The guesswork of a quantum ensemble quantifies the minimum number of guesses needed in average to correctly guess the state of the ensemble, when only one state can be queried at a time. Here, we derive analytical solutions of the guesswork problem subject to a finite set of conditions, including the analytical solution for any qubit ensemble with uniform probability distribution. As explicit examples, we compute the guesswork for any qubit regular polygonal and polyhedral ensemble.
The guesswork is an information-theoretic quantity which can be seen as an alternate security criterion to entropy. Recent work has established the theoretical framework for guesswork in the presence of quantum side information, which we extend both theoretically and experimentally. We consider guesswork when the side information consists of the BB84 states and their higher-dimensional generalizations. With this side information, we compute the guesswork for two different scenarios for each dimension. We then perform a proof-of-principle experiment using Laguerre-Gauss modes to experimentally …
Error probability is a popular and well-studied optimization criterion in discriminating non-orthogonal quantum states. It captures the threat from an adversary who can only query the actual state once. However, when the adversary is able to use a brute-force strategy to query the state, discrimination measurement with minimum error probability does not necessarily minimize the number of queries to get the actual state. In light of this, we take Massey's guesswork as the underlying optimization criterion and study the problem of minimum guesswork discrimination. We show that this problem can b…
What is the minimum number of guesses needed on average to correctly guess a realization of a random variable? The answer to this question led to the introduction of the notion of a quantity called guesswork by Massey in 1994, which can be viewed as an alternate security criterion to entropy. In this paper, we consider the guesswork in the presence of quantum side information, and show that a general sequential guessing strategy is equivalent to performing a single measurement and choosing a guessing strategy from the outcome. We use this result to deduce entropic one-shot and asymptotic bound…
The design and operation of a quantum-mechanical device as a laboratory instrument puts models written in equations of quantum mechanics in contact with instruments. This contact is recordable in files of a Classical Digital Process-control Computer (CPC) used both to calculate with the equations and to manage the instruments. By noticing that equations and instruments make contact in a CPC, we rewrite equations of quantum mechanics to explicitly include functions of CPC-commands to the instruments. This sets up a proof that a scientist's choice in linking mathematical models to instruments is…
Proofs of the security of quantum key distribution are propositions about models written in the mathematical language of quantum mechanics, and the issue is the linking of such models to actual devices in an experiment on security. To explore this issue, we adapt Wittgenstein's method of language games to view quantum language in its application to experimental activity involving transmitting and receiving devices. We sketch concepts with which to think about models in relation to experiments, without assuming the experiments accord with any model included is a concept of one quantum-mechanica…
The characterization of the quantum ensemble is a fundamental issue in quantum information theory and foundations. The ensemble is also useful for various quantum information processing. To characterize the quantum ensemble, in this article, we generalize the coherence measure of a state to the quantum ensemble. Exploiting the fidelity and affinity between the ensemble, we propose a quantumness quantifier for the quantum ensemble. It is shown that the proposed quantifier satisfies the necessary axioms of a bonafide measure of quantumness. Finally, we compute the quantumness of a few well-known…
In this paper, we investigate the classicality and quantumness of a quantum ensemble. We define a quantity called classicality to characterize how classical a quantum ensemble is. An ensemble of commuting states that can be manipulated classically has a unit classicality, while a general ensemble has a classicality less than 1. We also study how quantum an ensemble is by defining a related quantity called quantumness. We find that the classicality of an ensemble is closely related to how perfectly the ensemble can be cloned, and that the quantumness of an ensemble is essentially responsible fo…
Quantum machine learning seeks to exploit the underlying nature of a quantum computer to enhance machine learning techniques. A particular framework uses the quantum property of superposition to store sets of parameters, thereby creating an ensemble of quantum classifiers that may be computed in parallel. The idea stems from classical ensemble methods where one attempts to build a stronger model by averaging the results from many different models. In this work, we demonstrate that a specific implementation of the quantum ensemble of quantum classifiers, called the accuracy-weighted quantum ens…
We propose a protocol to achieve high fidelity quantum state teleportation of a macroscopic atomic ensemble using a pair of quantum-correlated atomic ensembles. We show how to prepare this pair of ensembles using quasiperfect quantum state transfer processes between light and atoms. Our protocol relies on optical joint measurements of the atomic ensemble states and magnetic feedback reconstruction.
We propose a general method to maximize the fidelity of writing, storage and reading of quantum information (QI) in a spectrally inhomogeneous spin ensemble used as quantum memory. The method is based on preselecting the optimal spectral portion of the ensemble by a judiciously designed pulse. It allows drastic improvement of quantum memory realized by spin ensembles that store QI from a resonator or an optical beam.
Quantum ensembles form easily accessible architectures for studying various phenomena in quantum physics, quantum information science, and spectroscopy. Here we review some recent protocols for measurements in quantum ensembles by utilizing ancillary systems. We also illustrate these protocols experimentally via nuclear magnetic resonance techniques. In particular, we shall review noninvasive measurements, extracting expectation values of various operators, characterizations of quantum states, and quantum processes, and finally quantum noise engineering.
The quantification of the quantumness of a quantum ensemble has theoretical and practical significance in quantum information theory. We propose herein a class of measures of the quantumness of quantum ensembles using the unitary similarity invariant norms of the commutators of the constituent density operators of an ensemble. Rigorous proof shows that they share desirable properties for a measure of quantumness, such as positivity, unitary invariance, concavity under probabilistic union, convexity under state decomposition, decreasing under coarse graining, and increasing under fine graining.…
We propose a parallel quantum computing mode for ensemble quantum computer. In this mode, some qubits can be in pure states while other qubits in mixed states. It enables a single ensemble quantum computer to perform $"$single-instruction-multi-data" type of parallel computation. In Grover's algorithm and Shor's algorithm, parallel quantum computing can provide additional speedup. In addition, it also makes a fuller use of qubit resources in an ensemble quantum computer. As a result, some qubits discarded in the preparation of an effective pure state in the Schulman-Varizani, and the Cleve-DiV…
We propose to use a collective excitation blockade mechanism to identify errors that occur due to disturbances of single atoms in ensemble quantum registers where qubits are stored in the collective population of different internal atomic states. A simple error correction procedure and a simple decoherence-free encoding of ensemble qubits in the hyperfine states of alkali atoms are presented.
We investigate a scheme for implementing quantum dense coding via atomic ensembles, where prior distribution of the quantum entangled state is not needed. Our scheme also combines another two distinct advantages: atomic ensembles qubits with long coherent time serve as memory qubits and phtonic qubit as flying qubit. Thus our suggestion may offer a simple and easy way of demonstrating quantum dense coding experimentally via atomic ensembles.
It is shown, that the only reason for possibility of using microcanonical ensemble is that there are probabilistic processes in microworld, that are not described by quantum mechanic. On a simple example it is demonstrated, that canonical distribution is not independent and equal to microcanonical, but is a result of averaging by microcanonical ensemble.
In this paper it has been described how to use the unitary dynamics of quantum mechanics to solve the prime factorization problem on a spin ensemble without any quantum entanglement. The ensemble quantum computation for the prime factorization is based on the basic principle that both a closed quantum system and its ensemble obey the same unitary dynamics of quantum mechanics if there is not any decoherence effect in both the quantum system and its ensemble. It uses the NMR multiple-quantum measurement techniques to output the quantum computational results that are the inphase multiple-quantum…
Problems in realization of silicon-based solid-state NMR quantum computer with ensemble addressing to qubits are considered. It is presented the extension of Kane's scheme to ensemble approach version with strip gates. For the initialization of nuclear quantum states it is proposed to use the solid-state effect in ENDOR technique whereby the nuclear spins can be practically fully polarized or, that is the same, indirect cooled to the spin temperature less than ~ 1 mK. It is suggested the possible planar silicon topology of such ensemble quantum computer and shown that the measurement with stan…
It is revealed that ensembles consisting of multipartite quantum states can exhibit different kinds of nonlocalities. An operational measure is introduced to quantify nonlocalities in ensembles consisting of bipartite quantum states. Various upper and lower bounds for the measure are estimated and the exact values for ensembles consisting of mutually orthogonal maximally entangled bipartite states are evaluated.
An open quantum system in steady state $\hatρ_{ss}$ can be represented by a weighted ensemble of pure states $\hatρ_{ss}=\sum_{k}\wp_{k}\ket{ψ_k} \bra{ψ_k}$ in infinitely many ways. A physically realizable (PR) ensemble is one for which some continuous measurement of the environment will collapse the system into a pure state $\ket{ψ(t)}$, stochastically evolving such that the proportion of time for which $\ket{ψ(t)} = \ket{ψ_{k}}$ equals $\wp_{k}$. Some, but not all, ensembles are PR. This constitutes the preferred ensemble fact, with the PR ensembles being the preferred ensembles. We present …
Locally accessible information is a useful information-theoretic physical quantity of an ensemble of multiparty quantum states. We find it has properties akin to quantum as well as classical correlations of single multiparty quantum states. It satisfies monotonicity under local quantum operations and classical communication. However we show that it does not follow monogamy, an important property usually satisfied by quantum correlations, and actually violates any such relation to the maximal extent. Violation is obtained even for locally indistinguishable, but globally orthogonal, multisite en…
In this paper, we introduce a new conception of pseudorandom phase ensemble to simulate a quantum ensemble. A pseudorandom sequence is inseparability and integral that are demonstrated only for a whole sequence not for a single phase unit, which is similar to that of quantum ensembles and a quantum particle. By using the ensemble conception, we demonstrate non-locality properties for classical fields similar to quantum entanglement.
We propose a method to achieve quantum supremacy using ensembles of qubits, using only spin squeezing, basis rotations, and Fock state measurements. Each ensemble is assumed to be controllable only with its total spin. Using a repeated sequence of random basis rotations followed by squeezing, we show that the probability distribution of the final measurements quickly approaches a Porter-Thomas distribution. We show that the sampling probability can be related to a #P-hard problem with a complexity scaling as $(N+1)^M$, where $N$ is the number of qubits in an ensemble and $ M $ is the number of…
We study how to efficiently manipulate and store quantum information between optical fields and atomic ensembles. We show how various non-dissipative transfer schemes can be used to transfer and store quantum states such as squeezed vacuum states or entangled states into the long-lived ground state spins of atomic ensembles.
Bernstein and Varizani have given the first quantum algorithm to solve parity problem in which a strong violation of the classical imformation theoritic bound comes about. In this paper, we refine this algorithm with fewer resource and implement a two qubits algorithm in a single query on an ensemble quantum computer for the first time.
We present a scheme for scalable quantum information processing (QIP) with atomic ensembles and flying photons. Using the Rydberg blockade, we encode the qubits in the collective atomic states, which could be manipulated fast and easily due to the enhanced interaction, in comparison to the single-atom case. We demonstrate that our proposed gating could be applied to generation of two-dimensional cluster states for measurement-based quantum computation. Moreover, the atomic ensembles also function as quantum repeaters useful for long distance quantum state transfer. We show the possibility of o…
We demonstrate the implementation of a quantum algorithm for estimating the number of matching items in a search operation using a two qubit nuclear magnetic resonance (NMR) quantum computer.
We propose an effective realization of a complete set of elementary quantum gates in the solid-state quantum computer based on the multi-atomic coherent (MAC-) ensembles in the QED cavity. Here, we use the two-ensemble qubit encoding and swapping-based operations that together provide implementation of any encoded single-qubit operation by three elementary gates and the encoded controlled-NOT operation is performed in a single step. This approach simplifies a physical realization of universal quantum computing and adds the immunity to a number of errors. We also demonstrate that the proposed a…
We propose to encode quantum information in rotational excitations in a molecular ensemble. Using a stripline cavity field for quantum state transfer between the molecular ensemble and a Cooper pair box two-level system, our proposal offers a linear scaling of the number of qubits in our register with the number of rotationally excited states available in the molecules.
Incorporating protection against quantum errors into adiabatic quantum computing (AQC) is an important task due to the inevitable presence of decoherence. Here we investigate an error-protected encoding of the AQC Hamiltonian, where qubit ensembles are used in place of qubits. Our Hamiltonian only involves total spin operators of the ensembles, offering a simpler route towards error-corrected quantum computing. Our scheme is particularly suited to neutral atomic gases where it is possible to realize large ensemble sizes and produce ensemble-ensemble entanglement. We identify a critical ensembl…
We show that differently constructed ensembles having the same density matrix may be physically distinguished by observing fluctuations of some observables. An explicit expression for fluctuations of an observable in an ensemble is given. This result challenges Peres's fundamental postulate and seems to be contrary to the widely-spread belief that ensembles with the same density matrix are physically identical. This leads us to suggest that the current liquid NMR quantum computing is truly quantum-mechanical in nature.
We propose an interesting scheme for distributed orbital state quantum cloning with atomic ensembles based on the quantum Zeno dynamics. These atomic ensembles which consist of identical three-level atoms are trapped in distant cavities connected by a single-mode integrated optical star coupler. These qubits can be manipulated through appropriate modulation of the coupling constants between atomic ensemble and classical field, and the cavity decay can be largely suppressed as the number of atoms in the ensemble qubits increases. The fidelity of each cloned qubit can be obtained with analytic r…
How an Equi-ensemble Description Systematically Outperforms the Weighted-ensemble Variational Quantum Eigensolver
ICGM, Université de Montpellier, CNRS, ENSCM（蒙彼利埃大学，法国国家科学研究中心，国立高等化学学校）；Dipartimento di Ingegneria e Scienze dell’Informazione e Matematica, Università dell’Aquila（阿奎拉大学）
In this paper, we introduce an optical analogy to quantum Fourier tanformation based on a pseudorandom phase ensemble. The optical analogy also brings about exponential speedup over classical Fourier tanformation. Using the analogy, we demonstrate three classcial fields to realize Fourier transform similar to three quantum particles.
We study the quantumness of correlations for ensembles of bi- and multi-partite systems and relate it to the task of quantum data hiding. Quantumness is here intended in the sense of minimum average disturbance under local measurements. We consider a very general framework, but focus on local complete von Neumann measurements as cause of the disturbance, and, later on, on the trace-distance as quantifier of the disturbance. We discuss connections with entanglement and previously defined notions of quantumness of correlations. We prove that a large class of quantifiers of the quantumness of cor…
Atomic ensembles, comprising clouds of atoms addressed by laser fields, provide an attractive system for both the storage of quantum information, and the coherent conversion of quantum information between atomic and optical degrees of freedom. In a landmark paper, Duan et al. (DLCZ) [1] showed that atomic ensembles could be used as nodes of a quantum repeater network capable of sharing pairwise quantum entanglement between systems separated by arbitrarily large distances. In recent years, a number of promising experiments have demonstrated key aspects of this proposal [2-7]. Here, we describe …
Inspired by recent developments in the control and manipulation of quantum dot nuclear spins, which allow for the transfer of an electron spin state to the surrounding nuclear-spin ensemble for storage, we propose a quantum repeater scheme that combines individual quantum dot electron spins and nuclear-spin ensembles, which serve as spin-photon interfaces and quantum memories respectively. We consider the use of low-strain quantum dots embedded in high-cooperativity optical microcavities. Quantum dot nuclear-spin ensembles allow for the long-term storage of entangled states, and heralded entan…
We discuss the issues surrounding the implementation of quantum computation in rare-earth-ion doped solids. We describe a practical scheme for two qubit gate operations which utilise experimentally available interactions between the qubits. Possibilities for a scalable quantum computer are discussed.
The Gram matrix of a set of quantum pure states plays key roles in quantum information theory. It has been highlighted that the Gram matrix of a pure-state ensemble can be viewed as a quantum state, and the quantumness of a pure-state ensemble can thus be quantified by the coherence of the Gram matrix [Europhys. Lett. \textbf{134} 30003]. Instead of the $l_1$-norm of coherence and the relative entropy of coherence, we utilize the generalized $α$-$z$-relative Rényi entropy of coherence of the Gram matrix to quantify the quantumness of a pure-state ensemble and explore its properties. We show th…
Large scale quantum information processing requires stable and long-lived quantum memories. Here, using atom-photon entanglement, we propose an experimentally feasible scheme to realize decoherence-free quantum memory with atomic ensembles, and show one of its applications, remote transfer of unknown quantum state, based on laser manipulation of atomic ensembles, photonic state operation through optical elements, and single-photon detection with moderate efficiency. The scheme, with inherent fault-tolerance to the practical noise and imperfections, allows one to retrieve the information in the…
Classical random matrix ensembles were originally introduced in physics to approximate quantum many-particle nuclear interactions. However, there exists a plethora of quantum systems whose dynamics is explained in terms of few-particle (predominantly two-particle) interactions. The random matrix models incorporating the few-particle nature of interactions are known as embedded random matrix ensembles. In the present paper, we provide a brief overview of these two ensembles and illustrate how the embedded ensembles can be successfully used to study decoherence of a qubit interacting with an env…
We introduce tqix.pis, a library of tqix, for quantum dynamics simulation of spin ensembles. The library emulates a dynamic process by a quantum circuit, including initializing a quantum state, executing quantum operators, and measuring the final state. It utilizes collective processes in spin ensembles to reduce the dimension from exponentially to quadratically with the number of particles, i.e., the quantum state spans in Dicke basis. It also facilitates the simulation time with multi-core processors and Graphics Processing Units. The library is thus applicable for the simulation of ensemble…
We present experimental NMR demonstration of a scheme of reversible projective measurement, which allows extracting information on outcomes and probabilities of a projective measurement in a non-destructive way, with a minimal net effect on the quantum state of an ensemble. The scheme uses reversible dynamics and weak measurement of the intermediate state. The experimental system is an ensemble of 133Cs (S = 7/2) nuclei in a liquid-crystalline matrix.
An expression is proposed for the quantum mechanical state of a pre- and post-selected ensemble, which is an ensemble determined by the final as well as the initial state of the quantum systems involved. It is shown that the probabilities calculated from the proposed state agree with previous expressions, for cases where they both apply. The same probabilities are found when they are calculated in the forward- or reverse-time directions. This work was prompted by several problems raised by Shimony recently in relation to the state, and time symmetry, of pre- and post-selected ensembles.
We consider the problem of optimal asymptotically faithful compression for ensembles of mixed quantum states. Although the optimal rate is unknown, we prove upper and lower bounds and describe a series of illustrative examples of compression of mixed states. We also discuss a classical analogue of the problem.
We present a protocol to evaluate the expectation value of the correlations of measurement outcomes for ensembles of quantum systems, and use it to experimentally demonstrate--under an assumption of fair sampling--the violation of an inequality that is satisfied by any non-contextual hidden-variables (NCHV) theory. The experiment is performed on an ensemble of molecular nuclear spins in the solid state, using established Nuclear Magnetic Resonance (NMR) techniques for quantum information processing (QIP).
We report the first experimental realization of single-qubit manipulation for single spinwaves stored in an atomic ensemble quantum memory. In order to have high-fidelity gate operations, we make use of stimulated Raman transition and controlled Lamor precession jointly. We characterize the gate performances with quantum state tomography and quantum process tomography, both of which imply that high-fidelity operations have been achieved. Our work complements the experimental toolbox of atomic-ensemble quantum memories by adding the capability of single-qubit manipulation, thus may have importa…
This paper considers quantum communication involving an ensemble of states. Apart from the von Neumann entropy, it considers other measures one of which may be useful in obtaining information about an unknown pure state and another that may be useful in quantum games. It is shown that under certain conditions in a two-party quantum game, the receiver of the states can increase the entropy by adding another pure state.
We investigate numerically a single-pulse implementation of a quantum Control-Not (CN) gate for an ensemble of Ising spin systems at room temperature. For an ensemble of four-spin ``molecules'' we simulate the time-evolution of the density matrix, for both digital and superpositional initial conditions. Our numerical calculations confirm the feasibility of implementation of quantum CN gate in this system at finite temperature, using electromagnetic $π$-pulse.
For a mixed quantum state with density matrix $ρ$ there are infinitely many ensembles of pure quantum states, which average to $ρ$. Starting from Laplace principle of insufficient reason (not to give \emph{a priori} preference to any particular state), we derive a `natural' distribution of pure states averaging to $ρ$, which is `more spread' than all the others.
Here we made an analysis of the principles of a semiconductor NMR quantum computer and its developments. The known variant of an individual-access computer (B. Kane) and alternative solid-state bulk-ensemble approach versions allowing to avoid some difficulties in implementing the first variant are considered.
