Andreas Keil
The accessible information of general signal states is obtained by performing a generalized measurement. In the case that the signal alphabet consists of two states of a qubit system, it is proved that a von Neumann (orthogonal) measurement is sufficient to reach the accessible information.
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The decomposition of matrices associated to two-qubit and three-qubit orthogonal gates is studied, and based on the decomposition the synthesis of these gates is investigated. The optimal synthesis of general two-qubit orthogonal gate is obtained. For two-qubit unimodular orthogonal gate, it requires at most 2 CNOT gates and 6 one-qubit Ry gates. For the general three-qubit unimodular orthogonal gate, it can be synthesized by 16 CNOT gates and 36 one-qubit Ry and Rz gates in the worst case.
In the Hilbert space of n qubits, we introduce the symplectic space (n odd) and the orthogonal space (n even) via the spin-flip operator. Under this mathematical structure we discuss some properties of n qubits, including homomorphically mapping the local operations of n qubits into the symplectic group or orthogonal group, and prove that the generalized ``magic basis'' is just the bi-orthonormal basis (that is, the orthonormal basis of both Hilbert space and the orthogonal space ). Finally, an example is given to discuss the application in physics of this mathematical structure.
An optimal universal cloning transformation is derived that produces M copies of an unknown qubit from a pair of orthogonal qubits. For M>6, the corresponding cloning fidelity is higher than that of the optimal copying of a pair of identical qubits. It is shown that this cloning transformation can be implemented probabilistically via parametric down-conversion by feeding the signal and idler modes of a nonlinear crystal with orthogonally polarized photons.
A protocol for non-destructive descrimination of arbitrary set of orthogonal quantum states was proposed by V. S. Manu et al., using an algorithm based on quantum phase estimation. IBM Corporation has released a superconductivity based 5-qubit (5-qubit transmon bowtie chip 3 and IBM 5-qubit real processor) quantum computer named Quantum Experience and placed it on cloud. In this paper we take advantage of the online availability of those real quantum processors(ibmqx2 amd ibmqx4) and carry out the above protocol that has experimentally demonstrated earlier using NMR quantum processor. Here, we…
There is a natural orthogonal basis of the 6-qubit decoherence-free (DF) space robust against collective noise. Interestingly, most of the basis states can be obtained from one another just permuting qubits. This property: (a) is useful for encoding qubits in DF subspaces, (b) allows the implementation of the Bennett-Brassard 1984 (BB84) protocol in DF subspaces just permuting qubits, which completes a the method for quantum key distribution using DF states proposed by Boileau et al. [Phys. Rev. Lett. 92, 017901 (2004)], and (c) points out that there is only one 6-qubit DF state which is essen…
Formulas for Mutually Orthogonal Quantum States in Two-Qubit Systems: Orthogonal Schmidt Decompositions
该研究针对两量子比特系统，推导相互正交纯态的施密特分解公式，基于纠缠结构分类正交集，分析含最大纠缠态的正交基，并证明不存在3个直积态加1个纠缠态构成的正交基。
The "entanglement cost" of a bipartite measurement is the amount of shared entanglement two participants need to use up in order to carry out the given measurement by means of local operations and classical communication. Here we numerically investigate the entanglement cost of generic orthogonal measurements on two qubits. Our results strongly suggest that for almost all measurements of this kind, the entanglement cost is strictly greater than the average entanglement of the eigenstates associated with the measurements, implying that the nonseparability of a two-qubit orthogonal measurement i…
An orthogonal product basis (OPB) of a finite-dimensional Hilbert space $H=H_1\otimes H_2\otimes\cdots\otimes H_n$ is an orthonormal basis of $H$ consisting of product vectors $x_1\otimes x_2\otimes\cdots\otimes x_n$. We show that the problem of classifying the OPBs of an $n$-qubit system can be reduced to a purely combinatorial problem. We solve this combinatorial problem in the case of four qubits and obtain 33 multiparameter families of OPBs. Each OPB of four qubits is equivalent, under local unitary operations and qubit permutations, to an OPB belonging to at least one of these families.
We present an analysis of transfer of quantum information between the collective spin degrees of freedom of a large ensemble of two-level systems and a single central qubit. The coupling between the central qubit and the individual ensemble members may be varied and thus provides access to more than a single storage mode. Means to store and manipulate several independent qubits are derived for the case where the variation in coupling strengths does not allow addressing of orthogonal modes of the ensemble. While our procedures and analysis may apply to a number of different physical systems, fo…
The common use in literature of orthogonal measurements in obtaining quantum discord for two-qubit states is discussed and compared with more general measurements. We prove the optimality of orthogonal measurements for rank 2 states. While for rank 3 and 4 mixed states they are not optimal, we present strong numerical evidence showing that they give the correct quantum discord up to minimal corrections. Based on the connection, through purification with an ancilla, between discord and entanglement of formation (EoF), we give a tight upper bound for the EoF of a $2\otimes N$ mixed state of rank…
We investigate the transfer and exchange information between a single qubit system excited by a rectangular pulse. The dynamics of the system is treated within and outside rotating wave approximation (RWA). The initial state of the qubit plays an important role for sending information with high fidelity. Within RWA, and as the fidelity of the transformed information increases the exchange information with the environment increases. For increasing values of atomic detuning, the fidelity decreases faster and the exchange information has an upper limit. Outside RWA,the fidelity of the transformed…
Nonlocality via multiqubit orthogonal product bases
本文研究多量子比特正交乘积基的局域可区分性，识别出无纠缠非定域基，并提出借助Bell态量子隐形传态合并系统的区分方案。
Orthogonal frequency-division multiplexing for simultaneous gate operations on multiple qubits via a shared control line
本文提出一种基于正交频分复用的可扩展微波控制方案，通过单根电缆传输微波实现多个量子比特的同时门操作，提升量子处理器的规模化能力。
The effect of non-orthogonality of an entangled non-orthogonal state based quantum channel is investigated in detail in the context of the teleportation of a qubit. Specifically, average fidelity, minimum fidelity and minimum assured fidelity (MASFI) are obtained for teleportation of a single qubit state using all the Bell type entangled non-orthogonal states known as quasi Bell states. Using Horodecki criterion, it is shown that the teleportation scheme obtained by replacing the quantum channel (Bell state) of the usual teleportation scheme by a quasi Bell state is optimal. Further, the perfo…
We present a physically motivated variational wave function for the ground state of the asymmetric quantum Rabi model (AQRM). The wave function is a weighted superposition of squeezed coherent states entangled with non-orthogonal qubit states, and relies only on three variational parameters in the regimes of interest where the squeezing effect becomes negligible. The variational expansion describes the ground state remarkably well in almost all parameter regimes, especially with arbitrary bias. We use the variational result to calculate various relevant physical observables of the ground state…
This paper considers a class of qubit channels for which three states are always sufficient to achieve the Holevo capacity. For these channels it is known that there are cases where two orthogonal states are sufficient, two non-orthogonal states are required, or three states are necessary. Here a systematic theory is given which provides criteria to distinguish cases where two states are sufficient, and determine whether these two states should be orthogonal or non-orthogonal. In addition, we prove a theorem on the form of the optimal ensemble when three states are required, and present effici…
The quantromon: A qubit-resonator system with orthogonal qubit and readout modes
提出名为quantromon的双模电路，通过设计内在的交叉Kerr耦合实现正交的量子比特与读出模式，在实验中展现出对失谐的弱依赖性、内在Purcell保护及98.3%的无参量放大器单次读出保真度，有望简化量子处理器测量电路。
The superposition principle is at the heart of quantum mechanics and at the root of many paradoxes arising when trying to extend its predictions to our everyday world. Schroedinger's cat is the prototype of such paradoxes and here, in contrast to many others, we choose to investigate it from the operational point of view. We experimentally demonstrate a universal strategy for producing an unambiguously distinguishable type of superposition, that of an arbitrary pure state and its orthogonal. It relies on only a limited amount of information about the input state to first generate its orthogona…
In accordance with the principle of superposition and operator rule, the state of the whole system composed of the state of the particles to be teleported and quantum channel can be expanded by Bell bases and transformation operator. Theoretically, if determinant of transformation operators is not zero, the teleportation can be realized only by performing an inverse transformation. Actually, if the transformation operator is not a unitary operation, then by using one auxiliary qubits, the teleportation can be realized only by performing a collective unitary transformation. Moreover, the furthe…
A quantum analog of the fundamental classical NOT gate is a quantum gate that would transform any input qubit state onto an orthogonal state. Intriguingly, this universal NOT gate is forbidden by the laws of quantum physics. This striking phenomenon has far-reaching implications concerning quantum information processing and encoding information about directions and reference frames into quantum states. It also triggers the question under what conditions the preparation of quantum states orthogonal to input states becomes possible. Here we report on experimental demonstration of orthogonalizati…
A group theoretic framework is introduced that simplifies the description of known quantum error-correcting codes and greatly facilitates the construction of new examples. Codes are given which map 3 qubits to 8 qubits correcting 1 error, 4 to 10 qubits correcting 1 error, 1 to 13 qubits correcting 2 errors, and 1 to 29 qubits correcting 5 errors.
Entanglement properties of IBM Q 53 qubit quantum computer are carefully examined with the noisy intermediate-scale quantum (NISQ) technology. We study GHZ-like states with multiple qubits (N=2 to N=7) on IBM Rochester and compare their maximal violation values of Mermin polynomials with analytic results. A rule of N-qubits orthogonal measurements is taken to further justify the entanglement less than maximal values of local realism (LR). The orthogonality of measurements is another reliable criterion for entanglement except the maximal values of LR. Our results indicate that the entanglement …
Variational Quantum Non-Orthogonal Optimization
针对通用量子计算机量子比特有限且含噪的问题，提出将离散经典变量编码为非正交量子态并结合VQE与量子态层析成像的优化方案，显著减少所需量子比特数，在有限量子硬件上成功优化多项式。
In a recent paper (Phys. Rev. A 90, 022316 (2014) ), Goyeneche et al. established a link between the combinatorial notion of orthogonal arrays and k-uniform states and present open issue. (B) Find for what N there are 3-uniform states of N-qubits. In this paper, we demonstrate the existence of 3-uniform states of N-qubits for N=11,..,15".
We experimentally realize a nonlinear quantum protocol on single-photon qubits with linear optical elements and appropriate measurements. The quantum nonlinearity is induced by post-selecting the polarization qubit based on a measurement result obtained on the spatial degree of freedom of the single photon which plays the role of a second qubit. Initially, both qubits are prepared in the same quantum state and an appropriate two-qubit unitary transformation entangles them before the measurement on the spatial part. We analyze the result by quantum state tomography on the polarization degree of…
We study the local distinguishability of general multi-qubit states and show that local projective measurements and classical communication are as powerful as the most general local measurements and classical communication. Remarkably, this indicates that the local distinguishability of multi-qubit states can be decided efficiently. Another useful consequence is that a set of orthogonal $n$-qubit states is locally distinguishable only if the summation of their orthogonal Schmidt numbers is less than the total dimension $2^n$. When $n=2$ such a condition is also sufficient. Employing these resu…
We discuss (im)possibility of the exact cloning of orthogonal but genuinely entangled three qubit states aided with entangled ancila under local operation and classical communication. Whereas any two orthogonal GHZ states taken from the canonical GHZ basis, can be cloned with the help of a known GHZ state, surprisingly we find that no two W states can be cloned by using any known three qubit (possibly entangled) state as blank copy.
We introduce a new gate that transfers an arbitrary state of a qubit into a superposition of two quasi-orthogonal coherent states of a cavity mode, with opposite phases. This qcMAP gate is based on conditional qubit and cavity operations exploiting the energy level dispersive shifts, in the regime where they are much stronger than the cavity and qubit linewidths. The generation of multi-component superpositions of quasi-orthogonal coherent states, non-local entangled states of two resonators and multi-qubit GHZ states can be efficiently achieved by this gate.
A one way partial quantum bit commitment protocol is developed, using states with built-in classical correlation, completely independent of entanglement. It involves concealing information in a set of mutually non-orthogonal states and revealing it through measurements on a set of product states that are mutually orthogonal. Given $2^N$ choices to commit from, the protocol encodes each choice in a $N+1$ qubit state, from $2^N$ non-orthogonal states. A previously agreed upon $N$ qubit state corresponding to each choice, when coupled with the $N+1$ qubit state, yields an element belonging to a s…
Recently, some attention has been paid to falsifying the Leggett model, in which global probabilities characterizing a quantum state are represented by a combination of factorisable distributions. This idea was even verified in experiments, and generalized for larger subsystems, but thus far not in terms of the size of a subsystem. In this communication we show an inequality to reject the Leggett description for a subsystem of two qubits. We also point out some other interpretations of the derived expression.
Discriminating between orthogonal quantum systems without destroying their entanglement is of interest to quantum computation and communication. In this paper, we explicate the schemes for the non-destructive discrimination (NDD) of 16 orthogonal four qubit cluster states and 32 orthogonal five qubit cluster states respectively. This technique will find its applications in various branches of quantum information theory.
An example is given of a qubit quantum channel which requires four inputs to maximize the Holevo capacity. The example is one of a family of channels which are related to 3-state channels. The capacity of the product channel is studied and numerical evidence presented which strongly suggests additivity. The numerical evidence also supports a conjecture about the concavity of output entropy as a function of entanglement parameters. However, an example is presented which shows that for some channels this conjecture does not hold for all input states. A numerical algorithm for finding the capacit…
We consider a superconducting charge qubit coupled to distinct orthogonal electromagnetic field modes belonging to a coplanar wave guide and a microstrip transmission line resonators. This architecture allows the simultaneous implementation of a Jaynes-Cummings and anti-Jaynes-Cummings dynamics, a resonant method for generating mesoscopic qubit-field superpositions and for field-state reconstruction. Furthermore, we utilize this setup to propose a field measurement technique that is, in principle, robust to qubit dephasing and field relaxation due to a fast pre-measurement.
A remark on the Brown-Susskind conjecture
本文在Brown-Susskind猜想框架下，证明增加一对qubit时，可由固定数量2-qubit门生成的n-qubit酉算子集合的维数严格增长。
The absolute value of the hyperdeterminant of four qubits is a useful measure of genuine entanglement. We prove a recent conjecture of Gour and Wallach describing the pure maximally entangled four-qubit states with respect to this measure.
Classification of entanglement in multipartite quantum systems is an open problem solved so far only for bipartite systems and for systems composed of three and four qubits. We propose here a coarse-grained classification of entanglement in systems consisting of $N$ subsystems with an arbitrary number of internal levels each, based on properties of orthogonal arrays with $N$ columns. In particular, we investigate in detail a subset of highly entangled pure states which contains all states defining maximum distance separable codes. To illustrate the methods presented, we analyze systems of four…
This paper focuses on quantum information masking for quantum state in two-dimensional Hilbert space. We present a system of equations as the condition of quantum information masking. It is shown that quantum information contained in a single qubit state can be masked, if and only if the coefficients of quantum state satisfy the given system of equations. By observing the characteristics of non-orthogonal maskable quantum states, we obtain a related conclusion, namely, if two non-orthogonal two-qubit quantum states can mask a single qubit state, they have the same number of terms and the same …
In the context of von Neumann projective measurement scenario for a qubit system, it is widely believed that the mutual orthogonality between the post-interaction pointer states is the sufficient condition for achieving the ideal measurement situation. However, for experimentally verifying the observable probabilities, the real space distinction between the pointer distributions corresponding to post-interaction pointer states play crucial role. It is implicitly assumed that mutual orthogonality ensures the support between the post-interaction pointer distributions to be disjoint. We point out…
We show that nonorthogonal states achieve a higher level of entanglement when one party undergoes uniform acceleration. We also show that in this regime non-orthogonal states achieve a higher fidelity for teleportation. A quantum field as observed by an observer confined to a Rindler wedge acts as an open system. When one traces over the field modes in the causally disconnected region of space time, one finds that, for a qubit derived from the modes of a scalar field, the effective state space of a qubit is deformed. In order to show this we numerically calculate the Bures angle between states…
Extensive numerical integration results lead us to conjecture that the silver mean, that is, s = \sqrt{2}-1 = .414214 plays a fundamental role in certain geometries (those given by monotone metrics) imposable on the 15-dimensional convex set of two-qubit systems. For example, we hypothesize that the volume of separable two-qubit states, as measured in terms of (four times) the minimal monotone or Bures metric is s/3, and 10s in terms of (four times) the Kubo-Mori monotone metric. Also, we conjecture, in terms of (four times) the Bures metric, that that part of the 14-dimensional boundary of se…
Recently an orthogonal state based protocol of direct quantum communication without actual transmission of particles is proposed by Salih \emph{et al.}{[}Phys. Rev. Lett. \textbf{110} (2013) 170502{]} using chained quantum Zeno effect. As the no-transmission of particle claim is criticized by Vaidman {[}arXiv:1304.6689 (2013){]}, the condition (claim) of Salih \emph{et al.} is weaken here to the extent that transmission of particles is allowed, but transmission of the message qubits (the qubits on which the secret information is encoded) is not allowed. Remaining within this weaker condition i…
Multiqubit UPB: The method of formally orthogonal matrices
本文利用元素为单量子比特 Hilbert 空间单位向量变量的形式正交矩阵，构造多种新尺寸的多量子比特不可扩展乘积基，并给出 PPT 纠缠态的新构造方法。
A Degenerate Singlet-Triplet Qubit with All-Electrical Orthogonal Control
本研究展示了由锗双量子点空穴自旋构成的简并单重态-三重态量子比特，利用全电方式独立调控交换相互作用与塞曼能差，实现正交旋转，单量子比特门保真度达99.53%，为多量子比特规模化提供了途径。
Infeasibility of constructing a special orthogonal matrix for the deterministic remote preparation of arbitrary n-qubit state
本文将任意 n 量子比特态 DRSP 的特殊正交矩阵构造归约为异或线性方程组求解，提出多项式复杂度算法，并证明 n>3 时无解。
A class of Schwarz qubit maps with diagonal unitary and orthogonal symmetries
本研究刻画了一类具有对角酉与正交对称性的幺正Schwarz量子比特映射，揭示其正定性、算子Schwarz不等式与完全正定性的关联，推广至非幺正情形并拓展了Pauli量子信道的Fujiwara-Algoet条件。
We show that there are six inequivalent $4\times4$ unextendible product bases (UPBs) of size eight, when we consider only 4-qubit product vectors. We apply our results to construct Positive-Partial-Transpose entangled states of rank nine. They are at the same 4-qubit, $2\times2\times4$ and $4\times4$ states, and their ranges have product vectors. One of the six UPBs turns out to be orthogonal to an almost genuinely entangled space, in the sense that the latter does not contain $4\times4$ product vector in any bipartition of 4-qubit systems. We also show that the multipartite UPB orthogonal to …
Each platonic solid defines a single-qubit positive operator valued measure (POVM) by interpreting its vertices as points on the Bloch sphere. We construct simple circuits for implementing this kind of measurements and other simple types of symmetric POVMs on one qubit. Each implementation consists of a discrete Fourier transform and some elementary quantum operations followed by an orthogonal measurement in the computational basis.
On Strong Monogamy Conjecture in Four-Qubit System
本文将强一夫一妻性不等式从 concurrence 推广到 negativity，系统研究了四量子比特纯态，并解析给出满足与违反该关系的态类。
We know that we cannot split the information encoded in two non-orthogonal qubits into complementary parts deterministically. Here we show that each of the copies of the state randomly selected from a set of non orthogonal linearly independent states, splitting of quantum information can not be done even probabilistically. Here in this work we also show that under certain restricted conditions, we can probabilistically split the quantum information encoded in a qubit.
It is conjectured that the Holevo capacity of a product channel Ω\otimes Φis achieved when product states are used as input. Amosov, Holevo and Werner have also conjectured that the maximal p-norm of a product channel is achieved with product input states. In this paper we establish both of these conjectures in the case that Ωis arbitrary and Φis a CQ or QC channel (as defined by Holevo). We also establish the Amosov, Holevo and Werner conjecture when Ωis arbitrary and either Φis a qubit channel and p=2, or Φis a unital qubit channel and p is integer. Our proofs involve a new conjecture for th…
In a previous study (quant-ph/0207181), we formulated a conjecture that arbitrarily coupled qubits (describable by 4 x 4 density matrices) are separable with an a priori probability of 8/(11 π^2) = 0.0736881. For this purpose, we employed the normalized volume element of the Bures (minimal monotone) metric as a probability distribution over the fifteen-dimensional convex set of 4 x 4 density matrices. Here, we provide further/independent (quasi-Monte Carlo numerical integration) evidence of a stronger nature (giving an estimate of 0.0736858 vs. 0.0737012 previously) for this conjecture. Additi…
Optimizing Qubit Mapping with Quasi-Orthogonal Space-Time Block Codes and Quaternion Orthogonal Designs
本研究结合准正交空时分组码与四元数正交设计优化量子比特映射，实验表明多数情形下其纠错性能优于稳定子群，为量子信息处理提供可靠方案。
In this paper, we propose concurrence classes for an arbitrary multi-qubit state based on orthogonal complement of a positive operator valued measure, or POVM in short, on quantum phase. In particular, we construct concurrence for an arbitrary two-qubit state and concurrence classes for the three- and four-qubit states. And finally, we construct $W^{m}$ and $GHZ^{m}$ class concurrences for multi-qubit states. The unique structure of our POVM enables us to distinguish different concurrence classes for multi-qubit states.
We consider the task of deciding whether an unknown qubit state falls in a prescribed neighborhood of a reference state. We assume that several copies of the unknown state are given and apply a unitary operation pairwise on them combined with a post-selection scheme conditioned on the measurement result obtained on one of the qubits of the pair. The resulting transformation is a deterministic, nonlinear, chaotic map in the Hilbert space. We derive a class of these transformations capable of orthogonalizing nonorthogonal qubit states after a few iterations. These nonlinear maps orthogonalize st…
We analyze the problem of increasing the efficiency of single-photon sources or single-rail photonic qubits via linear optical processing and destructive conditional measurements. In contrast to previous work we allow for the use of coherent states and do not limit to photon-counting measurements. We conjecture that it is not possible to increase the efficiency, prove this conjecture for several important special cases, and provide extensive numerical results for the general case.
The 27-qubit Counterexample to the LU-LC Conjecture is Minimal
研究证明27个量子比特的图态是LU等价但非LC等价的反例，且在26个量子比特以内LU等价与LC等价一致。
Multiqubit orthogonal product bases
该研究通过形式矩阵与边着色多重图的关联，将多量子比特正交乘积基的分类简化为图同构，推导了其等价类数量的上下界及渐近行为，并提出了等价判定的两阶段指数复杂度算法。
Orthogonal-state-based Measurement Device Independent Quantum Communication
本文提出首个基于正交态的测量设备无关量子安全直接通信与量子对话协议，采用贝尔基诱骗量子比特，在集体噪声下性能优于共轭编码方案，并能转化为量子密钥分发协议，同时将安全直接通信距离加倍。
Parallel operations are important for both near-term quantum computers and larger-scale fault-tolerant machines because they reduce execution time and qubit idling. We propose and implement a pairwise-parallel gate scheme on a trapped-ion quantum computer. The gates are driven simultaneously on different sets of orthogonal motional modes of a trapped-ion chain. We demonstrate the utility of this scheme by creating a GHZ state in one step using parallel gates with one overlapping qubit. We also show its advantage for circuits by implementing a digital quantum simulation of the dynamics of an in…
Contrary to A.Borras et al.'s [1] conjecture, a genuine maximally seven-qubit entangled state is presented. We find a seven-qubit state whose marginal density matrices for subsystems of 1,2- qubits are all completely mixed and for subsystems of 3-qubits is almost completely mixed.
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