arXiv subjects

Karol Bartkiewicz

Publications and source records attributed to Karol Bartkiewicz.

At least 55 records · Page 3Linked to original sources

arXiv2016

Bell nonlocality and fully-entangled fraction measured in an entanglement-swapping device without quantum state tomography

We demonstrate an efficient experimental procedure based on entanglement swapping to determine the Bell nonlocality measure of Horodecki et al. [Phys. Lett. A 200, 340 (1995)] and the fully-entangled fraction of Bennett et al. [Phys. Rev. A 54, 3824 (1996)] of an arbitrary two-qubit polarization-encoded state. The nonlocality measure corresponds to the amount of the violation of the Clauser-Horne-Shimony-Holt (CHSH) optimized over all measurement settings. By using simultaneously two copies of a given state, we measure directly only six parameters. Our method requires neither full quantum state tomography of 15 parameters nor continuous scanning of the measurement bases used by two parties in the usual CHSH inequality tests with four measurements in each optimization step. We analyze how well the measured degrees of Bell nonlocality and other entanglement witnesses (including the fully-entangled fraction and a nonlinear entropic witness) of an arbitrary two-qubit state can estimate its entanglement. In particular, we measured these witnesses and estimated the negativity of various two-qubit Werner states. Our approach could especially be useful for quantum communication protocols based on entanglement swapping.

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arXiv2016

Measuring evolution of a photon in an interferometer with spectrally-resolved modes

In the year 2013, Danan et al. published a paper [Phys. Rev. Lett. 111, 240402 (2013)] demonstrating a counterintuitive behavior of photons in nested Mach-Zehnder interferometers. The authors then proposed an explanation based on the two-state vector formalism. This experiment and the authors' explanation raised a vivid debate within the scientific community. In this paper, we contribute to the ongoing debate by presenting an alternative experimental implementation of the Danan et al. scheme. We show that no counterintuitive behavior is observed when performing direct spectrally-resolved detection.

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arXiv2016

Experimental measurement of the collectibility of two-qubit states

We present a proof-of-principle experiment demonstrating measurement of the collectibility, a nonlinear entanglement witness proposed by Rudnicki et al. [Phys. Rev. Lett. 107, 150502 (2011)]. This entanglement witness works for both mixed and pure two-qubit states. In the later case it can be used to measure entanglement in terms of the negativity. We measured the collectibility for three distinct classes of photonic polarization-encoded two-qubit states, i.e., maximally entangled, separable and maximally mixed states. We demonstrate that the measurement procedure is feasible and robust against typical experimental shortcomings such as imperfect two-photon indistinguishability.

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arXiv2016

Temporal steering and security of quantum key distribution with mutually-unbiased bases against individual attacks

Temporal steering, which is a temporal analogue of Einstein-Podolsky-Rosen steering, refers to temporal quantum correlations between the initial and final state of a quantum system. Our analysis of temporal steering inequalities in relation to the average quantum bit error rates reveals the interplay between temporal steering and quantum cloning, which guarantees the security of quantum key-distribution based on mutually-unbiased bases against individual attacks. The key distributions analyzed here include the Bennett-Brassard 1984 protocol (BB84) and the six-state 1998 protocol by Bruss (B98). Moreover, we define a temporal steerable weight, which enables us to identify a kind of monogamy of temporal correlations that is essential to quantum cryptography and useful for analyzing various scenarios of quantum causality.

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arXiv2015

Increasing relative nonclassicality quantified by standard entanglement potentials by dissipation and unbalanced beam splitting

If a single-mode nonclassical light is combined with the vacuum on a beam splitter, then the output state is entangled. As proposed in [Phys. Rev. Lett. 94, 173602 (2005)], by measuring the output-state entanglement for a balanced lossless beam splitter, one can quantify the input-state nonclassicality. These measures of nonclassicality (referred to as entanglement potentials) can be based, in principle, on various entanglement measures, leading to the negativity (NP) and concurrence (CP) potentials, and the potential for the relative entropy of entanglement (REEP). We search for the maximal nonclassicality, which can be achieved by comparing two entanglement measures for arbitrary two-qubit states and those which can be generated from a photon-number qubit via a balanced lossless beam-splitter, where the qubit basis states are the vacuum and single-photon states. Surprisingly, we find that the maximal nonclassicality, measured by the REEP for a given value of the NP, can be increased (if NP<0.527) by using either a tunable beam splitter or by amplitude damping of the output state of the balanced beam splitter. We also show that the maximal nonclassicality, measured by the NP for a given value of the REEP, can be increased by dephasing. The entanglement itself is not increased by these local losses, but the possible ratios of different measures are affected. Moreover, we show that partially-mixed states can be more nonclassical than both pure states and completely-mixed states, by comparing the NP for a given value of the REEP. This implies that not all entanglement measures can be used as entanglement potentials. Alternatively, a single balanced lossless beam splitter is not always transferring the whole nonclassicality of its input state into the entanglement of its output modes. Applying a lossy beam splitter can solve this problem at least for the cases analyzed in this paper.

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arXiv2015

Priority Choice Experimental Two-qubit Tomography: Measuring One by One All Elements of Density Matrices

In standard optical tomographic methods, the off-diagonal elements of a density matrix $ρ$ are measured indirectly. Thus, the reconstruction of $ρ$, even if it is based on linear inversion, typically magnifies small errors in the experimental data. Recently, an optimal tomography [Phys. Rev. A 90, 062123 (2014)] has been proposed theoretically to measure one-by-one all the elements of $ρ$. Thus, the relative errors in the reconstructed state can be the same as those in the experimental data. We implemented this method for two-qubit polarization states performing both local and global measurements. For comparison, we also experimentally implemented other well-known tomographic protocols based solely on local measurements (of, e.g., the Pauli operators and James-Kwiat-Munro-White projectors) and those with mutually unbiased bases requiring both local and global measurements. We reconstructed seventeen of two-qubit polarization states including separable, partially and maximally entangled. Our experiments show the highest stability against errors of our method in comparison to the other quantum tomographies. In particular, we demonstrate that each optimally-reconstructed state} is embedded in the uncertainty circle of the smallest radius, both in terms of the trace distance and disturbance. We explain how to estimate experimentally the uncertainty radii for all the implemented tomographies and show that, for each reconstructed state, the relevant uncertainty circles intersect indicating the approximate location of the corresponding physical density matrix.

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arXiv2015

Scheme for a linear-optical controlled-phase gate with programmable phase shift

We present a linear-optical scheme for a controlled-phase gate with tunable phase shift programmed by a qubit state. In contrast to all previous tunable controlled-phase gates, the phase shift is not hard-coded into the optical setup, but can be tuned to any value from 0 to pi by the state of a so-called program qubit. Our setup is feasible with current level of technology using only linear-optical components. We provide an experimental feasibility study to assess the gate's implementability. We also discuss options for increasing the success probability up to 1/12 which approaches the success probability of a optimal non-programmable tunable controlled-phase gate.

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arXiv2015

Quantifying entanglement of a two-qubit system via measurable and invariant moments of its partially transposed density matrix

We describe a direct method to determine the negativity of an arbitrary two-qubit state in experiments. The method is derived by analyzing the relation between the purity, negativity, and a universal entanglement witness for two-qubit entanglement. We show how the negativity of a two-qubit state can be calculated from just three experimentally accessible moments of the partially transposed density matrix of a two-photon state. Moreover, we show that the negativity can be given as a function of only six invariants, which are linear combinations of nine invariants from the complete set of 21 fundamental and independent two-qubit invariants. We analyze the relation between these moments and the concurrence for some classes of two-qubit states (including the X states, as well as pure states affected by the amplitude-damping and phase-damping channels). We also discuss the possibility of using the universal entanglement witness as an entanglement measure for various classes of two-qubit states. Moreover, we analyze how noise affects the estimation of entanglement via this witness.

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arXiv2015

Method for universal detection of two-photon polarization entanglement

Detecting and quantifying quantum entanglement of a given unknown state poses problems that are fundamentally important for quantum information processing. Surprisingly, no direct (i.e., without quantum tomography) universal experimental implementation of a necessary and sufficient test of entanglement has been designed even for a general two-qubit state. Here we propose an experimental method for detecting a collective universal witness, which is a necessary and sufficient test of two-photon polarization entanglement. It allows us to detect entanglement for any two-qubit mixed state and to establish tight upper and lower bounds on its amount. A different element of this method is the sequential character of its main components, which allows us to obtain relatively complicated information about quantum correlations with the help of simple linear-optical elements. As such, this proposal realizes a universal two-qubit entanglement test within the present state of the art of quantum optics. We show the optimality of our setup with respect to the minimal number of measured quantities.

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arXiv2015

Statistical mixtures of states can be more quantum than their superpositions: Comparison of nonclassicality measures for single-qubit states

A bosonic state is commonly considered nonclassical (or quantum) if its Glauber-Sudarshan $P$ function is not a classical probability density, which implies that only coherent states and their statistical mixtures are classical. We quantify the nonclassicality of a single qubit, defined by the vacuum and single-photon states, by applying the following four well-known measures of nonclassicality: (1) the nonclassical depth, $τ$, related to the minimal amount of Gaussian noise which changes a nonpositive $P$ function into a positive one; (2) the nonclassical distance $D$, defined as the Bures distance of a given state to the closest classical state, which is the vacuum for the single-qubit Hilbert space; together with (3) the negativity potential (NP) and (4) concurrence potential, which are the nonclassicality measures corresponding to the entanglement measures (i.e., the negativity and concurrence, respectively) for the state generated by mixing a single-qubit state with the vacuum on a balanced beam splitter. We show that complete statistical mixtures of the vacuum and single-photon states are the most nonclassical single-qubit states regarding the distance $D$ for a fixed value of both the depth $τ$ and NP in the whole range $[0,1]$ of their values, as well as the NP for a given value of $τ$ such that $τ>0.3154$. Conversely, pure states are the most nonclassical single-qubit states with respect to $τ$ for a given $D$, NP versus $D$, and $τ$ versus NP. We also show the "relativity" of these nonclassicality measures by comparing pairs of single-qubit states: if a state is less nonclassical than another state according to some measure then it might be more nonclassical according to another measure. Moreover, we find that the concurrence potential is equal to the nonclassical distance for single-qubit states.

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arXiv2014

Optimal two-qubit tomography based on local and global measurements: Maximal robustness against errors as described by condition numbers

We present an error analysis of various tomographic protocols based on the linear inversion for the reconstruction of an unknown two-qubit state. We solve the problem of finding a tomographic protocol which is the most robust against errors in terms of the lowest value (i.e., equal to 1) of a condition number, as required by the Gastinel-Kahan theorem. In contrast, standard tomographic protocols, including those based on mutually unbiased bases, are nonoptimal for determining all 16 elements of an unknown two-qubit density matrix. Our method is based on the measurements of the 16 generalized Pauli operators, where twelve of them can be locally measured, and the other four require nonlocal Bell measurements. Our method corresponds to selectively measuring, one by one, all of the real and imaginary elements of an unknown two-qubit density matrix. We describe two experimentally feasible setups of this protocol for the optimal reconstruction of two photons in an unknown polarization state using conventional detectors and linear-optical elements. Moreover, we define the operators for the optimal reconstruction of the states of multiqubit or multilevel (qudit) systems.

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arXiv2014

Knowing "where the photons have been"

Linear-optical interferometers play a key role in designing circuits for quantum information processing and quantum communications. Even though nested Mach-Zehnder interferometers appear easy to describe, there are occasions when they provide unintuitive results. This paper explains the results of a highly discussed experiment performed by Danan et al. [Phys. Rev. Lett. 111, 240402 (2013)] using a standard approach. We provide a simple and intuitive one-state vector formalism capable of interpreting their experiment. Additionally, we cross-checked our model with a classical-physics based approach and found that both models are in complete agreement. We argue that the quantity used in the mentioned experiment is not a suitable which-path witness producing seemingly contra-intuitive results. To circumvent this issue, we establish a more reliable which-path witness and show that it yields well expected outcomes of the experiment.

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arXiv2014

Experimental implementation of optimal linear-optical controlled-unitary gates

We show that it is possible to reduce the number of two-qubit gates needed for the construction of an arbitrary controlled-unitary transformation by up to two times using a tunable controlled-phase gate. On the platform of linear optics, where two-qubit gates can only be achieved probabilistically, our method significantly reduces the amount of components and increases success probability of a two-qubit gate. The experimental implementation of our technique presented in this paper for a controlled single-qubit unitary gate demonstrates that only one tunable controlled-phase gate is needed instead of two standard controlled-NOT gates. Thus, not only do we increase success probability by about one order of magnitude (with the same resources), but also avoid the need for conducting quantum non-demolition measurement otherwise required to join two probabilistic gates. Subsequently, we generalize our method to a higher order, showing that n-times controlled gates can be optimized by replacing blocks of controlled-NOT gates with tunable controlled-phase gates.

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arXiv2014

Using quantum routers to implement quantum message authentication and Bell-state manipulation

In this paper we investigate the capability of quantum routing (quantum state fusion) to implement two useful quantum communications protocols. The analyzed protocols include quantum authentication of quantum messages and non-destructive linear-optical Bell state manipulation. We also present the concept of quantum decoupler -- a device implementing an inverse operation to quantum routing. We demonstrate that both quantum router and decoupler can work as specialized disentangling gates.

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arXiv2014

Efficient Amplification of Photonic Qubits by Optimal Quantum Cloning

We demonstrate that a phase-independent quantum amplifier of a polarization qubit is a complementary amplifier of the heralded qubit amplifier [N. Gisin, S. Pironio and N. Sangouard, Phys. Rev. Lett. 105, 070501 (2010)]. It employs the multi-functional cloner in 1 to 2 copying regime, capable of providing approximate copies of qubits given by various probability distributions, and is optimized for distributions with axial symmetry. Direct applications of the proposed solution are possible in quantum technologies, doubling the range where quantum information is coherently broadcast. It also outperforms natural nonlinear amplifiers that use stimulated emission in bulk nonlinear materials. We consider the amplifier to be an important tool for amplifying quantum information sent via quantum channels with phase-independent damping.

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arXiv2013

Entanglement estimation from Bell inequality violation

It is well known that the violation of Bell's inequality in the form given by Clauser, Horne, Shimony, and Holt (CHSH) in two-qubit systems requires entanglement, but not vice versa, i.e., there are entangled states which do not violate the CHSH inequality. Here we compare some standard entanglement measures with violations of the CHSH inequality (as given by the Horodecki measure) for two-qubit states generated by Monte Carlo simulations. We describe states that have extremal entanglement according to the negativity, concurrence, and relative entropy of entanglement for a given value of the CHSH violation. We explicitly find these extremal states by applying the generalized method of Lagrange multipliers based on the Karush-Kuhn-Tucker conditions. The found minimal and maximal states define the range of entanglement accessible for any two-qubit states that violate the CHSH inequality by the same amount. We also find extremal states for the concurrence versus negativity by considering only such states which do not violate the CHSH inequality. Furthermore, we describe an experimentally efficient linear-optical method to determine the highest Horodecki degree of the CHSH violation for arbitrary mixed states of two polarization qubits. By assuming to have access simultaneously to two copies of the states, our method requires only six discrete measurement settings instead of nine settings, which are usually considered.

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arXiv2013

Direct method for measuring of purity, superfidelity, and subfidelity of photonic two-qubit mixed states

The Uhlmann-Jozsa fidelity (or, equivalently, the Bures distance) is a basic concept of quantum communication and quantum information, which however is very difficult to measure efficiently without recourse to quantum tomography. Here we propose a direct experimental method to estimate the fidelity between two unknown two-qubit mixed states via the measurement of the upper and lower bounds of the fidelity, which are referred to as the superfidelity and subfidelity, respectively. Our method enables a direct measurement of the first- and second-order overlaps between two arbitrary two-qubit states. In particular, the method can be applied to measure the purity (or linear entropy) of a single two-qubit mixed state in a direct experiment. We also propose and critically compare several experimental strategies for measuring the sub- and superfidelities of polarization states of photons in various linear-optical setups.

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arXiv2013

State-dependent linear-optical qubit amplifier

We propose a linear-optical setup for heralded qubit amplification with tunable output qubit fidelity. We study its success probability as a function of output qubit fidelity showing that at the expense of lower fidelity, the setup can considerably increase probability of successful operation. These results are subsequently applied in a proposal for state dependent qubit amplification. Similarly to state-dependent quantum cloning, the a priori information about the input state allows to optimize the qubit amplification procedure to obtain better fidelity versus success probability trade-off.

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