An experiment proposed by Karl Popper to test the standard interpretation of quantum mechanics was realized by Kim and Shih. We use a quantum mechanical calculation to analyze Popper's proposal, and find a surprising result for the location of the virtual slit. We also analyze Kim and Shih's experiment, and demonstrate that although it ingeniously overcomes the problem of temporal spreading of the wave-packet, it is inconclusive about Popper's test. We point out that another experiment which (unknowingly) implements Popper's test in a conclusive way, has actually been carried out. Its results are in contradiction with Popper's prediction, and agree with our analysis.
Application of the uncertainty principle to conditional measurements is investigated, and found to be valid for measurements on separated sub-systems. In light of this, an apparent violation of the uncertainty principle obtained by Kim and Shih in their realization of Popper's experiment (quant-ph/9905039) is explained through analogy with a simple optical system.
An entangled pair of photons (1 and 2) are emitted to opposite directions. A narrow slit is placed in the path of photon 1 to provide precise knowledge of its position on the $y$ axis and this also determines the precise $y$ position of its twin, photon 2, due to quantum entanglement. Is photon 2 going to experience a greater uncertainty in momentum, i.e., a greater $Δp_{y}$, due to the precise knowledge of its position $y$? The experimental data shows $ΔyΔp_{y}<\hbar $ for photon 2. Can this recent realization of the historical thought experiment of Karl Popper signal a violation of the uncer…
Karl Popper had proposed an experiment to test the standard interpretation of quantum mechanics. The proposal survived for many year in the midst of no clear consensus on what results it would yield. The experiment was realized by Kim and Shih in 1999, and the apparently surprising result led to lot of debate. We review Popper's proposal and its realization in the light of current era when entanglement has been well studied, both theoretically and experimentally. We show that the "ghost-diffraction" experiment, carried out in a different context, conclusively resolves the controversy surroundi…
The realization of Karl Popper's EPR-like experiment by Shih and Kim (published 1999) produced the result that Popper hoped for: no ``action at a distance'' on one photon of an entangled pair when a measurement is made on the other photon. This experimental result is interpretable in local realistic terms: each photon has a definite position and transverse momentum most of the time; the position measurement on one photon (localization within a slit) disturbs the transverse momentum of that photon in a non-predictable way in accordance with the uncertainty principle; however, there is no effect…
In this paper we look at a particular realization of Popper's thought experiment with correlated quantum particles and argue that, from the point of view of a nonlinear quantum physics and contrary to the orthodox interpretation, Heisenberg's uncertainty principle is violated. Moreover, we show that this kind of experiments can easily be explained in an intuitive manner if we are willing to take a nonlinear approach.
The realization of Karl Popper's experiment by Shih and Kim (published 1999) produced the result that Popper hoped for: no ``action at a distance'' on one photon of an entangled pair when a measurement is made on the other photon. This experimental result is interpretable in local realistic terms: each photon has a definite position and transverse momentum most of the time; the position measurement on one photon (localization in a slit) disturbs the transverse momentum of that photon in a non-predictable way in accordance with the uncertainty principle; however, there is no effect on the other…
Popper conceived an experiment whose analysis led to a result that he deemed absurd. Popper wrote that his reasoning was based on the Copenhagen interpretation and therefore invalidated the latter. Actually, Popper's argument involves counterfactual reasoning and violates Bohr's complementarity principle. The absurdity of Popper's result only confirms Bohr's approach.
A thought experiment, proposed by Karl Popper, which has been experimentally realized recently, is critically examined. A basic flaw in Popper's argument which has also been prevailing in subsequent debates, is pointed out. It is shown that Popper's experiment can be understood easily within the Copenhagen interpretation of quantum mechanics. An alternate experiment, based on discrete variables, is proposed, which constitutes Popper's test in a clearer way. It refutes the argument of absence of nonlocality in quantum mechanics.
Popper's original thought experiment probed some fundamental and subtle rules of quantum mechanics. Two experiments have directly and indirectly tested Popper's hypothesis, but they seem to give contrasting results. The equations governing these two experiments and Popper's thought experiment will be derived from basic quantum principles. The experimental constants will be inputted and it will show that the two experiments agree with each other and with quantum theory.
We comment on Tabesh Qureshi, "Understanding Popper's Experiment," AJP 73, 541 (June 2005), in particular on the implications of its section IV. We show, in the situation envisaged by Popper, that analysis solely with conventional non-relativistic quantum mechanics suffices to exclude the possibility of superluminal communication.
An experiment proposed by Karl Popper is considered by many to be a crucial test of quantum mechanics. Although many loopholes in the original proposal have been pointed out, they are not crucial to the test. We use only the standard interpretation of quantum mechanics to point out what is fundamentally wrong with the proposal, and demonstrate that Popper's basic premise was faulty.
An experiment which could decide against the Copenhagen interpretation of quantum mechanics has been proposed by K. Popper and, subsequently, it has been criticized by M.J. Collett and R. Loudon. Here we show that both the above mentioned arguments are not correct because they are based on a misuse of basic quantum rules.
We present a detailed analysis of a previously published realization of Popper's experiment using entangled ghost imaging. Our analysis, which is based on optical diffraction integrals, shows that, for the configuration previously described, the transverse spread of an unmeasured particle (the signal photon here) does not increase in inverse proportion to the width of its virtual confinement when its entangled twin is confined in transverse dimension by a physical slit. Rather we show that the spread of the unmeasured particle carries no dependence on the width of its virtual confinement in th…
Karl Popper proposed a way to test whether a proposed relation of a quantum-mechanical state to perceived reality in the Copenhagen interpretation (CI) of quantum mechanics - namely that the state of a particle is merely an expression of ``what is known'' about the system - is in agreement with all experimental facts. A conceptual flaw in Popper's proposal is identified and an improved version of his experiment (called ``Extension step 1'') - which fully serves its original purpose - is suggested. The main purpose of this paper is to suggest to perform this experiment. The results of this expe…
I present the reconstruction of the involvement of Karl Popper in the community of physicists concerned with foundations of quantum mechanics, in the 1980s. At that time Popper gave active contribution to the research in physics, of which the most significant is a new version of the EPR thought experiment, alleged to test different interpretations of quantum mechanics. The genesis of such an experiment is reconstructed in detail, and an unpublished letter by Popper is reproduced in the present paper to show that he formulated his thought experiment already two years before its first publicatio…
In an effort to challenge the Copenhagen interpretation of quantum mechanics, Karl Popper proposed an experiment involving spatially separated entangled particles. In this experiment, one of the particles passes through a very narrow slit, and thereby its position becomes well-defined. This particle therefore diffracts into a large divergence angle; this effect can be understood as a consequence of the Heisenberg uncertainty principle. Popper further argued that its entangled partner would become comparably localized in position, and that, according to his understanding of the Copenhagen inter…
A test on quantum mechanics proposed long ago by Karl Popper is reconsidered with further detail and new insight. An ambiguity in the proposal, which turns out to be essential in order to make the test conclusive, is identified and taken into account for the first time. Its implications for recently performed photon experiments [such as in D. V. Strekalov \textit{et al.}, Phys. Rev.\ Lett. {\bf 74}, 3600 (1995)] are briefly analyzed.
Wheeler has strikingly illustrated the wave-particle duality by the delayed-choice thought experiment, in which the configuration of a 2-path interferometer is chosen after a single-photon light-pulsed has entered it. We present a quantitative theoretical analysis of an experimental realization of Wheeler's proposal.
We relate gate fidelities of experimentally realized quantum operations to the broadcasting property of their ideal operations, and show that the more parties a given quantum operation can broadcast to, the higher gate fidelities of its experimental realization are in general. This is shown by establishing the correspondence between two operational quantities, quantum state shareability and quantum broadcasting. This suggests that, to assess an experimental realization using gate fidelities, the worst case of realization such as noisy operations should be taken into account and then compared t…
We report an experimental realization of entanglement concentration using two polarization-entangled photon pairs produced by pulsed parametric down-conversion. In the meantime, our setup also provides a proof-in-principle demonstration of a quantum repeater. The quality of our procedure is verified by observing a violation of Bell's inequality by more than 5 standard deviations. The high experimental accuracy achieved in the experiment implies that the requirement of tolerable error rate in multi-stage realization of quantum repeaters can be fulfilled, hence providing a practical toolbox for …
We present a computational circuit which realizes contextually the Tele-UNOT gate and the universal optimal quantum cloning machine (UOQCM). We report the experimental realization of the probabilistic UOQCM with polarization encoded qubits. This is achieved by combining on a symmetric beam-splitter the input qubit with an ancilla in a fully mixed state.
We describe the first experimental realization of the Deutsch-Jozsa quantum algorithm to evaluate the properties of a 2-bit boolean function in the framework of one-way quantum computation. For this purpose a novel two-photon six-qubit cluster state was engineered. Its peculiar topological structure is the basis of the original measurement pattern allowing the algorithm realization. The good agreement of the experimental results with the theoretical predictions, obtained at $\sim$1kHz success rate, demonstrate the correct implementation of the algorithm.
We report experimental implementation of discrete Fourier transformation(DFT) on a nuclear magnetic resonance(NMR) quantum computer. Experimental results agree with theoretical results. Using the pulse sequences we introduced, DFT can be realized on any L-bit quantum number in principle.
We present the experimental realization of the optimal estimation protocol for a Pauli noisy channel. The method is based on the generation of 2-qubit Bell states and the introduction of quantum noise in a controlled way on one of the state subsystems. The efficiency of the optimal estimation, achieved by a Bell measurement, is shown to outperform quantum process tomography.
We demonstrate the implementation of quantum cheque, proposed by Roy Moulick and Panigrahi [Quantum Inf. Process (2016) 15: 2475], using the five-qubit IBM quantum computer. Appropriate single qubit, CNOT and Fredkin gates have been implemented for the realization of the quantum cheque transaction in a quantum networked banking system. Quantum state tomography reveals the accuracy of the implementation with comparable results from the theoretical and experimental density matrices.
In quantum information theory, entropic inequalities act as the necessary and sufficient conditions to noncontextuality. Here, we first experimentally demonstrate the violation of the entropic noncontextual inequality in a four-level quantum system, by using the five-qubit IBM quantum computer. The experimental result disproves the existence of a local realist model.
Nuclear magnetic resonance techniques are used to realize a quantum algorithm experimentally. The algorithm allows a simple NMR quantum computer to determine global properties of an unknown function requiring fewer function ``calls'' than is possible using a classical computer.
We report the first experimental realization of an ''optimal'' quantum device able to perform a Minimal Disturbance Measurement (MDM) on polarization encoded qubits saturating the theoretical boundary established between the classical knowledge acquired of any input state, i.e. the classical "guess", and the fidelity of the same state after disturbance due to measurement . The device has been physically realized by means of a linear optical qubit manipulation, post-selection measurement and a classical feed-forward process.
By a significant modification of the standard protocol of quantum state Teleportation two processes ''forbidden'' by quantum mechanics in their exact form, the Universal NOT gate and the Universal Optimal Quantum Cloning Machine, have been implemented contextually and optimally by a fully linear method. In particular, the first experimental demonstration of the Tele-UNOT Gate, a novel quantum information protocol has been reported (cfr. quant-ph/0304070). A complete experimental realization of the protocol is presented here.
We report the experimental realization and characterization of one 60-mode copy, and of two 30-mode copies, of a dual-rail quantum-wire cluster state in the quantum optical frequency comb of a bimodally pumped optical parametric oscillator. This is the largest entangled system ever created whose subsystems are all available simultaneously. The entanglement proceeds from the coherent concatenation of a multitude of EPR pairs by a single beam splitter, a procedure which is also a building block for the realization of hypercubic-lattice cluster states for universal quantum computing.
Due to its geometric nature, holonomic quantum computation is fault-tolerant against certain types of control errors. Although proposed more than a decade ago, the experimental realization of holonomic quantum computation is still an open challenge. In this Letter, we report the first experimental demonstration of nonadiabatic holonomic quantum computation in liquid NMR quantum information processors. Two non-commuting holonomic single-qubit gates, rotations about x-axis and about z-axis, and the two-qubit holonomic control-NOT gate are realized with high fidelity by evolving the work qubits a…
We report an experimental realization of one-way quantum computing on a two-photon four-qubit cluster state. This is accomplished by developing a two-photon cluster state source entangled both in polarization and spatial modes. With this special source, we implemented a highly efficient Grover's search algorithm and high-fidelity two qubits quantum gates. Our experiment demonstrates that such cluster states could serve as an ideal source and a building block for rapid and precise optical quantum computation.
We report an experimental realization of the Jaynes-Cummings-Hubbard (JCH) model using the internal and radial phonon states of two trapped ions. An adiabatic transfer corresponding to a quantum phase transition from a localized insulator ground state to a delocalized superfluid (SF) ground state is demonstrated. The SF phase of polaritonic excitations characteristic of the interconnected Jaynes-Cummings (JC) system is experimentally explored, where a polaritonic excitation refers to a combination of an atomic excitation and a phonon interchanged via a JC coupling.
The connection between the quantum-vacuum geometric phases (which originates from the vacuum zero-point electromagnetic fluctuation) and the non-normal product procedure is considered in the present Letter. In order to investigate this physically interesting geometric phases at quantum-vacuum level, we suggest an experimentally feasible scheme to test it by means of a noncoplanarly curved fiber made of gyrotropic media. A remarkable feature of the present experimental realization is that one can easily extract the nonvanishing and nontrivial quantum-vacuum geometric phases of left- and/or righ…
Using the spontaneous parametric down-conversion process in a type-I phase matching BBO crystal as single photon source, we perform an all-or-nothing-type Kochen-Specker experiment proposed by Simon \QTR{it}{et al}. [Phys. Rev. Lett. \QTR{bf}{85}, 1783 (2000)] to verify whether noncontextual hidden variables or quantum mechanics is right. The results strongly agree with quantum mechanics.
A two qubit quantum gate, namely the C-Phase, has been realized by exploiting the longitudinal momentum (i.e. the optical path) degree of freedom of a single photon. The experimental setup used to engineer this quantum gate represents an advanced version of the high stability closed-loop interferometric setup adopted to generate and characterize 2-photon 4-qubit Phased Dicke states. Some experimental results, dealing with the characterization of multipartite entanglement of the Phased Dicke states are also discussed in detail.
We generalize the quantum Prisoner's Dilemma to the case where the players share a non maximally entangled states. We show that the game exhibits an intriguing structure as a function of the amount of entanglement with two thresholds which separate a classical region, an intermediate region and a fully quantum region. Furthermore this quantum game is experimentally realized on our nuclear magnetic resonance quantum computer.
We demonstrate an implementation of unambiguous state discrimination of two equally probable single-qubit states via a one-dimensional photonic quantum walk experimentally. Furthermore we experimentally realize a quantum walk algorithm for implementing a generalized measurement in terms of positive operator value measurement on a single qubit. The measurement of the single-photons' positions corresponds to a measurement of an element of the positive operator value measurement on the polarizations of the single-photons.
In counterfactual QKD information is transfered, in a secure way, between Alice and Bob even when no particle carrying the information is in fact transmitted between them. In this letter we fully implement the scheme for counterfactual QKD proposed in [T. Noh, \PRL \textbf{103}, 230501 (2009)], demonstrating for the first time that information can be transmitted between two parties without the transmission of a carrier.
We report the realization of a nuclear magnetic resonance (NMR) quantum computer which combines the quantum Fourier transform (QFT) with exponentiated permutations, demonstrating a quantum algorithm for order-finding. This algorithm has the same structure as Shor's algorithm and its speed-up over classical algorithms scales exponentially. The implementation uses a particularly well-suited five quantum bit molecule and was made possible by a new state initialization procedure and several quantum control techniques.
We report the first experimental demonstration of an all-optical one-way implementation of Deutsch's quantum algorithm on a four-qubit cluster state. All the possible configurations of a balanced or constant function acting on a two-qubit register are realized within the measurement-based model for quantum computation. The experimental results are in excellent agreement with the theoretical model, therefore demonstrating the successful performance of the algorithm.
In this paper, we report an experimental realization of quantum switch using nuclear spins and magnetic resonant pulses. The nuclear spins of H and C in carbon-13 labelled chloroform are used to carry the information, then nuclear magnetic resonance pulses are applied to perform either bypass or cross function to achieve the switching. Compared with a traditional space or time domain switch, this switching architecture is much more scalable, therefore a high throughput switching device can be built simply by increasing the number of I/O ports. In addition, it can be used not only as a device t…
The three-qubit conditional swap gate(Fredkin gate) is a universal gate that can be used to create any logic circuit and has many direct usages. In this paper, we experimentally realized Fredkin gate with only three transition pulses in solution of alanine. It appears that no experimental realization of Fredkin gate with fewer pulses has yet been reported up to now. In addition, the simple structure of our scheme makes it easy to be implemented in experiments.
Random access memory is an indispensable device for classical information technology. Analog to this, for quantum information technology, it is desirable to have a random access quantum memory with many memory cells and programmable access to each cell. We report an experiment that realizes a random access quantum memory of 105 qubits carried by 210 memory cells in a macroscopic atomic ensemble. We demonstrate storage of optical qubits into these memory cells and their read-out at programmable times by arbitrary orders with fidelities exceeding any classical bound. Experimental realization of …
Sequential weak measurements of non-commuting observables is not only fundamentally interesting in quantum measurement but also shown potential in various applications. The previous reported methods, however, can only realize limited sequential weak measurements experimentally. In this Letter, we propose the realization of sequential measurements of arbitrary observables and experimentally demonstrate for the first time the measurement of sequential weak values of three non-commuting Pauli observables by using genuine single photons. The results presented here will not only improve our underst…
We compare several optical implementations of phase-covariant cloning machines. The experiments are based on copying of the polarization state of a single photon in bulk optics by special unbalanced beam splitter or by balanced beam splitter accompanied by a state filtering. Also the all-fiber based setup is discussed, where the information is encoded into spatial modes, i.e., the photon can propagate through two optical fibers. Each of the four implementations possesses some advantages and disadvantages that are discussed.
The three-box problem is a gedankenexperiment designed to elucidate some interesting features of quantum measurement and locality. A particle is prepared in a particular superposition of three boxes, and later found in a different (but nonorthogonal) superposition. It was predicted that appropriate "weak" measurements of particle position in the interval between preparation and post-selection would find the particle in two different places, each with certainty. We verify these predictions in an optical experiment and address the issues of locality and of negative probability.
To realize long-distance quantum communication and quantum network, it is required to have multiplexed quantum memory with many memory cells. Each memory cell needs to be individually addressable and independently accessible. Here we report an experiment that realizes a multiplexed DLCZ-type quantum memory with 225 individually accessible memory cells in a macroscopic atomic ensemble. As a key element for quantum repeaters, we demonstrate that entanglement with flying optical qubits can be stored into any neighboring memory cells and read out after a programmable time with high fidelity. Exper…
The controlled-NOT gate and controlled square-root NOT gate play an important role in quantum algorithm. This article reports the experimental results of these two universal quantum logic gates (controlled square-root NOT gate and controlled-NOT gate) on a 7-qubit NMR quantum computer. Further, we propose a simple experimental method to measure and correct the error in the controlled phase-shift gate, which is helpful to construct a more perfect phase-shift gate experimentally and can also be used in more qubits discrete Fourier transformation.
Quantum state transfer between different sites is a significant problem for quantum networks and quantum computers. By selecting quantum walks with two coins as the basic model and two coin spaces as the communication carriers, we successfully implement quantum state transfer on various graphs (EPL, \textbf{124} (2018) 60009) \cite{Shang_2019}. Here, we demonstrate the experimental implementation of this scheme using IBM quantum experience platform. In particular, we show the transfer of Bell state, GHZ state and W state on complete graph on the quantum device. Also, we observe that our protoc…
We report the first experimental demonstration of a quantum controlled-NOT gate for different photons, which is classically feed-forwardable. In the experiment, we achieved this goal with the use only of linear optics, an entangled ancillary pair of photons and post-selection. The techniques developed in our experiment will be of significant importance for quantum information processing with linear optics.
Efficient teleportation is a crucial step for quantum computation and quantum networking. In the case of qubits, four different entangled Bell states have to be distinguished. We have realized a probabilistic, but in principle deterministic, Bell-state analyzer for two photonic quantum bits by the use of a nondestructive controlled-NOT gate based on entirely linear optical elements. This gate was capable of distinguishing between all of the Bell states with higher than 75% fidelity without any noise substraction due to utilizing quantum interference effects.
A quantum cryptosystem is proposed using single-photon states with different frequency spectra as information carriers. A possible experimental implementation of the cryptosystem is discussed.
Symmetric informationally complete positive operator-valued measurement (SIC-POVM) is one important class of quantum measurement which is crucial for various quantum information processing tasks. SIC-POVMs have the advantage of providing an unbiased estimator for quantum states with the minimal number of outcomes needed for full tomography. We present an experimental approach on a photonic quantum walk which can be used to implement SIC-POVMs on a single-qbubit. The projection measurements of single-photons' positions correspond to elements of SIC-POVM on the polarization of single-photons.
We propose and experimentally demonstrate that a Mach-Zehnder interferometer composed of polarized beam splitters and a pentaprism in the place of one of the mirrors works as a linear optical quantum controlled-NOT (CNOT) gate. To perform the information processing, the polarization and orbital angular momentum (OAM) of the photons act as the control and target qubits, respectively. The readout process is simple, requiring only a linear polarizer and a triangular diffractive aperture before detection. The viability and stability of the experiment makes the present proposal a valuable candidate…
We report on a quantum optical experimental implementation of teleportation of unknown pure quantum states. This realizes all the nonlocal aspects of the original scheme proposed by Bennett et al. and is equivalent to it up to a local operation. We exhibit results for the teleportation of a linearly polarized state and of an elliptically polarized state. We show that the experimental results cannot be explained in terms of a classical channel alone.
According to the theoretical results, the quantum searching algorithm can be generalized by replacing the Walsh-Hadamard(W-H) transform by almost any quantum mechanical operation. We have implemented the generalized algorithm using nuclear magnetic resonance techniques with a solution of chloroform molecules. Experimental results show the good agreement between theory and experiment.
Squeezing is a nonlinear Gaussian operation that is the key component in construction of other nonlinear Gaussian gates. In our implementation of the squeezing gate, the amount and the orientation of the squeezing can be controlled by an external driving signal with 1 MHz operational bandwidth. This opens a brand new area of dynamic Gaussian processing. In particular, the gate can be immediately employed as the feed-forward needed for the deterministic implementation of the quantum cubic gate, which is a key piece of universal quantum information processing.
We propose a scalable method on the basis of nth-order coupling operators to construct f-dependent phase transformations in the n-qubit modified Deutsch-Jozsa (D-J) quantum algorithm. The novel n-qubit entangling transformations are easily implemented via J-couplings between neighboring spins. The seven-qubit modified D-J quantum algorithm and seventh-order coupling transformations are then experimentally demonstrated with liquid state nuclear magnetic resonance (NMR) techniques. The method may offer the possibility of creating generally entangled states of n qubits and simulating n-body inter…
