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We address the fundamental task of converting $n$ uses of an unknown unitary transformation into a quantum state (i.e., storage) and later retrieval of the transformation. Specifically, we consider the case where the unknown unitary is selected with equal prior probability from two options. First, we prove that the optimal storage strategy involves the sequential application of the $n$ uses of the unknown unitary, and it produces the optimal state for discrimination between the two possible unitaries. Next, we show that incoherent "measure-and-prepare" retrieval achieves the maximum fidelity between the retrieved operation and the original (qubit) unitary. We then identify the retrieval strategy that maximizes the probability of successfully and perfectly retrieving the unknown transformation. In the regime in which the fidelity between the two possible unitaries is large the probability of success scales as $ P_{succ} = 1 - \mathcal{O}(n^{-2} ) $, which is a quadratic improvement with respect to the case in which the unitaries are drawn from the entire unitary group $U(d)$ with uniform prior probability. Finally, we present an optical experiment for this approach and assess the storage and retrieval quality using quantum tomography of states and processes. The results are discussed in relation to non-optimal measure-and-prepare strategy, highlighting the advantages of our protocol., Comment: 18 pages, 10 figures

Oblivious transfer (OT) is an important cryptographic primitive. Any multi-party computation can be realised with OT as building block. XOR oblivious transfer (XOT) is a variant where the sender Alice has two bits, and a receiver Bob obtains either the first bit, the second bit, or their XOR. Bob should not learn anything more than this, and Alice should not learn what Bob has learnt. Perfect quantum OT with information-theoretic security is known to be impossible. We determine the smallest possible cheating probabilities for unrestricted dishonest parties in non-interactive quantum XOT protocols using symmetric pure states, and present an optimal protocol, which outperforms classical protocols. We also "reverse" this protocol, so that Bob becomes sender of a quantum state and Alice the receiver who measures it, while still implementing oblivious transfer from Alice to Bob. Cheating probabilities for both parties stay the same as for the unreversed protocol. We optically implemented both the unreversed and the reversed protocols, and cheating strategies, noting that the reversed protocol is easier to implement., Comment: 23 pages, 6 figures; v2: added Subsection IV.A and other minor additions

We theoretically and experimentally investigate conditional enhancement of overall coherence of quantum states by probabilistic quantum operations that apply to the input state a quantum filter diagonal in the basis of incoherent states. We identify the optimal filters that for a given probability of successful filtering maximize the output coherence. We verify the performance of the studied quantum filters in a proof-of-principle experiment with linear optics, where a pair of two-level quantum systems is represented by polarization states of two photons. We comprehensively characterize the implemented two-qubit linear optical quantum filters by full quantum process tomography and we experimentally observe the optimal quantum coherence enhancement by quantum filtering., Comment: 10 pages, 7 figures

We design optimal interferometric schemes for implementation of two-qubit linear optical quantum filters diagonal in the computational basis. The filtering is realized by interference of the two photons encoding the qubits in a multiport linear optical interferometer, followed by conditioning on presence of a single photon in each output port of the filter. The filter thus operates in the coincidence basis, similarly to many linear optical unitary quantum gates. Implementation of the filter with linear optics may require an additional overhead in terms of reduced overall success probability of the filtering and the optimal filters are those that maximize the overall success probability. We discuss in detail the case of symmetric real filters and extend our analysis also to asymmetric and complex filters., Comment: 11 pages, 5 figures, REVTeX

We prove experimentally the predicted existence of a three-qubit quantum state with genuine multipartite entanglement which can be certified solely from its separable two-qubit reduced density matrices. The qubits are encoded into different degrees of freedom of a pair of correlated photons and the state is prepared by letting the photons to propagate through a linear optical circuit. The presence of genuine multipartite entanglement is verified by finding numerically a fully decomposable entanglement witness acting nontrivially only on the reductions of the global state. Our result confirms viability of detection of emerging global properties of composite quantum systems from their parts which lack the properties., Comment: 9 pages, 10 figures

Oblivious transfer is an important primitive in modern cryptography. Applications include secure multiparty computation, oblivious sampling, e-voting, and signatures. Information-theoretically secure perfect 1-out-of 2 oblivious transfer is impossible to achieve. Imperfect variants, where both participants' ability to cheat is still limited, are possible using quantum means while remaining classically impossible. Precisely what security parameters are attainable remains unknown. We introduce a theoretical framework for studying semirandom quantum oblivious transfer, which is shown to be equivalent to regular oblivious transfer in terms of cheating probabilities. We then use it to derive bounds on cheating. We also present a protocol with lower cheating probabilities than previous schemes, together with its optical realization. We show that a lower bound of 2/3 on the minimum achievable cheating probability can be directly derived for semirandom protocols using a different method and definition of cheating than used previously. The lower bound increases from 2/3 to approximately 0.749 if the states output by the protocol are pure and symmetric. The oblivious transfer scheme we present uses unambiguous state elimination measurements and can be implemented with the same technological requirements as standard quantum cryptography. The cheating probabilities are 3/4 and approximately 0.729 for sender and receiver respectively, which is lower than in existing protocols. Using a photonic test-bed, we have implemented the protocol with honest parties, as well as optimal cheating strategies., Comment: 22 pages, 1 figure, v2 moderate changes, published version

Coherent interaction of a quantum system with environment usually induces quantum decoherence. However, remarkably, in certain configurations the coherent system-environment coupling can be simultaneously explored to engineer a specific dark state of the environment that eliminates the decoherence. Here we report on experimental demonstration of such protocol for suppression of quantum decoherence by quantum decoherence itself. The protocol is based on indirect control of the environment via quantum measurements on quantum probes interacting with the environment prior to the system that should be protected. No direct manipulation with the environment is required to suppress the decoherence. In our proof-of-principle experiment, we demonstrate protection of a single qubit coupled to another single qubit. We implement the required quantum circuits with linear optics and single photons, which allows us to maintain very high degree of control and flexibility in the experiment. Our results clearly confirm the decoherence suppression achieved by the protocol and pave the way to its application to other physical platforms., Comment: 10 pages, 7 figures

Generation of particular polarization states of light, encoding information in polarization degree of freedom, and efficient measurement of unknown polarization are the key tasks in optical metrology, optical communications, polarization-sensitive imaging, and photonic information processing. Liquid crystal devices have proved to be indispensable for these tasks, though their limited precision and the requirement of a custom design impose a limit of practical applicability. Here we report fast preparation and detection of polarization states with unprecedented accuracy using liquid-crystal cells extracted from common twisted nematic liquid-crystal displays. To verify the performance of the device we use it to prepare dozens of polarization states with average fidelity 0.999(1) and average angle deviation 0.5(3) deg. Using four-projection minimum tomography as well as six-projection Pauli measurement, we measure polarization states employing the reported device with the average fidelity of 0.999(1). Polarization measurement data are processed by the maximum likelihood method to reach a valid estimate of the polarization state. In addition to the application in classical polarimetry, we also employ the reported liquid-crystal device for full tomographic characterization of a three-mode Greenberger--Horne--Zeilinger entangled state produced by a photonic quantum processor., Comment: data&code: https://github.com/BielakM/polarimeter

We propose an experimental method of recognizing quantum non-Gaussian multiphoton states. This is a native quantum property of Fock states, the fundamental quantum states with a constant number of particles. Our method allows experimental development and characterization of higher Fock states of light, reaching even beyond the current technical limits of their generation. We experimentally demonstrate that it is capable of distinguishing realistic quantum non-Gaussian light with the mean number of photons up to 5 despite detection efficiency of 50 %. We also provide evidence that our method can help to distinguish the number of single-photon emitters based only on their collective emission., Comment: 9 pages, 5 figures

We experimentally characterize a quantum photonic gate that is capable of converting multiqubit entangled states while acting only on two qubits. It is an important tool in large quantum networks, where it can be used for re-wiring of multipartite entangled states or for generating various entangled states required for specific tasks. The gate can be also used to generate quantum information processing resources, such as entanglement and discord. In our experimental demonstration, we converted a linear four-qubit cluster state into different entangled states, including GHZ and Dicke states. The high quality of the experimental results show that the gate has the potential of being a flexible component in distributed quantum photonic networks., Comment: 5 pages, 4 figures

One of the strengths of quantum information theory is that it can treat quantum states without referring to their particular physical representation. In principle, quantum states can be therefore fully swapped between various quantum systems by their mutual interaction and this quantum state transfer is crucial for many quantum communication and information processing tasks. In practice, however, the achievable interaction time and strength are often limited by decoherence. Here we propose and experimentally demonstrate a procedure for faithful quantum state transfer between two weakly interacting qubits. Our scheme enables a probabilistic yet perfect unidirectional transfer of an arbitrary unknown state of a source qubit onto a target qubit prepared initially in a known state. The transfer is achieved by a combination of a suitable measurement of the source qubit and quantum filtering on the target qubit depending on the outcome of measurement on the source qubit. We experimentally verify feasibility and robustness of the transfer using a linear optical setup with qubits encoded into polarization states of single photons., Comment: 9 pages, 5 figures

We propose and experimentally verify a cooling limit for a quantum channel going through an incoherent environment. The environment consists of a large number of independent non-interacting and non-interfering elementary quantum systems - qubits. The qubits travelling through the channel can only be randomly replaced by environmental qubits. We investigate a conditional cooling limit that exploits an additional probing output. The limit specifies when the single-qubit channel is quantum, i.e. it preserves entanglement. It is a fundamental condition for entanglement-based quantum technology., Comment: 5 pages, 4 figures, 1 sputnik

We experimentally demonstrate optical Mach-Zehnder interferometer utilizing displaced Sagnac configuration to enhance its phase stability. The interferometer with footprint of 27x40 cm offers individually accessible paths and shows phase deviation less than 0.4 deg during a 250 s long measurement. The phase drift, evaluated by means of Allan deviation, stays below 3 deg or 7 nm for 1.5 hours without any active stabilization. The polarization insensitive design is verified by measuring interference visibility as a function of input polarization. For both interferometer's output ports and all tested polarization states the visibility stays above 93%. The discrepancy in visibility for horizontal and vertical polarization about 3.5% is caused mainly by undesired polarization dependence of splitting ratio of the beam splitter used. The presented interferometer device is suitable for quantum-information and other sensitive applications where active stabilization is complicated and common-mode interferometer is not an option as both the interferometer arms have to be accessible individually., Comment: 4 pages, 3 figures, minor changes, references updated

We demonstrate a scheme to generate noncoherent and coherent correlations, i.e., a tunable degree of entanglement, between degrees of freedom of a single photon. Its nature is analogous to the tuning of the purity (first-order coherence) of a single photon forming part of a two-photon state by tailoring the correlations between the paired photons. Therefore, well-known tools such as the Clauser-Horne-Shimony-Holt (CHSH) Bell-like inequality can also be used to characterize entanglement between degrees of freedom. More specifically, CHSH inequality tests are performed, making use of the polarization and the spatial shape of a single photon. The four modes required are two polarization modes and two spatial modes with different orbital angular momentum., Comment: 7 pages, 5 figures. Updated to be consistent with published version

We introduce and experimentally explore the concept of quantum non-Gaussian depth of single-photon states with a positive Wigner function. The depth measures the robustness of a single-photon state against optical losses. The directly witnessed quantum non-Gaussianity withstands significant attenuation, exhibiting a depth of 18 dB, while the nonclassicality remains unchanged. Quantum non-Gaussian depth is an experimentally approachable quantity that is much more robust than the negativity of the Wigner function. Furthermore, we use it to reveal significant differences between otherwise strongly nonclassical single-photon sources., Comment: 6 pages, 3 figures, 1 onion

We propose an efficiently measurable lower bound on quantum process fidelity of N-qubit controlled-Z gates. This bound is determined by average output state fidelities for N partially conjugate product bases. A distinct advantage of our approach is that only fidelities with product states need to be measured while keeping the total number of measurements much smaller than what is necessary for full quantum process tomography. As an application, we use this method to experimentally estimate quantum process fidelity F of a three-qubit linear optical quantum Toffoli gate and we find that F>=0.83. We also demonstrate the entangling capability of the gate by preparing GHZ-type three-qubit entangled states from input product states., Comment: 9 pages, 4 figures, REVTeX4

We have studied how the quality of transfer of a qubit state depends on distinguishability of internal states of the particles carrying qubits. The transfer is implemented without any direct interaction, just by a partial exchange of photons, measurement on one of them, and conditional feed-forward correction. It appears that the quality of the transfer is only influenced by the level of distinguishability of the states of unaccessible internal degrees of freedom not used for information encoding. We have found a directly measurable parameter quantifying this level of distinguishability and proved it usefulness experimentally., Comment: 6 pages, 2 figures

We propose a protocol for conditional suppression of losses in direct quantum state transmission over a lossy quantum channel. The method works by noiselessly attenuating the input state prior to transmission through a lossy channel followed by noiseless amplification of the output state. The procedure does not add any noise hence it keeps quantum coherence. We experimentally demonstrate it in the subspace spanned by vacuum and single-photon states, and consider its general applicability., Comment: 5 pages, 4 figures, REVTeX4

We have successfully used a fast electronic feed forward to increase the success probability of a linear optical implementation of a programmable phase gate from 25% to its theoretical limit of 50%. The feed forward applies a conditional unitary operation which changes the incorrect output states of the data qubit to the correct ones. The gate itself rotates an arbitrary quantum state of the data qubit around the z-axis of the Bloch sphere with the angle of rotation being fully determined by the state of the program qubit. The gate implementation is based on fiber optics components. Qubits are encoded into spatial modes of single photons. The signal from the feed-forward detector is led directly to a phase modulator using only a passive voltage divider. We have verified the increase of the success probability and characterized the gate operation by means of quantum process tomography. We have demonstrated that the use of the feed forward does not affect either the process fidelity or the output-state fidelities.

An overwhelming majority of experiments in classical and quantum physics make a priori assumptions about the dimension of the system under consideration. However, would it be possible to assess the dimension of a completely unknown system only from the results of measurements performed on it, without any extra assumption? The concept of a dimension witness answers this question, as it allows one to bound the dimension of an unknown classical or quantum system in a device-independent manner, that is, only from the statistics of measurements performed on it. Here, we report on the experimental demonstration of dimension witnesses in a prepare and measure scenario. We use pairs of photons entangled in both polarization and orbital angular momentum to generate ensembles of classical and quantum states of dimensions up to 4. We then use a dimension witness to certify their dimensionality as well as their quantum nature. Our results open new avenues for the device-independent estimation of unknown quantum systems and for applications in quantum information science., Comment: See also similar, independent and jointly submitted work of J. Ahrens et al., quant-ph/1111.1277

We report on experimental verification of quantum non-Gaussianity of a heralded single photon state with positive Wigner function. We unambiguously demonstrate that the generated state cannot be expressed as a mixture of Gaussian states. A sufficient information to witness the quantum non-Gaussianity is obtained from a standard photon anti-correlation measurement.

We investigate optimal discrimination between two projective quantum measurements on a single qubit. We consider scenario where the measurement that should be identified can be performed twice and we show that adaptive discrimination strategy, entangled probe states, and feed-forward all help to increase the probability of correct identification of the measurement. We also experimentally demonstrate the studied discrimination strategies and test their performance. The employed experimental setup involves projective measurements on polarization states of single photons and preparation of required probe two-photon polarization states by the process of spontaneous parametric down-conversion and passive linear optics., Comment: 8 pages, 6 figures, accepted for publication in Physical Review A

We experimentally demonstrate a programmable single-qubit quantum gate. This device applies a unitary phase shift operation to a data qubit with the value of the phase shift being fully determined by the state of a program qubit. Our linear optical implementation is based on the encoding of qubits into polarization states of single photons, two-photon interference on a polarizing beam splitter, and measurement on the output program qubit. We fully characterize the programmable gate by quantum process tomography. The achieved average quantum process fidelity exceeding 97% illustrates very good performance of the gate for all values of the encoded phase shift. We also show that by using a different set of program states the device can operate as a programmable partial polarization filter., Comment: 5 pages, 5 figures, RevTeX4