As is well-known in the context of topological insulators and superconductors, short-range-correlated fermionic pure Gaussian states with fundamental symmetries are systematically classified by the periodic table. We revisit this topic from a quantum-information-inspired operational perspective without referring to any Hamiltonians, and apply the formalism to bosonic Gaussian states as well as (both fermionic and bosonic) locality-preserving unitary Gaussian operations. We find that while bosonic Gaussian states are all trivial, there exist nontrivial bosonic Gaussian operations that cannot be continuously deformed into the identity under the locality and symmetry constraint. Moreover, we unveil unexpectedly complicated relations between fermionic Gaussian states and operations, pointing especially out that some of the former can be disentangled by the latter under the same symmetry constraint, while some cannot. In turn, we find that some topological operations are genuinely dynamical, in the sense that they cannot create any topological states from a trivial one, yet they are not connected to the identity. The notions of disentanglability and genuinely dynamical topology can be unified in a general picture of unitary-to-state homomorphism, and apply equally to interacting topological phases and quantum cellular automata.
Non-Gaussian states and operations are crucial for various continuous-variable quantum information processing tasks. To quantitatively understand non-Gaussianity beyond states, we establish a resource theory for non-Gaussian operations. In our framework, we consider Gaussian operations as free operations, and non-Gaussian operations as resources. We define entanglement-assisted non-Gaussianity generating power and show that it is a monotone that is non-increasing under the set of free super-operations, i.e., concatenation and tensoring with Gaussian channels. For conditional unitary maps, this…
In a recent paper [Bardyn et al. Phys. Rev. X 8, 011035 (2018)], it was shown that the generalization of the many-body polarization to mixed states can be used to construct a topological invariant which is also applicable to finite-temperature and non-equilibrium Gaussian states of lattice fermions. The many-body polarization defines an ensemble geometric phase (EGP) which is identical to the Zak phase of a fictitious Hamiltonian, whose symmetries determine the topological classification. Here we show that in the case of Gaussian states of bosons the corresponding topological invariant is alwa…
Interconversion of pure Gaussian states using non-Gaussian operations
我们分析的条件下，本地操作和经典通信使纠缠变换内的一组二分纯高斯态。在[Quant.]中找到了一组充分必要条件。Inf.Comp.3，211（2003）]用于限制于高斯局部操作和经典通信的这种状态之间的相互转换。在这里，我们利用优控制理论，以获得更一般的（充分的）条件，超越高斯局部操作的二分纯高斯态之间的相互转换。虽然我们的技术适用于每一方的任意数量的模式，但它使我们能够展示出令人惊讶的2 x 2高斯状态的简单示例，这些状态必须需要非高斯局部操作才能相互转换。
The coherence resource theory needs to study the operational value and efficiency which can be broadly formulated as the question: when can one coherent state be converted into another under incoherent operations. We answer this question completely for one-mode continuous-variable systems by characterizing conversion of coherent Gaussian states under incoherent Gaussian operations in terms of their first and second moments. The no-go theorem of purification of coherent Gaussian states is also built. The structure of incoherent Gaussian operations of two-mode continuous-variable systems is disc…
Quantum Non-Gaussian states are considered as a useful resource for many tasks in quantum information processing, from quantum metrology and quantum sensing to quantum communication and quantum key distribution. Another useful tool that is growing attention is the newly constructed quantum switch. Its applications in many tasks in quantum information have been proved to be outperforming many existing schemes in quantum communication and quantum thermometry. In this contribution, we are addressing this later to be very useful to engineer highly non-Gaussian states from Gaussian operations whose…
Non-Gaussian operations have been studied intensively in recent years due to their ability to increase the secret key rate for certain CV-QKD protocols. However, most previous studies on such protocols are carried out in a single-mode setting, even though in reality any quantum state contains multi-mode components in frequency space. In this work we investigate the use of non-Gaussian operations in a multi-mode CV-QKD system. Our main finding is that, contrary to single-mode CV-QKD systems, in generic multi-mode CV-QKD systems it is possible to use non-Gaussian operations to increase the optim…
Beam-splitter operations are an indispensable resource for processing quantum information encoded in bosonic modes. However, in hybrid quantum systems, it can be challenging to implement reliable beam-splitters between two distinct bosonic modes due to various experimental imperfections. Without beam-splitters, realizing arbitrary Gaussian operations between bosonic modes can become highly non-trivial or even infeasible. In this work, we develop novel interference-based protocols for engineering Gaussian operations in multi-mode hybrid bosonic systems without requiring beam-splitters. Specific…
We determine the optimal method of discriminating and comparing quantum states from a certain class of multimode Gaussian states and their mixtures when arbitrary global Gaussian operations and general Gaussian measurements are allowed. We consider the so-called constant-$\hat{p}$ displaced states which include mixtures of multimode coherent states arbitrarily displaced along a common axis. We first show that no global or local Gaussian transformations or generalized Gaussian measurements can lead to a better discrimination method than simple homodyne measurements applied to each mode separate…
Gaussian quantum states of bosonic systems are an important class of states. In particular, they play a key role in quantum optics as all processes generated by Hamiltonians up to second order in the field operators (i.e. linear optics and quadrature squeezing) preserve Gaussianity. A powerful approach to calculations and analysis of Gaussian states is using phase-space variables and symplectic transformations. The purpose of this note is to serve as a concise reference for performing phase-space calculations on Gaussian states. In particular, we list symplectic transformations for commonly us…
Continuous-variable systems realized in quantum optics play a major role in quantum information processing, and it is also one of the promising candidates for a scalable quantum computer. We introduce a resource theory for continuous-variable systems relevant to universal quantum computation. In our theory, easily implementable operations---Gaussian operations combined with feed-forward---are chosen to be the free operations, making the convex hull of the Gaussian states the natural free states. Since our free operations and free states cannot perform universal quantum computation, genuine non…
The study of thermal operations allows one to investigate the ultimate possibilities of quantum states and of nanoscale thermal machines. Whilst fairly general, these results typically do not apply to continuous variable systems and do not take into account that, in many practically relevant settings, system-environment interactions are effectively bilinear. Here we tackle these issues by focusing on Gaussian quantum states and channels. We provide a complete characterisation of the most general Gaussian thermal operation acting on an arbitrary number of bosonic modes, which turn out to be all…
We investigate work extraction from non-interacting fermions under arbitrary unitary operations and the more restricted class of Gaussian unitary operations that can be feasibly implemented. We characterize general quantum states in fermionic systems according to their ability to yield work (or not) under such transformations and study the limit for which multiple copies of passive states in fermionic systems can be activated for work extraction. We find that a sufficient number of copies of non-thermal passive states can achieve this, yielding an upper bound on the number of copies needed.
Quantum states that can yield work in a cyclical Hamiltonian process form one of the primary resources in the context of quantum thermodynamics. Conversely, states whose average energy cannot be lowered by unitary transformations are called passive. However, while work may be extracted from non-passive states using arbitrary unitaries, the latter may be hard to realize in practice. It is therefore pertinent to consider the passivity of states under restricted classes of operations that can be feasibly implemented. Here, we ask how restrictive the class of Gaussian unitaries is for the task of …
We quantify the maximum amount of entanglement of formation (EoF) that can be achieved by continuous-variable states under passive operations, which we refer to as EoF-potential. Focusing, in particular, on two-mode Gaussian states we derive analytical expressions for the EoF-potential for specific classes of states. For more general states, we demonstrate that this quantity can be upper-bounded by the minimum amount of squeezing needed to synthesize the Gaussian modes, a quantity called squeezing of formation. Our work, thus, provides a new link between non-classicality of quantum states and …
Non-Gaussian operations in continous variable (CV) quantum key distribution (QKD) have been limited to photon subtraction on squeezed vacuum states only. This is mainly due to the ease of calculating the covariance matrix representation of such states. In this paper we study the effects of general non-Gaussian operations corresponding to photon addition, catalysis and subtraction on squeezed coherent states on CV measurement device independent (MDI) QKD. We find that non-Gaussianity coupled with coherence can yield significantly longer transmission distances than without. Particularly we obser…
We derive a theoretical framework for the experimental certification of non-Gaussian features of quantum states using double homodyne detection. We rank experimental non-Gaussian states according to the recently defined stellar hierarchy and we propose practical Wigner negativity witnesses. We simulate various use-cases ranging from fidelity estimation to witnessing Wigner negativity. Moreover, we extend results on the robustness of the stellar hierarchy of non-Gaussian states. Our results illustrate the usefulness of double homodyne detection as a practical measurement scheme for retrieving i…
In our work, we compare three teleportation protocols: the original protocol, the photon subtraction protocol, and the protocol with a cubic phase gate. We evaluate the fidelity of each protocol using the example of teleportation of the squeezed state and the Schrodinger's cat state. We show that, under equal conditions, the teleportation scheme with a cubic phase gate achieves significantly higher fidelity than the other protocols considered.
The required set of operations for universal continuous-variable quantum computation can be divided into two primary categories: Gaussian and non-Gaussian operations. Furthermore, any Gaussian operation can be decomposed as a sequence of phase-space displacements and symplectic transformations. Although Gaussian operations are ubiquitous in quantum optics, their experimental realizations generally are approximations of the ideal Gaussian unitaries. In this work, we study different performance criteria to analyze how well these experimental approximations simulate the ideal Gaussian unitaries. …
Non-Gaussian operations have been studied intensively in recent years due to their ability to enhance the entanglement of quantum states. However, most previous studies on such operations are carried out in a single-mode setting, even though in reality any quantum state contains multi-mode components in frequency space. Whilst there have been general frameworks developed for multi-mode photon subtraction (PS) and photon addition (PA), an important gap exists in that no framework has thus far been developed for multi-mode photon catalysis (PC). In this work we close that gap. We then apply our …
We examine the problem of state transformations in the framework of Gaussian thermal resource theory in the presence of catalysts. To this end, we introduce an expedient parametrisation of covariance matrices in terms of principal mode temperatures and asymmetries, and consider both weak and strong catalytic scenarios. We show that strong catalysts (where final correlations with the system are forbidden) are useless for the single mode case, in that they do not expand the set of states reachable from a given initial state through Gaussian thermal operations. We then go on to prove that weak ca…
We propose a measure of nonclassical correlation $N_{\mathcal F}^{\mathcal G}$ in terms of local Gaussian unitary operations based on square of the fidelity $\mathcal F$ for bipartite continuous-variable systems. This quantity is easier to calculate or estimate and is a remedy for the local ancilla problem associated with the geometric measurement-induced nonlocality. A simple computation formula of $N_{\mathcal F}^{\mathcal G}$ for any $(1+1)$-mode Gaussian states is presented and an estimation of $N_{\mathcal F}^{\mathcal G}$ for any $(n+m)$-mode Gaussian states is given. For any $(1+1)$-mod…
It is known that distillation in continuous variable resource theories is impossible when restricted to Gaussian states and operations. To overcome this limitation, we enlarge the theories to include convex mixtures of Gaussian states and operations. This extension is operationally well-motivated since classical randomness is easily accessible. We find that resource distillation becomes possible for convex Gaussian resource theories-albeit in a limited fashion. We derive this limitation by studying the convex roof extension of a Gaussian resource measure and then go on to show that our bound i…
