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Marek Zukowski

Publications and source records attributed to Marek Zukowski.

At least 19 recordsLinked to original sources
arXiv2017

Normalized Stokes operators for polarization correlations of entangled optical fields

Stokes parameters are a standard tool in quantum optics. They involve averaged intensities at exits of polarizers. If the overall measured intensity fluctuates, as e.g. for states with undefined photon numbers, the instances of its increased value contribute more to the parameters. One can introduce normalized quantum Stokes operators. Operationally, for a given single run of the experiment, their values are differences of measured intensities (or photon numbers) at the two exits of a polarizer divided by their sum. Effects of intensity fluctuations are removed. Switching to normalized Stokes operators results in more sensitive entanglement conditions. We also show a general method of deriving an entanglement indicator for optical fields which use polarization correlations, which starts with any two-qubit entanglement witness. This allows to vastly expand the family of such indicators.

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arXiv2016

The Magical Number Seven: An Unexpected Dimensional Threshold in Quantum Communication Complexity

Entanglement-assisted classical communication and transmission of a quantum system are the two quantum resources for information processing. Many information tasks can be performed using either quantum resource. However, this equivalence is not always present since entanglement assisted classical communication is known to sometimes be the better performing resource. Here, we show not only the opposite phenomenon; that there exists tasks for which transmission of a quantum system is a more powerful resource than entanglement assisted classical communication, but also that such phenomena can have a surprisingly strong dependence on the dimension of Hilbert space. We introduce a family of communication complexity problems parametrized by dimension of Hilbert space and study the performance of each quantum resource. We find that for low dimensions, the two resources perform equally well, whereas for dimension seven and above, the equivalence is suddenly broken and transmission of a quantum system becomes more powerful than entanglement assisted classical communication. Moreover, we find that transmission of a quantum system may even outperform classical communication assisted by the stronger-than-quantum correlations obtained from the principle of Macroscopic Locality.

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arXiv2016

Higher dimensional communication complexity problems: classical protocols vs quantum ones based on Bell's Theorem or prepare-transmit-measure schemes

Communication complexity problems (CCPs) are tasks in which separated parties attempt to compute a function whose inputs are distributed among the parties. Their communication is limited so that not all inputs can be sent. We show that broad classes of Bell inequalities can be mapped to CCPs and that a quantum violation of a Bell inequality is a necessary and sufficient condition for an enhancement of the related CCP beyond its classical limitation. However, one can implement CCPs by transmitting a quantum system, encoding no more information than is allowed in the CCP, and extract information by performing measurements. We show that for a large class of Bell inequalities, the improvement of the CCP associated to a quantum violation of a Bell inequality can be no greater than the improvement obtained from quantum prepare-transmit-measure strategies.

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arXiv2016

Simple criteria for noise resistance of two qudit entanglement

Too much noise kills entanglement. This is the main problem in its production and transmission. We use a handy approach to indicate noise resistance of entanglement of a bi-partite system described by $d\times d$ Hilbert space. Our analysis uses a geometric approach based on the fact that if a scalar product of a vector $\vec{s}$ with a vector $\vec {e}$ is less than the square of the norm of $\vec{e}$, then $\vec{s}\neq\vec{e}$. We use such concepts for correlation tensors of separable and entangled states. As a general form correlation tensors for pairs of qudits, for $d>2$, is very difficult to obtain, because one does not have a Bloch sphere for pure one qudit states, we use a simplified approach. The criterion reads: if the largest Schmidt eigenvalue of a correlation tensor is smaller than the square of its norm, then the state is entangled. this criterion is applied in the case of various types of noise admixtures to the initial (pure) state. These include white noise, colored noise, local depolarizing noise and amplitude damping noise. A broad set of numerical and analytical results is presented. As the other simple criterion for entanglement is violation of Bell's inequalities, we also find critical noise parameters to violate specific family of Bell inequalities (CGLMP), for maximally entangled states. We give analytical forms of our results for $d$ approaching infinity.

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arXiv2016

Bell Inequalities for Quantum Optical Fields

We show that the "practical" Bell inequalities, which use intensities as the observed variables, commonly used in quantum optics and widely accepted in the community, suffer from an inherent loophole, which severely limits the range of local hidden variable theories of light, which are invalidated by their violation. We present alternative inequalities which do not suffer from any (theoretical) loophole. The new inequalities use redefined correlation functions, which involve averaged products of local rates rather than intensities. Surprisingly, the new inequalities detect entanglement in situations in which the "practical" ones fail. Thus, we have two for the price on one: full consistency with Bell's Theorem, and better device-independent detection of entanglement.

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arXiv2015

Secret Sharing with a Single d-level Quantum System

We give an example of a wide class of problems for which quantum information protocols based on multi-system entanglement can be mapped into much simpler ones involving one system. Secret sharing is a cryptographic primitive which plays a central role in various secure multiparty computation tasks and management of keys in cryptography. In secret sharing protocols, a classical message is divided into shares given to recipient parties in such a way that some number of parties need to collaborate in order to reconstruct the message. Quantum protocols for the task commonly rely on multi-partite GHZ entanglement. We present a multiparty secret sharing protocol which requires only sequential communication of a single quantum d-level system (for any prime d). It has huge advantages in scalabilility and can be realized with the state of the art technology. n be realized with the state of the art technology.

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arXiv2015

Detection efficiency loophole in Pusey-Barrett-Rudolph theorem

Detection efficiency loophole poses a significant problem for experimental tests of Bell inequalities. Recently discovered Pusey-Barrett-Rudolph (PBR) theorem suffers from the same vulnerability. In this paper we calculate the critical detection efficiency, below which the PBR argument for the ontic nature of quantum state is inconclusive. This is done for the maximally $ψ$-epistemic models. We use two different definitions of this property. The optimal number of parties, for which the critical detection efficiency is the lowest is given. We also approach the problem from the opposite direction. We provide a function which enables us to specify which epistemic models are ruled out by the results of an experiment with a given detection efficiency.

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arXiv2015

Beyond Gisin's Theorem and its Applications: Violation of Local Realism by Two-Party Einstein-Podolsky-Rosen Steering

We demonstrate here that for a given mixed multi-qubit state if there are at least two observers for whom mutual Einstein-Podolsky-Rosen steering is possible, i.e. each observer is able to steer the other qubits into two different pure states by spontaneous collapses due to von Neumann type measurements on his/her qubit, then nonexistence of local realistic models is fully equivalent to quantum entanglement (this is not so without this condition). This result leads to an enhanced version of Gisin's theorem (originally: all pure entangled states violate local realism). Local realism is violated by all mixed states with the above steering property. The new class of states allows one e.g. to perform three party secret sharing with just pairs of entangled qubits, instead of three qubit entanglements (which are currently available with low fidelity). This significantly increases the feasibility of having high performance versions of such protocols. Finally, we discuss some possible applications.

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arXiv2015

Bell's theorem tells us NOT what quantum mechanics IS, but what quantum mechanics IS NOT

Non-locality, or quantum-non-locality, are buzzwords in the community of quantum foundation and information scientists, which purportedly describe the implications of Bell's theorem. When such phrases are treated seriously, that is it is claimed that Bell's theorem reveals non-locality as an inherent trait of the quantum description of the micro-world, this leads to logical contradictions, which will be discussed here. In fact, Bell's theorem, understood as violation of Bell inequalities by quantum predictions, is consistent with Bohr's notion of complementarity. Thus, if it points to anything, then it is rather the significance of the principle of Bohr, but even this is not a clear implication. Non-locality is a necessary consequence of Bell's theorem only if we reject complementarity by adopting some form of realism, be it additional hidden variables, additional hidden causes, etc., or counterfactual definiteness. The essay contains two largely independent parts. The first one is addressed to any reader interested in the topic. The second, discussing the notion of local causality, is addressed to people working in the field.

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arXiv2015

On the Paradoxical Book of Bell

This is an essay-review on a recently re-issued book of John Bell "Speakable and Unspeakable in Quantum Mechanics". The discussion concentrates around the Bell Theorem, its assumptions, consequences and frequent overinterpretations.

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arXiv2015

Quantum non-locality - It ain't necessarily so...

Bell's theorem is 50 years old. Still there is a controversy about its implications. Much of it has its roots in confusion regarding the premises from which the theorem can be derived. Some claim that a derivation of Bell's inequalities requires just locality assumption, and nothing more. Violations of the inequalities are then interpreted as ``nonlocality'' or ``quantum nonlocality''. We show that such claims are unfounded and that every derivation of Bell's inequalities requires a premise -- in addition to locality and freedom of choice -- which is either assumed tacitly, or unconsciously, or is embedded in a single compound condition (like Bell's ``local causality''). The premise is equivalent to the assumption of existence of additional variables which do not appear in the quantum formalism (in form of determinism, or joint probability for outcomes of all conceivable measurements, or ``additional causes`'', or ``hidden variables'', ``complete description of the state'' or counterfactual definiteness, etc.). A certain irony is that perhaps the main message of violation of Bell's inequalities is that our notion of locality should be based on an operationally well-defined no-signalling condition, rather than on local causality.

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arXiv2014

Noise resistance of violation of local causality for pure three-qutrit entangled states

Bell's Theorem started with two qubits, spins $1/2$. It is a no-go statement on classical (local causal) models of quantum correlations. Only after 25 years, it turned out that for three qubits the situation is even more mind boggling. General statements concerning higher dimensional systems, qutrits etc., started to appear even later, once the spin (higher than $1/2$) picture was replaced by a more broad one, allowing all possible observables. This work is continuation of the Gdansk effort to take advantage of the fact that Bell Theorem can be put in form of a linear programming problem, which in turn can be translated into a computer code. Our results are numerical and classify the strength of non-classicality of various families of three-qutrit states, as measured by resistance to noise. This is a previously uncharted territory. The results may be helpful in suggesting which three-qutrit states are handy for applications in quantum information protocols. One of the surprises is that the W state turns out to have a stronger non-classicality than the GHZ state.

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arXiv2014

Experimental Tests of Classical and Quantum Dimensions

We report on an experimental test of classical and quantum dimension. We have used a dimension witness which can distinguish between quantum and classical systems of dimension 2,3 and 4 and performed the experiment for all five cases. The witness we have chosen is a base of semi-device independent cryptographic and randomness expansion protocols. Therefore, the part of the experiment, in which qubits were used, is a realization of these protocols. In our work we also present an analytic method for finding the maximal quantum value of the witness along with corresponding measurements and preparations. This method is quite general and can be applied to any linear dimension witness.

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arXiv2013

Greenberger-Horne-Zeilinger theorem for N qudits

We generalize Greenberger-Horne-Zeilinger (GHZ) theorem to an arbitrary number of D-dimensional systems. Contrary to conventional approaches using compatible composite observables, we employ incompatible and concurrent observables, whose common eigenstate is still a generalized GHZ state. It is these concurrent observables which enable to prove a genuinely N-partite and D-dimensional GHZ theorem. Our principal idea is illustrated for a four-partite system with D which is an arbitrary multiple of 3. By extending to N qudits, we show that GHZ theorem holds as long as N is not divisible by all nonunit divisors of D, smaller than N.

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arXiv2013

Experimental multi-location remote state preparation

Transmission of quantum states is a central task in quantum information science. Remote state preparation (RSP) has the same goal as teleportation, i.e. transferring quantum information without sending physically the information carrier, but in RSP the sender knows the state which is to be transmitted. We present experimental demonstrations of RSP for two and three locations. In our experimental scheme Alice (the preparer) and her three partners share four and six photon polarization entangled singlets. This allows us to perform RSP of two or three copies of a single qubit states, a two qubit Bell state, and a three qubit W, or inverse W state. A possibility to prepare a two-qubit non-maximally entangled and GHZ states is also discussed. The ability to remotely prepare an entangled states by local projections at Alice is a distinguishing feature of our scheme.

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arXiv2012

Nonclassicality of pure two-qutrit entangled states

We report an exhaustive numerical analysis of violations of local realism by two qutrits in all possible pure entangled states. In Bell type experiments we allow any pairs of local unitary U(3) transformations to define the measurement bases. Surprisingly, Schmidt rank-2 states, resembling pairs of maximally entangled qubits, lead to the most noise-robust violations of local realism. The phenomenon seems to be even more pronounced for four and five dimensional systems, for which we tested a few interesting examples.

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arXiv2011

Correlation tensor criteria for genuine multiqubit entanglement

We present a development of a geometric approach to entanglement indicators. The method is applied to detect genuine multiqubit entanglement. The criteria are given in form of non-linear conditions imposed on correlation tensors. Thus they involve directly observable quantities, and in some cases require only few specific measurements to find multiqubit entanglement. The non-linearity of each of the criteria allows detection of entanglement in wide classes of states. In contrast to entanglement witnesses, which in the space of Hermitian operators define a hyperplane, the new conditions define a geometric figure encapsulating the non-fully entangled states within it.

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