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arXiv:2108.00221 · Quantum Science and Technology

Experimental demonstration of optimal probabilistic enhancement of quantum coherence

Robert Stárek, Michal Mičuda, Michal Kolář, Radim Filip, Jaromír Fiurášek

Published Jul 2, 2021• 5 citations
arXivHTMLPDF

Abstract

Abstract 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.

DOI
10.1088/2058-9565/ac10ef

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Abstract 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.
Quantum coherence is a fundamental resource in modern quantum physics with important applications in quantum technologies. In composite quantum systems, various forms of coherence emerge and play an important role, such as the global coherence, coherence of local subsystems, and the recently introduced mutual coherence. We investigate states that maximize the mutual coherence in various subspaces of the overall two-qubit Hilbert space and discover a nontrivial asymmetric optimal state in the three-dimensional subspace. We experimentally generate this optimal state from two factorized photonic qubits by a strictly incoherent probabilistic quantum operation that projects the input state onto the desired three-dimensional subspace. For comparison, we also experimentally test the preparation of states with maximal mutual coherence by unitary transformations of input product states. These proof-of-principle tests demonstrate the initial steps of control of mutual quantum coherence in qubit systems.
We propose and investigate bounds on the quantum process fidelity of quantum filters, i.e., probabilistic quantum operations represented by a single Kraus operator KKK. These bounds generalize the Hofmann bounds on the quantum process fidelity of unitary operations [H. F. Hofmann, Phys. Rev. Lett. 94, 160504 (2005)] and are based on probing the quantum filter with pure states forming two mutually unbiased bases. Determination of these bounds therefore requires far fewer measurements than full quantum process tomography. We find that it is particularly suitable to construct one of the probe bases from the right eigenstates of KKK, because in this case the bounds are tight in the sense that if the actual filter coincides with the ideal one, then both the lower and the upper bounds are equal to 1. We theoretically investigate the application of these bounds to a two-qubit optical quantum filter formed by the interference of two photons on a partially polarizing beam splitter. For an experimentally convenient choice of factorized input states and measurements we study the tightness of the bounds. We show that more stringent bounds can be obtained by more sophisticated processing of the data using convex optimization and we compare our methods for different choices of the input probe states.
Conditional quantum optical processes enable a wide range of technologies from generation of highly non-classical states to implementation of quantum logic operations. The process fidelity that can be achieved in a realistic implementation depends on a number of system parameters. Here we experimentally examine Fock state filtration, a canonical example of a broad class of conditional quantum operations acting on a single optical field mode. This operation is based upon interference of the mode to be manipulated with an auxiliary single-photon state at a beam splitter, resulting in the entanglement of the two output modes. A conditional projective measurement onto a single photon state at one output mode heralds the success of the process. This operation, which implements a measurement-induced nonlinearity, is capable of suppressing particular photon-number probability amplitudes of an arbitrary quantum state. We employ coherent-state process tomography to determine the precise operation realized in our experiment, which is mathematically represented by a process tensor. To identify the key sources of experimental imperfection, we develop a realistic model of the process and identify three main contributions that significantly hamper its efficacy. The experimentally reconstructed process tensor is compared with the model, yielding a fidelity better than 0.95. This enables us to identify three key challenges to overcome in realizing a filter with optimal performance—namely the single-photon nature of the auxiliary state, high mode overlap of the optical fields involved, and the need for photon-number-resolving detection when heralding. The results show that the filter does indeed exhibit a non-linear response as a function of input photon number and preserves the phase relation between Fock layers of the output state, providing promise for future applications.
Noiseless quantum amplifiers are probabilistic quantum devices that enhance the amplitude of coherent states without adding any noise, which has far reaching applications in quantum optics and quantum information processing. Here, we report on an experimental implementation of an advanced noiseless quantum amplifier for coherent states of light that is based on the conditional addition of two photons followed by the conditional subtraction of two photons. We comprehensively characterize the noiselessly amplified coherent states via quantum state tomography and analyze the amplification gain and noise properties of the amplifier. We observe very good agreement between the experiment and theoretical predictions. Our work reveals that sequences of multiple photon additions and subtractions represent an efficient and experimentally feasible alternative to multiplexing that was originally proposed to boost the performance of noiseless quantum amplifiers. Beyond noiseless quantum amplification, our experiment represents a significant step forward towards engineering complex quantum operations on traveling light beams by coherent combinations of various sequences of multiphoton additions and subtractions.
Abstract The resource theory of coherence studies the operational value of superpositions in quantum technologies. A key question in this theory concerns the efficiency of manipulation and interconversion of the resource. Here, we solve this question completely for qubit states by determining the optimal probabilities for mixed-state conversions via stochastic incoherent operations. Extending the discussion to distributed scenarios, we introduce and address the task of assisted incoherent state conversion, where the process is enhanced by making use of correlations with a second party. Building on these results, we demonstrate experimentally that the optimal state-conversion probabilities can be achieved in a linear optics setup. This paves the way towards real world applications of coherence transformations in current quantum technologies.
Quantum technologies are rapidly enhancing our ability to generate and manipulate coherent superpositions of different energy levels. Envisaging a new generation of energy-efficient quantum devices, here we ask how well coherence can be manipulated without drawing energy from the surrounding environment. We start from the task of converting a coherent superposition of energy eigenstates into another. For this task we identify the optimal energy-preserving operations, both in the deterministic and in the probabilistic scenario. We then design a recursive protocol, wherein a branching sequence of probabilistic filters increase the probability of success while reaching maximum fidelity at each iteration. Building on the recursive protocol, we construct efficient approximations of the optimal fidelity-probability tradeoff, by taking coherent superpositions of the different branches generated by probabilistic filtering. The benefits of this construction are illustrated in a number of applications to phase estimation, quantum cloning, coherent state amplification, and ancilla-driven computation. Finally, we extend our results to transitions where the input state is generally mixed and we apply our findings to the task of purifying quantum coherence.