Marek Zukowski
University of Gdansk, Physics, Faculty Member
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obtained by casting a single photon on a balanced beamsplitter, where e.g. |10〉b1,b2 , indicates one photon excitation in the Fock space of exit mode b1 and the vacuum of the Fock space relative to exit mode b2, see Fig.(1). The form of... more
obtained by casting a single photon on a balanced beamsplitter, where e.g. |10〉b1,b2 , indicates one photon excitation in the Fock space of exit mode b1 and the vacuum of the Fock space relative to exit mode b2, see Fig.(1). The form of such state appears to be similar to the singlet state of two level systems, which is known to maximally violate a Bell’s inequality. The two states are however intrinsically different in terms of the number of particles involved and |ψ〉b1,b2 can be thought of as a plain superposition of the photon in either of the beams.
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The title of our work is a paraphrase of the title of Asher Peres' paper \textit{Unperformed experiments have no results}. We show what are the lessons to be learned from the gedankenexperiments presented by Frauchiger and Renner... more
The title of our work is a paraphrase of the title of Asher Peres' paper \textit{Unperformed experiments have no results}. We show what are the lessons to be learned from the gedankenexperiments presented by Frauchiger and Renner (claim that quantum theory cannot consistently describe the use of itself), and Brukner (a no-go theorem for observer independent facts). One has to remember Bohr's remark "the unambiguous account of proper quantum phenomena must, in principle, include a description of all relevant features of experimental arrangement", which specifically to the gedankenexperiments means: in all your quantum mechanical thinking about measurements, think in terms of the full quantum measurement theory. The theory sees measurement as composed of two stages: pre-measurement (entanglement, i.e. quantum correlation, of the measured system with the pointer variable), and next decoherence via interaction with an environment, which leaves a record of the result. T...
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Mathematics and Physics
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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... more
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 a...
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We review series of multiqubit Bell's inequalities which apply to correlation functions and present conditions that quantum states must satisfy to violate such inequalities.
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Mathematics, Applied Mathematics, Computer Science, Physics, Quantum Information, and 9 moreLinear Programming, Quantum entanglement, Quantum, Interior Point Methods, Applied Mathematics and Computational Science, Numerical Analysis and Computational Mathematics, Impossibility, Electrical And Electronic Engineering, and Simplex
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With two independent parametric down-converters one can realize an “event-ready” Bell-EPR experiment. Monitoring for sharply coincident idlers results in entangling and pre-selecting the independent signals, which are then fed into an... more
With two independent parametric down-converters one can realize an “event-ready” Bell-EPR experiment. Monitoring for sharply coincident idlers results in entangling and pre-selecting the independent signals, which are then fed into an interferometric setup. We give the general conditions for high visibility and particle collection efficiency for Bell-type experiments involving two independent sources. These ideas can also lead to a realizable GHZ experiment.
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Mathematics and Physics
Multiphoton entanglement is the basis of many quantum communication schemes, quantum cryptographic protocols, and fundamental tests of quantum theory. Spontaneous parametric down-conversion is the most effective source for polarization... more
Multiphoton entanglement is the basis of many quantum communication schemes, quantum cryptographic protocols, and fundamental tests of quantum theory. Spontaneous parametric down-conversion is the most effective source for polarization entangled photon pairs. Here we show, that a entangled 4-photon state can be directly created by parametric down-conversion. This state exhibit perfect quantum correlations and a high robustness of entanglement against photon loss. We have used this state for four-particle test of local realistic theories. Therefore this state can be used for new types of quantum communication. We also report on possibilities for the experimentally realization of a 3-photon entangled state, the so called W-state, and discuss some of its properties.
We prove that for every Bell’s inequality and for a broad class of protocols, there always exists a multi-party communication complexity problem, for which the protocol assisted by states which violate the inequality is more efficient... more
We prove that for every Bell’s inequality and for a broad class of protocols, there always exists a multi-party communication complexity problem, for which the protocol assisted by states which violate the inequality is more efficient than any classical protocol. Moreover, for that advantage Bell’s inequality violation is a necessary and sufficient criterion. Thus, violation of Bell’s inequalities has a significance beyond that of a non-optimal-witness of non-separability.
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Biochemistry, Bioinformatics, Evolutionary Biology, Environmental Science, Computer Science, and 15 moreDevelopmental Biology, Climate Change, Computational Biology, Biotechnology, Cancer, Biology, Cell Cycle, Ecology, Drug Discovery, Evolution, Astrophysics, Astronomy, DNA, Cell Signalling, and Earth Science
The problem of the choice of the electromagnetic gauge is investigated in the framework of collision theory in the presence of strong radiation fields. Charged-particle potential scattering is considered as an example. The analysis is... more
The problem of the choice of the electromagnetic gauge is investigated in the framework of collision theory in the presence of strong radiation fields. Charged-particle potential scattering is considered as an example. The analysis is based on the dipole approximation for the radiation field, and on the velocity and length gauges. Distinguishing features of field-assisted particle scattering are, among others,
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ABSTRACT
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We present a generalized Greenberger-Horne-Zeilinger (GHZ) theorem, which involves more than two local measurement settings for some parties, and cannot be reduced to one with less settings. Our results hold for an odd number of parties.... more
We present a generalized Greenberger-Horne-Zeilinger (GHZ) theorem, which involves more than two local measurement settings for some parties, and cannot be reduced to one with less settings. Our results hold for an odd number of parties. We use a set of observables, which are incompatible but share a common eigenstate, here a GHZ state. Such observables are called concurrent. The idea is illustrated with an example of a three-qutrit system and then generalized to systems of higher dimensions, and more parties. The GHZ paradoxes can lead to, e.g., secret sharing protocols.
The two qubit (spin 1/2) singlet state has invariant perfect EPR correlations: if two observers measure {\em any} identical observables the results are always perfectly (anti-)correlated. We show that no such correlations exists in... more
The two qubit (spin 1/2) singlet state has invariant perfect EPR correlations: if two observers measure {\em any} identical observables the results are always perfectly (anti-)correlated. We show that no such correlations exists in $d\otimes d$ pure or mixed bipartite quantum states if $d\geq3$. This points that two qubit singlets are high-quality quantum information carriers in long distance transmission: their correlations are unaffected by identical random unitary transformations of both qubits. Pairs of entangled qu$d$its, $d>2$, do not have this property. Thus, qu$d$it properties should be rather exploited only in protocols in which transmission is not a long distance one.
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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... more
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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The emission of two photon pairs from type-II parametric down conversion results in a highly entangled 4-photon state. We describe the features of this new state and its application for the first 4-particle test of local realism.
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Shared entanglement and communication of a quantum system are the two quantum resources for information processing. They exhibit a very intimate relationship. Qualitatively, many information processing tasks can be performed using either... more
Shared entanglement and communication of a quantum system are the two quantum resources for information processing. They exhibit a very intimate relationship. Qualitatively, many information processing tasks can be performed using either quantum resource. Quantitatively, the two resources often yield the same numbers for efficiencies in information processing. However, this equivalence is not always present and there are known cases when shared entanglement is more useful as a resource. Here we show the opposite behaviour: that there exists a family of games where communication of a quantum system is a more powerful resource than sharing entanglement. We introduce our family of games based on the CGLMP inequality, and investigate their efficiency with each quantum resource. We find that for low dimensions, the two resources are equivalent. However, for dimension seven and above, the equivalency is suddenly broken and communication of a quantum system becomes more powerful than shari...
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The paradox of Greenberger, Horne and Zeilinger (1989) (GHZ) (see also Greenberger et al (1990)) has shed new light on the debate on the foundations of quantum physics. Simply, the premises of the Einstein-Podolsky-Rosen (EPR) argument to... more
The paradox of Greenberger, Horne and Zeilinger (1989) (GHZ) (see also Greenberger et al (1990)) has shed new light on the debate on the foundations of quantum physics. Simply, the premises of the Einstein-Podolsky-Rosen (EPR) argument to show incompleteness of quantum mechanics, are inconsistent when applied to maximally entangled states of at least three particles. The EPR program breaks down at the very outset, as their definition of the elements of reality (via the perfect correlations and locality) is void for three or more entangled particles.
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... Eh,, Eym)/IIEqm112,<2(2/76)`x,0 , where Eqm denotes the quantum prediction (for N particles in a GHZ state), ( , ) is a ... can always transform it back to sin ( l + 2) . Let us now look at the above "canonical"... more
... Eh,, Eym)/IIEqm112,<2(2/76)`x,0 , where Eqm denotes the quantum prediction (for N particles in a GHZ state), ( , ) is a ... can always transform it back to sin ( l + 2) . Let us now look at the above "canonical" experiment from the perspective of a local hidden variable theory [ 3,4 ...
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Bell's theorem applies to the normalizable approximations of original Einstein-Podolsky-Rosen (EPR) state. The constructions of the proof require measurements difficult to perform, and dichotomic observables. By noticing the fact that... more
Bell's theorem applies to the normalizable approximations of 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 ...
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ABSTRACT Without Abstract