We demonstrate that local transformations on a composite quantum system can be enhanced in the presence of certain entangled states. These extra states act much like catalysts in a chemical reaction: they allow otherwise impossible local transformations to be realised, without being consumed in any way. In particular, we show that this effect can considerably improve the efficiency of entanglement concentration procedures for finite states.
We consider entanglement-assisted remote quantum state manipulation of bi-partite mixed states. Several aspects are addressed: we present a class of mixed states of rank two that can be transformed into another class of mixed states under entanglement-assisted local operations with classical communication, but for which such a transformation is impossible without assistance. Furthermore, we demonstrate enhancement of the efficiency of purification protocols with the help of entanglement-assisted operations. Finally, transformations from one mixed state to mixed target states which are sufficie…
We show that all pure entangled states of two $d$-dimensional quantum systems (i.e., two qudits) can be generated from an initial separable state via a universal Yang--Baxter matrix if one is assisted by local unitary transformations.
We find a minimal set of necessary and sufficient conditions for the existence of a local procedure that converts a finite pure state into one of a set of possible final states. This result provides a powerful method for obtaining optimal local entanglement manipulation protocols for pure initial states. As an example, we determine analytically the optimal distillable entanglement for arbitrary finite pure states. We also construct an explicit protocol achieving this bound.
Zurek's derivation of the Born rule from envariance (environment-assisted invariance) is tightened up, somewhat generalized, and extended to encompass all possibilities. By this, besides Zurek's most important work, also the works of 5 other commentators of the derivation are taken into account, and selected excerpts commented upon. All this is done after a detailed theory of twin unitaries, which are the other face of envariance.
Architectures of donor-electron based qubits in silicon near an oxide interface are considered theoretically. We find that the precondition for reliable logic and read-out operations, namely the individual identification of each donor-bound electron near the interface, may be accomplished by fine-tuning electric and magnetic fields, both applied perpendicularly to the interface. We argue that such magnetic fields may also be valuable in controlling two-qubit entanglement via donor electron pairs near the interface.
Machine Learning finds application in the quantum control and readout of qubits. In this work we apply Artificial Neural Networks to assist the manipulation and the readout of a prototypical molecular spin qubit - an Oxovanadium(IV) moiety - in two experiments designed to test the amplitude and the phase recognition, respectively. We first successfully use an artificial network to analyze the output of a Storage/Retrieval protocol with four input pulses to recognize the echo positions and, with further post selection on the results, to infer the initial input pulse sequence. We then apply an A…
Entanglement of pure states of bipartite quantum systems has been shown to have a unique measure in terms of the von Neumann entropy of the reduced states of either of its subsystems. The measure is established under entanglement manipulation of an asymptotically large number of copies of the states. In this paper, different asymptotic measures of entanglement assigned to arbitrary sequences of bipartite pure states are shown to coincide only when the sequence is information stable, in terms of the quantum spectral information rates of the sequence of subsystem states. Additional bounds on the…
We derive a sufficient condition for a set of pure states, each entangled in two remote $N$-dimensional systems, to be transformable to $k$-dimensional-subspace equivalent entangled states ($k\leq N$) by same local operations and classical communication. If $k=N$, the condition is also necessary. This condition reveals the function of the relative marginal density operators of the entangled states in the entanglement manipulation without sufficient information of the initial states.
We analyze approximate transformations of pure entangled quantum states by local operations and classical communication, finding explicit conversion strategies which optimize the fidelity of transformation. These results allow us to determine the most faithful teleportation strategy via an initially shared partially entangled pure state. They also show that procedures for entanglement manipulation such as entanglement catalysis [Jonathan and Plenio, Phys. Rev. Lett. 83, 3566 (1999)] are robust against perturbation of the states involved, and motivate the notion of non-local fidelity, which qua…
We show that in some cases, catalyst-assisted entanglement transformation cannot be implemented by multiple-copy transformation for pure states. This fact, together with the result we obtained in [R. Y. Duan, Y. Feng, X. Li, and M. S. Ying, Phys. Rev. A 71, 042319 (2005)] that the latter can be completely implemented by the former, indicates that catalyst-assisted transformation is strictly more powerful than multiple-copy transformation. For purely probabilistic setting we find, however, these two kinds of transformations are geometrically equivalent in the sense that the sets of pure states …
We consider generic pure $n$-qubit states and a general class of pure states of arbitrary dimensions and arbitrarily many subsystems. We characterize those states which can be reached from some other state via Local Operations assisted by finitely many rounds of Classical Communication ($LOCC_{\mathbb{N}}$). For $n$ qubits with $n>3$ we show that this set of states is of measure zero, which implies that the maximally entangled set is generically of full measure if restricted to the practical scenario of $LOCC_{\mathbb{N}}$. Moreover, we identify a class of states for which any $LOCC_{\mathbb{N…
We introduce the general catalysts for pure entanglement transformations under local operations and classical communications in such a way that we disregard the profit and loss of entanglement of the catalysts per se. As such, the possibilities of pure entanglement transformations are greatly expanded. Remarkably, we find an interesting phenomenon that, in some situations, incomparable pairs ${| ψ> ,| ϕ> \} $ and ${| χ> ,| χ^{\prime}> \} $ can assist each other mutually so as to realize the transformation $| ψ> | χ> \to| ϕ> | χ^{\prime}>$. We also design an efficient algorithm to detect whethe…
Optical control of nanoscale objects has recently developed into a thriving field of research with far-reaching promises for precision measurements, fundamental quantum physics and studies on single-particle thermodynamics. Here, we demonstrate the optical manipulation of silicon nanorods in high vacuum. Initially, we sculpture these particles into a silicon substrate with a tailored geometry to facilitate their launch into high vacuum by laser-induced mechanical cleavage. We manipulate and trace their center-of-mass and rotational motion through the interaction with an intense intra-cavity fi…
We present two method for optimal entanglement concentration from pure entangled states by local actions only. However a prior knowledge of the Schmidt coefficients is required. The first method is optimally efficient only when a finite ensemble of pure entangled states are available whereas the second method realizes the single pair optimal concentration probability. We also propose an entanglement assisted method which is again optimally efficient even for a single pair. We also discuss concentrating entanglement from N-partite cat like states.
The remarkable phenomenon of catalyst tells us that adding a catalyst could help state transformation. In this paper, we consider the problem of catalyst-assisted probabilistic coherence distillation for mixed states under strictly incoherent operations. To this end, we first present the necessary and sufficient conditions for distilling a target pure coherent state from an initial mixed state via stochastic strictly incoherent operations and the maximal probability of obtaining the target pure state from the initial state. With the help of these results, we present the necessary and sufficien…
We evaluate the one-shot entanglement of assistance for an arbitrary bipartite state. This yields another interesting result, namely a characterization of the one-shot distillable entanglement of a bipartite pure state. This result is shown to be stronger than that obtained by specializing the one-shot hashing bound to pure states. Finally, we show how the one-shot result yields the operational interpretation of the asymptotic entanglement of assistance proved in [Smolin et al., Phys. Rev. A 72, 052317 (2005)].
In this paper we summarize the necessary condition for incomparable states which can be catalyzed under entanglement-assisted LQCC (ELQCC). When we apply an extended condition for entanglement transformation to entanglement-assisted local manipulation we obtain a fundamental limit for entanglement catalysts. Some relative questions are also discussed.
We experimentally demonstrate the achievement of the entanglement assisted capacity for classical information transmission over a depolarizing channel. The implementation is based on the generation and local manipulation of 2-qubit Bell states, which are finally measured at the receiver by a complete Bell state analysis. The depolarizing channel is realized by introducing quantum noise in a controlled way on one of the two qubits. This work demonstrates the achievement of the maximum allowed amount of information that can be shared in the presence of noise and the highest reported value in the…
We analyze the steady state entanglement generated in a coherently coupled dimer system subject to dephasing noise as a function of the degree of Markovianity of the evolution. By keeping fixed the effective noise strength while varying the memory time of the environment, we demonstrate that non-Markovianity is an essential, quantifiable resource that may support the formation of steady state entanglement whereas purely Markovian dynamics governed by Lindblad master equations lead to separable steady states. This result illustrates possible mechanisms leading to long-lived entanglement in pure…
We study the effect of action noise on state-to-state control protocols. Action noise creates dephasing in the instantaneous eigenbasis of the Hamiltonian and hampers the fidelity of the final state with respect to the target state. We find that for shorter protocols the noise more strongly influences the dynamics and degrades fidelity. We suggest improving the fidelity by inducing stronger dephasing rates along the process. The effects of action noise on the dynamics and its manipulation is described for a general Hamiltonian and is then studied by examples.
It is shown that a finite number of conditions are {\em not} sufficient to determine the locality of transformations between two probability distributions of pure states as well as the locality of transformations between two $d\times d$ mixed states with $d\geq 4$. As an example, an infinite, but minimal, set of necessary and sufficient conditions for the existence of a local procedure that converts one probability distribution of two pure pair of qubits into another one is found.
Noise-assisted transport in quantum systems occurs when quantum time-evolution and decoherence conspire to produce a transport efficiency that is higher than what would be seen in either the purely quantum or purely classical cases. In disordered systems, it has been understood as the suppression of coherent quantum localisation through noise, which brings detuned quantum levels into resonance and thus facilitates transport. We report several new mechanisms of environment-assisted transport in ordered systems, in which there is no localisation to overcome and where one would naively expect tha…
We show that two ways of manipulation of quantum entanglement, namely, entanglement-assisted local transformation [D. Jonathan and M. B. Plenio, Phys. Rev. Lett. {\bf 83}, 3566 (1999)] and multiple-copy transformation [S. Bandyopadhyay, V. Roychowdhury, and U. Sen, Phys. Rev. A {\bf 65}, 052315 (2002)], are equivalent in the sense that they can asymptotically simulate each other's ability to implement a desired transformation from a given source state to another given target state with the same optimal success probability. As a consequence, this yields a feasible method to evaluate the optimal…
We studied pure state transformations using local operations assisted by finitely many rounds of classical communication ($LOCC_{\mathbb{N}}$) in C. Spee, J.I. de Vicente, D. Sauerwein, B. Kraus, arXiv:1606.04418 (2016). Here, we first of all present the details of some of the proofs and generalize the construction of examples of state transformations via $LOCC_{\mathbb{N}}$ which require a probabilistic step. However, we also present explicit examples of SLOCC classes where any separable transformation can be realized by a protocol in which each step is deterministic (all-det-$LOCC_{\mathbb{N…
Entanglement bits or ``ebits'' have been proposed as a quantitative measure of a fundamental resource in quantum information processing. For such an interpretation to be valid, it is important to show that the same number of ebits in different forms or concentrations are inter-convertible in the asymptotic limit. Here we draw attention to a very important but hitherto unnoticed aspect of entanglement manipulation --- the classical communication cost. We construct an explicit procedure which demonstrates that for bi-partite pure states, in the asymptotic limit, entanglement can be concentrated …
We introduce a simple, experimentally realisable, entanglement manipulation protocol for exploring mixed state entanglement. We show that for both non-maximally entangled pure, and mixed polarisation-entangled two qubit states, an increase in the degree of entanglement and purity, which we define as concentration, is achievable.
Quantum memories can be used not only for the storage of quantum information, but also for substantial manipulation of ensembles of quantum states. Therefore, the speed of such manipulation and the ability to write and retrieve the signals of relatively short duration becomes important. Previously there have been considered the limits on efficiency of the cavity-enhanced atomic Raman memories for the signals whose duration is not much larger than the cavity field lifetime, that is, beyond the bad cavity limit. We investigate in this work the four-wave mixing noise that arises by the retrieval …
A quantum multimeter is a programmable device that can implement measurements of different observables depending on the programming quantum state inserted into it. The advantage of this arrangement over a single purpose device is in its versatility: one can realize various measurements simply by changing the programming state. The classical manipulation of measurement output data is known as post-processing. In this work we study the post-processing assisted quantum programming, which is a protocol where quantum programming and classical post-processing are combined. We provide examples showin…
If a system undergoes symmetric dynamics, then the final state of the system can only break the symmetry in ways in which it was broken by the initial state, and its measure of asymmetry can be no greater than that of the initial state. It follows that for the purpose of understanding the consequences of symmetries of dynamics, in particular, complicated and open-system dynamics, it is useful to introduce the notion of a state's asymmetry properties, which includes the type and measure of its asymmetry. We demonstrate and exploit the fact that the asymmetry properties of a state can also be un…
We show that the process of entanglement distillation is irreversible by showing that the entanglement cost of a bound entangled state is finite. Such irreversibility remains even if extra pure entanglement is loaned to assist the distillation process.
We consider the transformation of multi-partite states in the single copy setting under positive-partial-transpose-preserving operations (PPT-operations) and obtain both qualitative and quantitative results. Firstly, for some pure state transformations that are impossible under local operations and classical communication (LOCC), we demonstrate that they become possible with a surprisingly large success probability under PPT-operations. Furthermore, we clarify the convertibility of arbitrary multipartite pure states under PPT-operations, and show that a drastic simplification in the classifica…
We consider the entanglement manipulation capabilities of the universal covariant quantum cloner or quantum processor circuit for quantum bits. We investigate its use for cloning a member of a bipartite or a genuine tripartite entangled state of quantum bits. We find that for bipartite pure entangled states a nontrivial behavior of concurrence appears, while for GHZ entangled states a possibility of the partial extraction of bipartite entanglement can be achieved.
Suppose two distant observers Alice and Bob share a pure bipartite quantum state. By applying local operations and communicating with each other using a classical channel, Alice and Bob can manipulate it into some other states. Previous investigations of entanglement manipulations have been largely limited to a small number of strategies and their average outcomes. Here we consider a general entanglement manipulation strategy and go beyond the average property. For a pure entangled state shared between two separated persons Alice and Bob, we show that the mathematical interchange symmetry of t…
Quantum entanglement is among the most fundamental, yet from classical intuition also most surprising properties of the fully quantum nature of physical reality. We report several experiments performed on IBM's Quantum Experience demonstrating envariance -- entanglement assisted invariance. Envariance is a recently discovered symmetry of composite quantum systems, which is at the foundational origin of physics and a quantum phenomenon of pure states. These very easily reproducible and freely accessible experiments on Quantum Experience provide simple tools to study the properties of envariance…
The practical use of non-Hermitian (i.e., typically, PT-symmetric) phenomenological quantum Hamiltonians is discussed as requiring an explicit reconstruction of the {\em ad hoc} Hilbert-space metrics which would render the time-evolution unitary. Just the N-dimensional matrix toy models Hamiltonians are considered, therefore. For them, the matrix elements of alternative metrics are constructed via solution of a coupled set of polynomial equations, using the computer-assisted symbolic manipulations for the purpose. The feasibility and some consequences of such a model-construction strategy are …
The main goal of quantum metrology is to obtain accurate values of physical parameters using quantum probes. In this context, we show that abstention, i.e., the possibility of getting an inconclusive answer at readout, can drastically improve the measurement precision. We focus on phase estimation and quantify the required amount of abstention for a given precision. We also develop analytical tools to obtain the asymptotic behavior of the precision and required rate of abstention for arbitrary pure qubit states.
In order to cope with the fact that there exists no single maximally entangled state (up to local unitaries) in the multipartite setting, we introduced in [J. I. de Vicente, C. Spee and B. Kraus, Phys. Rev. Lett. 111, 110502 (2013)] the maximally entangled set of n-partite quantum states. This set consists of the states that are most useful under conversion of pure states via Local Operations assisted by Classical Communication (LOCC). We will review our results here on the maximally entangled set of three- and generic four-qubit states. Moreover, we will discuss the preparation of arbitrary (…
Single-shot entanglement manipulation of states and channels revisited
University of Calgary（卡尔加里大学）；Institute for Quantum Science and Technology, University of Calgary（卡尔加里大学量子科学与技术研究所）；Institute for Quantum Computing, Baidu Research（百度研究院量子计算研究所）
The problem of the determination of the Hilbert-space metric which renders a given Hamiltonian $H$ self-adjoint is addressed from the point of view of applicability of computer-assisted algebraic manipulations. An exactly solvable example of the so called Gegenbauerian quantum-lattice oscillator is recalled for the purpose. Both the construction of suitable metric (basically, the solution of the Dieudonne's operator equation) and the determination of its domain of positivity are shown facilitated by the symbolic algebraic manipulations and by MAPLE-supported numerics and graphics.
We present an experimentally implementable method to couple Josephson charge qubits and to generate and detect macroscopic entangled states. A large-junction superconducting quantum interference device is used in the qubit circuit for both coupling qubits and implementing the readout. Also, we explicitly show how to achieve a microwave-assisted macroscopic entanglement in the coupled-qubit system.
We analytically obtain the maximum probability of converting a finite number of copies of an arbitrary two-qubit pure state to a single copy of a maximally entangled two-qubit pure state via entanglement assisted local operations and classical communications using a two-qubit catalyst state. We show that the optimal catalyst for this transformation is always more entangled than the initial state but any two-qubit state can act as a (non-optimal) catalyst. Interestingly, the entanglement of the optimal two-qubit catalyst state is shown to decrease with that of the initial state. Entanglement as…
We develop a unified framework to characterize one-shot transformations of dynamical quantum resources in terms of resource quantifiers, establishing universal conditions for exact and approximate transformations in general resource theories. Our framework encompasses all dynamical resources represented as quantum channels, including those with a specific structure --- such as boxes, assemblages, and measurements --- thus immediately applying in a vast range of physical settings. For the particularly important manipulation tasks of distillation and dilution, we show that our conditions become …
We construct a quantum-control-assisted multi-observable variance-based uncertainty relation, and the uncertainty relation obtained indicates that we can prepare a quantum state, in which the measurement results of any observables can be predicted precisely with the help of quantum control and entanglement resource. The new variance-based uncertainty relation provides a concept of "multiparticle entanglement resolution lines" for multiparticle entangled pure states, that can delineate different multiparticle entanglement classes, and thus it can be considered as an analyzer of multiparticle en…
As a result of a non-trivial mixing matrix, neutrinos cannot be simultaneously in a flavor and mass eigenstate. We formulate and discuss information entropic relations that quantify the associated quantum uncertainty. We also formulate a protocol to determine the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) matrix from quantum manipulations and measurements on an entangled lepton-neutrino pair. The entangled state features neutrino oscillations in a conditional probability involving measurements on the lepton and the neutrino. They can be switched off by choosing a specific observable on the lepton …
Quantum coherence, which quantifies the superposition properties of a quantum state, plays an indispensable role in quantum resource theory. A recent theoretical work [Phys. Rev. Lett. \textbf{116}, 070402 (2016)] studied the manipulation of quantum coherence in bipartite or multipartite systems under the protocol Local Incoherent Operation and Classical Communication (LQICC). Here we present the first experimental realization of obtaining maximal coherence in assisted distillation protocol based on linear optical system. The results of our work show that the optimal distillable coherence rate…
Suppose several parties jointly possess a pure multipartite state, |ψ>. Using local operations on their respective systems and classical communication (i.e. LOCC) it may be possible for the parties to transform deterministically |ψ> into another joint state |ϕ>. In the bipartite case, Nielsen majorization theorem gives the necessary and sufficient conditions for this process of entanglement transformation to be possible. In the multipartite case, such a deterministic local transformation is possible only if both the states in the same stochastic LOCC (SLOCC) class. Here we generalize Nielsen m…
Laser cooling and trapping of atoms and atomic ions has led to numerous advances including the observation of exotic phases of matter, development of exquisite sensors and state-of-the-art atomic clocks. The same level of control in molecules could also lead to profound developments such as controlled chemical reactions and sensitive probes of fundamental theories, but the vibrational and rotational degrees of freedom in molecules pose a formidable challenge for controlling their quantum mechanical states. Here, we use quantum-logic spectroscopy (QLS) for preparation and nondestructive detecti…
Motivated by the problem of designing quantum repeaters, we study entanglement distillation between two parties, Alice and Bob, starting from a mixed state and with the help of "repeater" stations. To treat the case of a single repeater, we extend the notion of entanglement of assistance to arbitrary mixed tripartite states and exhibit a protocol, based on a random coding strategy, for extracting pure entanglement. The rates achievable by this protocol formally resemble those achievable if the repeater station could merge its state to one of Alice and Bob even when such merging is impossible. …
Environmental noise usually hinders the efficiency of charge transport through coherent quantum systems; an exception is dephasing-assisted transport (DAT). We show that linear triple quantum dots in a transport configuration and subjected to pure dephasing exhibit DAT if the coupling to the drain reservoir exceeds a threshold. DAT occurs for arbitrarily weak dephasing and the enhancement can be directly controlled by the coupling to the drain. Moreover, for specific settings, the enhanced current is accompanied by a reduction in relative shot noise. We identify the quantum Zeno effect and lon…
In the ideal quantum Zeno effect, repeated quantum projective measurements can freeze the coherent dynamics of a quantum system. However, in the weak quantum Zeno regime, measurement back-actions can allow the sensing of semi-classical field fluctuations. In this regard, we theoretically show how to combine the controlled manipulation of a quantum two-level system, used as a probe, with a sequence of projective measurements to have direct access to the noise correlation function. We experimentally test the effectiveness of the proposed noise sensing method on a properly engineered Bose-Einstei…
We compute on all quantum states several measures that characterise asymptotic quantum coherence manipulation under restricted classes of operations. We focus on the distillable coherence, i.e. the maximum rate of production of approximate pure bits of coherence starting from independent copies of an input state $ρ$, and on the coherence cost, i.e. the minimum rate of consumption of pure coherence bits that is needed to generate many copies of $ρ$ with vanishing error. We obtain the first closed-form expression for the distillable coherence under strictly incoherent operations (SIO), proving t…
