detect proper N-partite entanglement. We present an inequality which reveals five-partite entanglement despite only four-partite correlations. Classes of inequalities introduced here can be put into a handy form of a single non-linear inequality. An example is given of an N qubit state, which strongly violates such an inequality, despite having no N-qubit correlations. This surprising property might be of potential value for quantum information tasks.

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arXiv2012

Multisetting Bell inequalities for $N$ spins-1 avoiding KS contradiction

Bell's theorem for systems more complicated than two qubits faces a hidden, as yet undiscussed, problem. One of the methods to derive Bell's inequalities is to assume existence of joint probability distribution for measurement results for all settings in the given experiment. However for spins-1, one faces the problem that eigenvalues of observables do not allow a consistent algebra if one allows all possible settings on each side (Bell 1966 contradiction), or some specific sets (leading to a Kochen-Specker 1967 contradiction). We show here that by choosing special set of settings which never lead to inconsistent algebra of eigenvalues, one can still derive multisetting Bell inequalities, and that they are robustly violated. Violation factors increase with the number of subsystems. The inequalities involve only spin observables, we do not allow all possible qutrit observables, still the violations are strong.

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arXiv2012

Package of facts and theorems for efficiently generating entanglement criteria for many qubits

We present a package of mathematical theorems, which allow to construct multipartite entanglement criteria. Importantly, establishing bounds for certain classes of entanglement does not take an optimization over continuous sets of states. These bonds are found from the properties of commutativity graphs of operators used in the criterion. We present two examples of criteria constructed according to our method. One of them detects genuine 5-qubit entanglement without ever referring to correlations between all five qubits.

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arXiv2012

Theoretical Falsification of Leggett Conjecture for Two Qubits or One Ququat

Recently, some attention has been paid to falsifying the Leggett model, in which global probabilities characterizing a quantum state are represented by a combination of factorisable distributions. This idea was even verified in experiments, and generalized for larger subsystems, but thus far not in terms of the size of a subsystem. In this communication we show an inequality to reject the Leggett description for a subsystem of two qubits. We also point out some other interpretations of the derived expression.

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arXiv2011

Decoherence through Spin Chains: Toy Model

The description of the dynamics of closed quantum systems, governed by the Schroedinger equation at first sight seems incompatible with the Lindblad equation describing open ones. By analyzing closed dynamics of a spin-1/2 chain we reconstruct exponential decays characteristic for the latter model. We identify all necessary ingredients to efficiently model this behavior, such as an infinitely large environment and the coupling to the system weak in comparison to the internal couplings in the bath.

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arXiv2009

One-Qubit and Two-Qubit Codes in Noisy State Transfer

Quantum state transfer is a procedure, which allows to exchange quantum information between stationary qubit systems. It is anticipated that the transfer will find applications in solid-state quantum computing. In this contribution, we discuss the effects of various, physically relevant models of decoherence on a toy model of six qubit linearly coupled by the exchange interaction. In many cases we observe the advantage of the two-qubit encoding, which can be associated with the fact that this encoding does not require the state initialization.

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arXiv2008

Extending Bell inequalities to more parties

We describe a method of extending Bell inequalities from $n$ to $n+1$ parties and formulate sufficient conditions for our method to produce tight inequalities from tight inequalities. The method is non trivial in the sense that the inequalities produced by it, when applied to entangled quantum states may be violated stronger than the original inequalities. In other words, the method is capable of generating inequalities which are more powerfull indicators of non-classical correlations than the original inequalities.

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