A preparation game is a task whereby a player sequentially sends a number of quantum states to a referee, who probes each of them and announces the measurement result. The measurement setting in each round, as well as the final score of the game, are decided by the referee based on the past history of settings and measurement outcomes. Many experimental tasks in quantum information, such as entanglement quantification or magic state detection, can be cast as preparation games. In this paper, we introduce general methods to design $n$-round preparation games, with tight bounds on the average game scores achievable by players subject to constraints on their preparation devices. We illustrate our results by devising new adaptive measurement protocols for entanglement detection and quantification. Surprisingly, we find that the standard procedure in entanglement detection, namely, estimating $n$ times the average value of a given entanglement witness, is in general sub-optimal for detecting the entanglement of a specific quantum state. On the contrary, there exist $n$-round experimental scenarios where detecting the entanglement of a known state optimally requires adaptive measurement schemes.
Communication games are collaborative information processing tasks involving a number of players with limited communication. Such games are useful tools for studying physical theories. A physical theory exhibits preparation contextuality whenever observed behaviour cannot be explained by a preparation noncontextual model. Here we show that there is a fundamental connection between the performance in communication games and the degree of preparation (non)contextuality. For this purpose, we present a general framework that allows us to construct communication games such that the game performance…
A communication game consists of distributed parties attempting to jointly complete a task with restricted communication. Such games are useful tools for studying limitations of physical theories. A theory exhibits preparation contextuality whenever its predictions cannot be explained by a preparation noncontextual model. Here, we show that communication games performed in operational theories reveal the preparation contextuality of that theory. For statistics obtained in a particular family of communication games, we show a direct correspondance with correlations in space-like separated event…
The optimal success probability of a communication game sets fundamental limitations on an operational theory. Quantum advantage of parity oblivious random access code (PORAC), a communication game, over classical resources reveals the preparation contextuality of quantum theory [Phys. Rev. Lett. 102, 010401 (2009)]. Optimal quantum advantage in the N-dit PORAC game for finite dimensions is an open problem. Here, we show that the degree of uncertainty allowed in an operational theory determines the amount of preparation contextuality. We connect the upper bound of fine-grained uncertainty rela…
A theory is universal contextual if its prediction cannot be reproduced by an ontological model satisfying both preparation and measurement noncontextuality assumptions. In this report, we first generalize the logical proofs of quantum preparation and measurement contextuality for qubit system for any odd number of preparations and measurements. Based on the logical proof, we derive testable universally non-contextual inequalities violated by quantum theory. We then propose a class of two-party communication games and show that the average success probability of winning such games is solely li…
Kochen-Specker (KS) theorem lies at the heart of the foundations of quantum mechanics. It establishes impossibility of explaining predictions of quantum theory by any noncontextual ontological model. Spekkens generalized the notion of KS contextuality in [Phys. Rev. A 71, 052108 (2005)] for arbitrary experimental procedures (preparation, measurement, and transformation procedure). Interestingly, later on it was shown that preparation contextuality powers parity-oblivious multiplexing [Phys. Rev. Lett. 102, 010401 (2009)], a two party information theoretic game. Thus, using resources of a given…
A quantum game can be viewed as a state preparation in which the final output state results from the competing preferences of the players over the set of possible output states that can be produced. It is therefore possible to view state preparation in general as being the output of some appropriately chosen (notional) quantum game. This reverse engineering approach in which we seek to construct a suitable notional game that produces some desired output state as its equilibrium state may lead to different methodologies and insights. With this goal in mind we examine the notion of preference in…
Communication games are one of the widely used tools that are designed to demonstrate quantum supremacy over classical resources. In that, two or more parties collaborate to perform an information processing task to achieve the highest success probability of winning the game. We propose a specific two-party communication game in the prepare-measure scenario that relies on an encoding-decoding task of specific information. We first demonstrate that quantum theory outperforms the classical preparation non-contextual theory, and the optimal quantum success probability of such a communication game…
We provide an interesting two-party parity oblivious communication game whose success probability is solely determined by the Bell expression. The parity-oblivious condition in an operational quantum theory implies the preparation non-contextuality in an ontological model of it. We find that the aforementioned Bell expression has two upper bounds in an ontological model; the usual local bound and a non-trivial preparation non-contextual bound arising from the non-trivial parity-oblivious condition, which is smaller that the local bound. We first demonstrate the communication game when both Ali…
We study the effects of preparation of input states in a quantum tomography experiment. We show that maps arising from a quantum process tomography experiment (called process maps) differ from the well know dynamical maps. The difference between the two is due to the preparation procedure that is necessary for any quantum experiment. We study two preparation procedures, stochastic preparation and preparation by measurements. The stochastic preparation procedure yields process maps that are linear, while the preparations using von Neumann measurements lead to non-linear processes, and can only …
We study preparation of states for open quantum mechanics. For non-Markovian systems that are initially correlated with the environment, the affects of the preparation procedure are nontrivial. This is due to the indirect affects on the state of the environment induced via the correlations with the system and the act of preparation on the system. We give three concrete examples of preparation procedure to elucidate our claims.
State preparation is a process encoding the classical data into the quantum systems. Based on quantum phase estimation, we propose the specific quantum circuits for a deterministic state preparation algorithm and a probabilistic state preparation algorithm. To discuss the gate complexity in these algorithms, we decompose the diagonal unitary operators included in the phase estimation algorithms into the basic gates. Thus, we associate the state preparation problem with the decomposition problem of the diagonal unitary operators. We analyse the fidelities in the two algorithms and discuss the s…
In quantum information and communication, optical schemes provide simple and intuitive experimental implementations. Of particular importance is quantum state preparation. In this thesis, the creation of polarisation entanglement using a particular class of optical circuits is studied. I give a mathematical description of this class of circuits in terms of Hermite polynomials. In this context, single photon resolution and single photon sensitivity detectors are discussed and compared with detector cascading. In addition, I study applications of state preparation such as quantum teleportation a…
Storage and distribution of quantum information are key elements of quantum information processing and quantum communication. Here, using atom-photon entanglement as the main physical resource, we experimentally demonstrate the preparation of a distant atomic quantum memory. Applying a quantum teleportation protocol on a locally prepared state of a photonic qubit, we realized this so-called remote state preparation on a single, optically trapped 87Rb atom. We evaluated the performance of this scheme by the full tomography of the prepared atomic state, reaching an average fidelity of 82%.
We present an algorithm that prepares multidimensional Gaussian wavefunctions on qubit arrays and an application of such wavefunctions to multidimensional resampling, a technique useful in quantum digital simulation.
We present a scheme to prepare a quantum state in a ion trap with probability approaching to one by means of ion trap quantum computing and Grover's quantum search algorithm acting on trapped ions.
Consider a joint quantum state of a system and its environment. A measurement on the environment induces a decomposition of the system state. Using algorithmic information theory, we define the preparation information of a pure or mixed state in a given decomposition. We then define an optimal decomposition as a decomposition for which the average preparation information is minimal. The average preparation information for an optimal decomposition characterizes the system-environment correlations. We discuss properties and applications of the concepts introduced above and give several examples.
In this paper we discuss a quantum multi-tasking protocol for preparation of known one-qubit and two-qubit states respectively in two different locations. The ideal remote state preparation protocol is discussed in the first place in which a five-qubit entangled state is utilized. The design for the preparation of such entanglement is also presented and run on IBM quantum composer platform. The effects of three types of noises on the protocol are discussed and in all these cases the reduced fidelities of the process are calculated. The variations of these fidelities with respect to different p…
Quantum Amplitude Estimation (QAE) can achieve a quadratic speed-up for applications classically solved by Monte Carlo simulation. A key requirement to realize this advantage is efficient state preparation. If state preparation is too expensive, it can diminish the quantum advantage. Preparing arbitrary quantum states has exponential complexity with respect to the number of qubits, thus, is not applicable. Currently known efficient techniques require problems based on log-concave probability distributions, involve learning an unknown distribution from empirical data, or fully rely on quantum a…
We demonstrate an experimental realization of remote state preparation via the quantum teleportation algorithm, using an entangled photon pair in the polarization degree of freedom as the quantum resource. The input state is encoded on the path of one of the photons from the pair. The improved experimental scheme allows us to control the preparation and teleportation of a state over the entire Bloch sphere with a resolution of the degree of mixture given by the coherence length of the photon pair. Both the preparation of the input state and the implementation of the quantum gates are performed…
Quantum error correction and fault-tolerant quantum computation are two fundamental concepts which make quantum computing feasible. While providing a theoretical means with which to ensure the arbitrary accuracy of any quantum circuit, fault-tolerant error correction is predicated upon the robust preparation of logical states. An optimal direct circuit and a more complex fault-tolerant circuit for the preparation of the [[7,1,3]] Steane logical-zero are simulated in the presence of discrete quantum errors to quantify the regime within which fault-tolerant preparation of logical states is prefe…
We prove that there is no quantum speed-up when using quantum Monte-Carlo to estimate the mean (and other moments) of analytically-defined log-concave probability distributions prepared as quantum states using the Grover-Rudolph method.
Black-box quantum state preparation is an important subroutine in many quantum algorithms. The standard approach requires the quantum computer to do arithmetic, which is a key contributor to the complexity. Here we present a new algorithm that avoids arithmetic. We thereby reduce the number of gates by a factor of 286-374 over the best prior work for realistic precision; the improvement factor increases with the precision. As quantum state preparation is a crucial subroutine in many approaches to simulating physics on a quantum computer, our new method brings useful quantum simulation closer t…
We study the following problem: Is it possible to explain the quantum interference of probabilities in the purely corpuscular model for elementary particles? We demonstrate that (by taking into account perturbation effects of measurement and preparation procedures) we can obtain $\cosθ$-perturbation (interference term) in probabilistic rule connecting preparation procedures for purely corpuscular objects. On one hand, our investigation demonstrated that there is nothing special in so called `quantum probabilities': the right choice of statistical ensembles gives the possibility to escape all `…
State preparation and measurement errors are commonly regarded as indistinguishable. The problem of distinguishing state preparation (SPAM) errors from measurement errors is important to the field of characterizing quantum processors. In this work, we propose a method to separately characterize SPAM errors using a novel type of algorithmic cooling protocol called measurement-based algorithmic cooling (MBAC). MBAC assumes the ability to perform (potentially imperfect) projective measurements on individual qubits, which is available on many modern quantum processors. We demonstrate that MBAC can…
We propose a variational quantum algorithm to prepare ground states of 1D lattice quantum Hamiltonians specifically tailored for programmable quantum devices where interactions among qubits are mediated by Quantum Data Buses (QDB). For trapped ions with the axial Center-Of-Mass (COM) vibrational mode as single QDB, our scheme uses resonant sideband optical pulses as resource operations, which are potentially faster than off-resonant couplings and thus less prone to decoherence. The disentangling of the QDB from the qubits by the end of the state preparation comes as a byproduct of the variatio…
Black-box quantum state preparation is a fundamental primitive in quantum algorithms. Starting from Grover, a series of techniques have been devised to reduce the complexity. In this work, we propose to perform black-box state preparation using the technique of linear combination of unitaries (LCU). We provide two algorithms based on a different structure of LCU. Our algorithms improve upon the existed best results by reducing the required additional qubits and Toffoli gates to 2log(n) and n, respectively, in the bit precision n. We demonstrate the algorithms using the IBM Quantum Experience c…
We consider the optimal control problem in a two-qubit system with bounded amplitude. Two cases are studied: quantum state preparation and entanglement creation. Cost functions, fidelity and concurrence, are optimized over bang-off controls for different values of the total duration, respectively. For quantum state preparation problem, three critical time points are determined with high precision, and optimal controls are obtained for different durations. A better estimation of the quantum speed limit is obtained, so is the time-optimal control. For entanglement creation problem, two critical …
The preparation of a quantum superposition is the key to the success of many quantum algorithms and quantum machine learning techniques. The preparation of an incomplete or a non-uniform quantum superposition with certain properties is a non-trivial task. In this paper, an $n$-qubits variational quantum circuit using partial negation and controlled partial negation operators will be proposed to prepare an arbitrary quantum superposition. The proposed quantum circuit follows the symmetries of the unitary Lie group. The speed of the preparation process and the accuracy of the prepared superposit…
The preparation of Gibbs thermal states is an important task in quantum computation with applications in quantum simulation, quantum optimization, and quantum machine learning. However, many algorithms for preparing Gibbs states rely on quantum subroutines which are difficult to implement on near-term hardware. Here, we address this by (i) introducing an objective function that, unlike the free energy, is easily measured, and (ii) using dynamically generated, problem-tailored ansätze. This allows for arbitrarily accurate Gibbs state preparation using low-depth circuits. To verify the effective…
We estimate the resources required to prepare the ground state of a quantum many-body system on a quantum computer of intermediate size. This estimate is made possible using a combination of quantum many-body methods and analytic upper bounds. Our routine can also be used to optimize certain design parameters for specific problem instances. Lastly, we propose and benchmark an improved quantum state preparation procedure. We find that it reduces the circuit T-depth by a factor as large as $10^6$ for intermediate-size lattices.
We report a scheme for deterministic preparation of non-Gaussian quantum states on-demand. In contrast to probabilistic approaches for preparation of non-Gaussian quantum states, conditioned on photon subtraction or addition, we present a scheme that can prepare non-Gaussian quantum states on-demand, by applying a unitary transformation which removes the Gaussianity of measurement statistics of field quadratures, namely a quadrature rotation via transmission through a beam-splitter, using a two-mode photon-number squeezed state as input. The resulting state exhibits a quantum vortex structure …
Dynamics of zeroth order quantum coherences and preparation of the pseudopure states in homonuclear systems of dipolar coupling spins is closely examined. It has been shown an extreme important role of the non-diagonal part of zeroth order coherence in construction of the pseudopure state. Simulations of the preparation process of pseudopure states with the real molecular structures (a rectangular (-chloro- -nitrobenzene molecule), a chain (hydroxyapatite molecule), a ring (benzene molecule), and a double ring (cyclopentane molecule)) open the way to experimental testing of the obtained result…
The amount of information transferred during standard quantum teleportation or remote state preparation is equal to the preparation information of the transmitted state, rather than the classical communication required by respective protocol. This is shown by noting that the information required to specify the operation that verifies the transmitted state is identical to the preparation information, at the given level of precision m (in bits). Depending on the resolution of the projective Hilbert space, the preparation information can be made arbitrarily precise and hence indefinitely larger t…
We show that dissipative quantum state preparation processes can be protected against qubit dephasing by interlacing the state preparation control with dynamical decoupling (DD) control consisting of a sequence of short $π$-pulses. The inhomogeneous broadening can be suppressed to second order of the pulse interval, and the protection efficiency is nearly independent of the pulse sequence but determined by the average interval between pulses. The DD protection is numerically tested and found to be efficient against inhomogeneous dephasing on two exemplary dissipative state preparation schemes …
Remote state preparation (RSP) enables a sender to remotely prepare the quantum state of a receiver without sending the state itself. Recently, it has been recognized that quantum discord is a necessary resource for RSP. Here, we theoretically and experimentally investigate whether RSP can outperform dynamic classical remote state preparation processes. We show that such classical processes can describe certain RSPs powered by quantum discord. Rather, we argue that a new kind of Einstein-Podolsky-Rosen steering for dynamical processes, called quantum process steering, is the resource required …
We consider a system of two spins that are coupled via an isotropic Heisenberg Hamiltonian. For the first time, a two-step method for the preparation of an arbitrary quantum state of two qubits in the form of the Schmidt decomposition is proposed. The simplified version of this method is applied to the physical system of an atom having with a nuclear spin $1/2$ and one valence electron. As an example, the preparation of two-spin quantum states in the $^{31}$P system is considered.
The role played by quantum discord in mixed-state computation is widely debated since, in spite of evidence of its importance in creating quantum advantages, even in the absence of entanglement, there are not direct proofs of its necessity in these computational tasks. Recently the presence of discord was shown to be necessary and sufficient for remote state preparation for a broad class of quantum channels [B. Dakić et al., Nat. Phys. 8, 666 (2012)]. Here, we show that this property is not universal. There are states whose discord cannot be considered as a quantum resource, since it has been …
Quantum state preparation is an important class of quantum algorithms that is employed as a black-box subroutine in many algorithms, or used by itself to generate arbitrary probability distributions. We present a novel state preparation method that utilizes less quantum computing resource than the existing methods. Two variants of the algorithm with different emphases are introduced. One variant uses fewer qubits and no controlled gates, while the other variant potentially requires fewer gates overall. A general analysis is given to estimate the number of qubits necessary to achieve a desired …
We propose two controlled remote state preparation protocols via partially entangled channels. One prepares a single-qubit state and the other prepares a two-qubit state. Different from other controlled remote state preparation schemes which also utilize partially entangled channels, neither auxiliary qubits nor two-qubit unitary transformations are required in our schemes and the success probabilities are independent of the coefficients of the quantum channel. The success probabilities are 50% and 25% for arbitrary single-qubit states and two-qubit states, respectively. We also show that the …
The conventional postulate for the probabilistic interpretation of quantum mechanics is asymmetric in preparation and measurement, making retrodiction reliant on inference by use of Bayes' theorem. Here, a more fundamental symmetric postulate is presented, from which both predictive and retrodictive probabilities emerge immediately, even where measurement devices more general than those usually considered are involved. It is shown that the new postulate is perfectly consistent with the conventional postulate.
Foundations of the theory of quantum Turing machines are investigated. The protocol for the preparation and the measurement of quantum Turing machines is discussed. The local transition functions are characterized for fully general quantum Turing machines. A new halting protocol is proposed without augmenting the halting qubit and is shown to work without spoiling the computation.
We examine a single-pulse preparation of the uniform superpositional wave function, which includes all basis states, in a spin quantum computer. The effective energy spectrum and the errors generated by this pulse are studied in detail. We show that, in spite of the finite width of the energy spectrum bands, amplitude and phase errors can be made reasonably small.
