Dariusz Chruscinski, Andrzej Kossakowski
Using well known duality between quantum maps and states of composite systems we introduce the notion of Schmidt number of a quantum channel. It enables one to define classes of quantum channels which partially break quantum entanglement. These classes generalize the well known class of entanglement breaking channels.
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We consider composability of quantum channels from a limited amount of entanglement via local operations and classical communication (LOCC). We show that any $k$-partially entanglement breaking channel can be composed from an entangled state with Schmidt number of $k$ via one-way LOCC. From the entanglement assisted construction we can reach an alternative definition of partially entanglement breaking channels.
Complementarity and entanglement are fundamental features of Quantum Mechanics that were recently related in triality equalities that involve quantum coherence, the wave aspect of a qubit, and quantum predictability and quantum entanglement, the particle aspect of a qubit. In this article, we give an operational connection between redictability and entanglement in entanglement swapping from initially partially entangled states. For this, we show that the predictability of the pre-measurement one-qubit density matrix is directly related to the probability of the partially entangled component of…
We show the rather counterintuitive result that entangled input states can strictly enhance the distinguishability of two entanglement-breaking channels.
Entanglement is a key issue in the quantum physics which gives rise to resources for achieving tasks that are not possible within the realm of classical physics. Quantum entanglement varies with the evolution of the quantum systems. It is of significance to investigate the entanglement dynamics in terms of quantum channels. We study the entanglement-breaking channels and present the necessary and sufficient conditions for a quantum channel to an entanglement-breaking one for qubit systems. Furthermore, a concept of strong entanglement-breaking channel is introduced. The amendment of entangleme…
Entanglement-breaking channels are quantum channels transforming entangled states to separable states. Despite a detailed discussion of their operational structure, to be found in the literature, studies on dynamical characteristics of this type of maps are yet limited. We consider one of the basic questions: for Lindblad-type dynamics, when does a given channel break entanglement? We discuss the finite-dimensional case where the quantification of entanglement via entanglement witnesses is utilized. For the general setup, we use the method of quantum speed limit to derive lower bounds on entan…
Nonclassicality and entanglement are notions fundamental to quantum information processes involving continuous variable systems. That these two notions are intimately related has been intuitively appreciated for quite some time. An aspect of considerable interest is the behaviour of these attributes of a state under the action of a noisy channel. Inspired by the notion of entanglement-breaking channels, we define the concept of nonclassicality-breaking channels in a natural manner. We show that the notion of nonclassicality-breaking is essentially equivalent---in a clearly defined sense of the…
Complete complementarity relations, as e.g. $P(ρ_{A})^{2} + C(ρ_{A})^{2} + E(|Ψ\rangle_{AB})^{2}=1$, constrain the local predictability, $P$, and local coherence, $C$, and the entanglement, $E$, of bipartite pure states. For pairs of qubits prepared initially in a particular class of partially entangled pure states with null local coherence, these relations were used in Ref. [Phys. Lett. A, 451, 128414 (2022)] to provide an operational connection between local predictability of the pre-measurement states with the probability of the maximally entangled components of the states after the Bell-ba…
On the characterization of partially entanglement breaking and annihilating channels
该文分析部分纠缠破缺通道，提出识别保施密特数非资源破缺通道的方案，引入部分纠缠湮灭通道，研究三类量子通道的关联，丰富了量子通道的表征理论。
We present a nonlocal entanglement concentration scheme for reconstructing some maximally entangled multipartite states from partially entangled ones by exploiting cross-Kerr nonlinearities to distinguish the parity of two polarization photons. Compared with the entanglement concentration schemes based on two-particle collective unitary evolution, this scheme does not require the parties to know accurately information about the partially entangled states--i.e., their coefficients. Moreover, it does not require the parties to possess sophisticated single-photon detectors, which makes this proto…
This paper considers the use an entanglement breaking channel in the construction of a secure bit-commitment protocol. It is shown that this can be done via a depolarizing quantum channel.
It is shown that spontaneous symmetry breaking does not modify the ground-state entanglement of two spins, as defined by the concurrence, in the XXZ- and the transverse field Ising-chain. Correlation function inequalities, valid in any dimensions for these models, are presented outlining the regimes where entanglement is unaffected by spontaneous symmetry breaking.
Quantum entanglement, a fundamental property ensuring security of key distribution and efficiency of quantum computing, is extremely sensitive to decoherence. Different procedures have been developed in order to recover entanglement after propagation over a noisy channel. However, besides a certain amount of noise, entanglement is completely lost. In this case the channel is called entanglement breaking and any multi-copy distillation methods cannot help to restore even a bit of entanglement. We report the experimental realization of a new method which restores entanglement from a single photo…
We present the generalized version of Wang's protocol[A.M.Wang, Phys.Rev.A 74,032317 (2006)] for the remote implementation(sometimes referred to as quantum remote control) of partially unknown quantum operations. The protocol only requires no more than half of the entanglements used in Bidirectional Quantum State Teleportation. We also propose a protocol for another form of quantum remote control. It can remotely implement a unitary operation which is a combination of the projective representations of a group. Moreover, we prove that the Schmidt rank of the entanglements cannot not be less tha…
We provide an evidence for the validity of strong monogamy inequality of multi-party quantum entanglement using square of convex-roof extended negativity(SCREN). We first consider a large class of multi-qudit mixed state that are in a partially coherent superposition of a generalized W-class state and the vacuum, and provide some useful properties about this class of states. We show that monogamy inequality of multi-qudit entanglement in terms of SCREN holds for this class of states. We further show that SCREN strong monogamy inequality of multi-qudit entanglement also holds for this class of …
We discuss the cases where local decoherence selectively degrades one type of entanglement more than other types. A typical case is called state ordering change, in which two input states with different amounts of entanglement undergoes a local decoherence and the state with the larger entanglement results in an output state with less entanglement than the other output state. We are also interested in a special case where the state with the larger entanglement evolves to a separable state while the other output state is still entangled, which we call selective entanglement breaking. For three-…
It shown that when one of the components of a product channel is entanglement breaking, the output state with maximal p-norm is always a product state. This result complements Shor's theorem that both minimal entropy and Holevo capacity are additive for entanglement breaking channels. It is also shown how Shor's results can be recovered from the p-norm results by considering their behavior for p close to one.
We give a representation for entanglement-breaking channels in separable Hilbert space that generalizes the "Kraus decomposition with rank one operators" and use it to describe the complementary channels. We also give necessary and sufficient condition of entanglement-breaking for a general quantum Gaussian channel. Application of this condition to one-mode channels provides several new cases where the additivity conjecture holds in full generality.
In this paper, we show that an arbitrary separable state can be the output of a certain entanglement-breaking channel corresponding exactly to the input of a maximally entangled state. A necessary and sufficient separability criterion and some sufficient separability criteria from entanglement-breaking channels are given.
The inevitable interaction between quantum systems and environment induces effects of decoherence which may be so strong as to destroy any initial entanglement between the systems, a phenomenon known as "entanglement breaking". Here we show the simplest examples where the combination of two entanglement-breaking channels into a joint correlated-noise environment reactivates the distribution of entanglement, with classes of entangled states which are perfectly transmitted from a middle station (Charlie) to two remote stations (Alice and Bob). Surprisingly, this reactivation is induced by the pr…
We investigate entanglement breaking times of Markovian evolutions in discrete and continuous time. In continuous time, we characterize which Markovian evolutions are eventually entanglement breaking, that is, evolutions for which there is a finite time after which any entanglement initially present has been destroyed by the noisy evolution. In the discrete time framework, we consider the entanglement breaking index, that is, the number of times a quantum channel has to be composed with itself before it becomes entanglement breaking. The PPT-square conjecture is that every PPT quantum channel …
Entanglement is essential to many quantum information applications, but it is easily destroyed by quantum decoherence arising from interaction with the environment. We report the first experimental demonstration of an entanglement-based protocol that is resilient to loss and noise which destroy entanglement. Specifically, despite channel noise 8.3 dB beyond the threshold for entanglement breaking, eavesdropping-immune communication is achieved between Alice and Bob when an entangled source is used, but no such immunity is obtainable when their source is classical. The results prove that entang…
Originated from the superposition principle in quantum mechanics, coherence has been extensively studied as a kind important resource in quantum information processing. We investigate the distinguishability of coherence-breaking channels with the help of quantum entanglement. By explicitly computing the minimal error probability of channel discrimination, it is shown that entanglement can enhance the capacity of coherence-breaking channel distinguishability with same types for some cases while cannot enhanced for some other cases. For coherence-breaking channels with different types, the chann…
We propose practical schemes for concentrating entanglement of a pair of unknown partially entangled Bell states and three-photon W states with cross-Kerr nonlinearity. In the schemes, utilizing local operations and classical communication, two separated parties can obtain one maximally entangled photon pair from two previously shared partially entangled photon pairs, and three separated parties can obtain one maximally entangled three-photon W state and a maximally entangled cluster state from two identical partially entangled three-photon W state with a certain success probability. Finally, …
Scalable Test of Genuine Multipartite Entanglement via Partially Randomized Measurements
本文提出基于部分随机测量的关联张量子 sector 长度判据，避免测量数目随量子比特数指数增长，在离子阱量子计算机上成功认证真正五体纠缠。
Entanglement swapping for partially entangled qudits and the role of quantum complementarity
本文研究了部分纠缠qudit的纠缠交换协议，探讨了量子互补性对纠缠分布的影响，并提出了更紧的纠缠上限猜想。
Entanglement-breaking channels are a quantum memory resource
本文证明纠缠破散通道在单系统多时间场景中仍为量子记忆资源，且在特定任务中优于经典记忆。
It is known that the minimal output entropy is additive for any product of entanglement breaking (EB) channels. The same is true for the Renyi entropy, where additivity is equivalent to multiplicativity of the $1 \rightarrow q$ norm for all $q \ge 1$. In this paper we consider the related question of multiplicativity of the $2 \rightarrow q$ norm for entanglement breaking channels. We prove that multiplicativity holds in this case for certain classes of EB channels, including both the CQ and QC channels.
We present two realistic entanglement concentration protocols (ECPs) for pure partially entangled photons. A partially entangled photon pair can be concentrated to a maximally entangled pair with only an ancillary single photon in a certain probability, while the conventional ones require two copies of partially entangled pairs at least. Our first protocol is implemented with linear optics and the second one is implemented with cross-Kerr nonlinearities. Compared with other ECPs, they do not need to know the accurate coefficients of the initial state. With linear optics, it is feasible with cu…
Entangled systems in experiments may be lost or offline in distributed quantum information processing. This inspires a general problem to characterize quantum operations which result in breaking of entanglement or not. Our goal in this work is to solve this problem both in single entanglement and network scenarios. We firstly propose a local model for characterizing all entangled states that are breaking for losing particles. This implies a simple criterion for witnessing single entanglement such as generalized GHZ states and Dicke states. It further provides an efficient witness for entangled…
We study the entanglement-breaking (EB) space, such that the entanglement of formation (EOF) of a bipartite quantum state is additive when its range is an EB subspace. We systematically construct the EB spaces in the Hilbert space $\bbC^m\otimes\bbC^3$, and the $2$-dimensional EB space in $\bbC^2\otimes\bbC^n$. We characterize the expression of two-qubit states of rank two with nonadditive EOF, if they exist. We further apply our results to construct EB spaces of an arbitrarily given dimensions. We show that the example in [PRL 89,027901(2002)] is a special case of our results. We further work…
A bipartite quantum channel represents the interaction between systems, generally allowing for exchange of information. A special class of bipartite channels are the no-signaling ones, which do not allow communication. In Ref. [1] it has been conjectured that all no-signaling channels are mixtures of entanglement-breaking and localizable channels, which require only local operations and entanglement. Here we provide the general realization scheme, giving a counterexample to the conjecture.
In the paper, we give a characterization of arbitrary $n$-mode Gaussian coherence breaking channels (GCBCs) and show the tensor product of a GCBC and arbitrary a Gaussian channel maps all input states into product states. The inclusion relation among GCBCs, Gaussian positive partial transpose channels (GPPTC), entanglement breaking channels (GEBC) and Gaussian classical-quantum channels (GCQC) is displayed. Finally, we prove that Gaussian classical ($χ$-) capacity for the tensor products of GCBCs and arbitrary Gaussian channels is additive.
Structural approximations to positive, but not completely positive maps are approximate physical realizations of these non-physical maps. They find applications in the design of direct entanglement detection methods. We show that many of these approximations, in the relevant case of optimal positive maps, define an entanglement breaking channel and, consequently, can be implemented via a measurement and state-preparation protocol. We also show how our findings can be useful for the design of better and simpler direct entanglement detection methods.
We describe a direct method to determine the negativity of an arbitrary two-qubit state in experiments. The method is derived by analyzing the relation between the purity, negativity, and a universal entanglement witness for two-qubit entanglement. We show how the negativity of a two-qubit state can be calculated from just three experimentally accessible moments of the partially transposed density matrix of a two-photon state. Moreover, we show that the negativity can be given as a function of only six invariants, which are linear combinations of nine invariants from the complete set of 21 fun…
We show that for the tensor product of an entanglement-breaking quantum channel with an arbitrary quantum channel, both the minimum entropy of an output of the channel and the Holevo-Schumacher-Westmoreland capacity are additive. In addition, for the tensor product of two arbitrary quantum channels, we give a bound involving entanglement of formation for the amount of subadditivity (for minimum entropy output) or superadditivity (for channel capacity) that can occur.
In this paper we give a general integral representation for separable states in the tensor product of infinite dimensional Hilbert spaces and provide the first example of separable states that are not countably decomposable. We also prove the structure theorem for the quantum communication channels that are entanglement-breaking, generalizing the finite-dimensional result of M. Horodecki, Ruskai and Shor. In the finite dimensional case such channels can be characterized as having the Kraus representation with operators of rank 1. The above example implies existence of infinite-dimensional enta…
We study finite-dimensional product Hilbert spaces, coupled spin systems, entanglement and energy level crossing. The Hamilton operators are based on the Pauli group. We show that swapping the interacting term can lead from unentangled eigenstates to entangled eigenstates and from an energy spectrum with energy level crossing to avoided energy level crossing.
When an entangled state is transformed into another one with probability one by local operations and classical communication, the quantity of entanglement decreases. This letter shows that entanglement lost in the manipulation can be partially recovered by an auxiliary entangled pair. As an application, a maximally entangled pair can be obtained from two partially entangled pairs with probability one. Finally, this recovery scheme reveals a fundamental property of entanglement relevant to the existence of incomparable states.
Quantum channels breaking entanglement, incompatibility, or nonlocality are defined as such because they are not useful for entanglement-based, one-sided device-independent, or device-independent quantum information processing, respectively. Here, we show that such breaking channels are related to complementary tests of macrorealism i.e., temporal separability, channel unsteerability, temporal unsteerability, and the temporal Bell inequality. To demonstrate this we first define a steerability-breaking channel, which is conceptually similar to entanglement and nonlocality-breaking channels and …
We propose a nonlocal entanglement concentration protocol (ECP) for $N$-photon systems in a partially entangled W state, resorting to some ancillary single photons and the parity-check measurement based on cross-Kerr nonlinearity. One party in quantum communication first performs a parity-check measurement on her photon in an $N$-photon system and an ancillary photon, and then she picks up the even-parity instance for obtaining the standard W state. When she obtains an odd-parity instance, the system is in a less-entanglement state and it is the resource in the next round of entanglement conce…
The occurrence of entanglement sudden death in the evolution of a bipartite system depends on both the initial state and the channel responsible for the evolution. An extreme case is that of entanglement braking channels, which are channels that acting on only one of the subsystems drives them to full disentanglement regardless of the initial state. In general, one can find certain combinations of initial states and channels acting on one or both subsystems that can result in entanglement sudden death or not. Neither the channel nor the initial state, but their combination, is responsible for …
We present a general method to derive entanglement breaking (EB) conditions for continuous-variable quantum gates. We start with an arbitrary entanglement witness, and reach an EB condition. The resultant EB condition is applicable not only for quantum channels but also for general quantum operations, namely, trace-non-increasing class of completely positive maps. We illustrate our method associated with a quantum benchmark based on the input ensemble of Gaussian distributed coherent states. We also exploit our idea for channels acting on finite dimensional systems and present a Schmidt-number…
We analyze quantum network primitives which are entanglement-breaking. We show superadditivity of quantum and classical capacity regions for quantum multiple-access channel and quantum butterfly network. Since the effects are especially visible at high noise they suggest that quantum information effects may be particularly helpful in the case of the networks with occasional high noise rates. To our knowledge the present effects provide the first qualitative borderline between superadditivities of bipartite and multipartite systems.
The determination of genuine entanglement is a central problem in quantum information processing. We investigate the tripartite state as the tensor product of two bipartite entangled states by merging two systems. We show that the tripartite state is a genuinely entangled state when the range of both bipartite states are entanglement-breaking subspaces. We further investigate the tripartite state when one of the two bipartite states has rank two. Our results provide the latest progress on a conjecture proposed in the paper [Yi Shen $\textit{et al}$, J. Phys. A 53, 125302 (2020)]. We apply our …
Entanglement concentration requires no classical communication, but the best prior art result for diluting to N copies of a partially entangled state requires an amount of communication on the order of sqrt(N) bits. Our main result is to prove this prior art result optimal up to a constant factor; any procedure for creating N partially entangled states from singlets requires Omega(sqrt(N)) bits of classical communication. Previously not even a constant bound was known for approximate entanglement transforms. We also prove a lower bound on the inefficiency of the process: to dilute singlets to …
Genuine multipartite entanglement underlies correlation experiments corroborating quantum mechanics and it is an expedient empowering many quantum technologies. One of many counterintuitive facets of genuine multipartite entanglement is its ability to exhibit an emergent character, that is, one can infer its presence in some multipartite states merely from a set of its separable marginals. Here, we show that the effect can be found also in the context of Gaussian states of bosonic systems. Specifically, we construct examples of multimode Gaussian states carrying genuine multipartite entangleme…
Entanglement breaking channels play a significant role in quantum information theory. In this work we investigate qubit channels through their property of `non-locality breaking', defined in a natural way but within the purview of CHSH nonlocality. This also provides a different perspective on the relationship between entanglement and nonlocality through the dual picture of quantum channels instead of through states. For a channel to be entanglement breaking it is sufficient to `break' the entanglement of maximally entangled states. We provide examples to show that for CHSH nonlocality breakin…
We investigate the nullspace structures of entanglement breaking channels, and related applications. We show that every operator space of trace zero matrices is the nullspace of an entanglement breaking channel. We derive a test for mixed unitarity of quantum channels based on complementary channel behaviour and entanglement breaking channel nullspaces. We identify conditions that guarantee the existence of private algebras for certain classes of entanglement breaking channels.
We report a bulk optics experiment demonstrating the possibility of restoring the entanglement distribution through noisy quantum channels by inserting a suitable unitary operation (filter) in the middle of the transmission process. We focus on two relevant classes of single-qubit channels consisting in repeated applications of rotated phase damping or rotated amplitude damping maps, both modeling the combined Hamiltonian and dissipative dynamics of the polarization state of single photons. Our results show that interposing a unitary filter between two noisy channels can significantly improve …
Nonlocal gate operation is based on sharing an ancillary pair of qubits in perfect entanglement. When the ancillary pair are partially entangled, the efficiency of the gate operation drops. Using general transformations, we devise probabilistic nonlocal gates, which perform the nonlocal operation conclusively when the ancillary pair are only partially entangled. We show that a controlled purification protocol can be implemented by the probabilistic nonlocal operation.
General formulas of entanglement concentration are derived by using an information-spectrum approach for the i.i.d. sequences and the general sequences of partially entangled pure states. That is, we derive general relations between the performance of the entanglement concentration and the eigenvalues of the partially traced state. The achievable rates with constant constraints and those with exponential constraints can be calculated from these formulas.
A simple scheme is presented for achieving effectively maximal pure-state entanglement between non-interacting atoms through purely collective decay and controlled symmetry breaking. The scheme requires no measurements or feedback or even knowledge of the initial states of the atoms. It relies on breaking the symmetry of the system Hamiltonian to ensure the existence of a unique attractive steady state and minimal control to achieve almost perfect overlap of this steady state with the maximally entangled singlet state. We demonstrate how our scheme can be implemented for two qubits encoded in …
We experimentally investigate the robustness of maximal and non-maximal Time-Bin entangled photons over distances up to 11 km. The entanglement is determined by controllable parameters and in all cases is shown to be robust, in that the photons maintain their degree of entanglement after transmission.
Quantum entanglement can be studied through the theory of completely positive maps in a number of ways, including by making use of the Choi-Jamilkowski isomorphism, which identifies separable states with entanglement breaking quantum channels, and optimal ensemble length with entanglement breaking rank. The multiplicative domain is an important operator structure in the theory of completely positive maps. We introduce a new technique to determine if a channel is entanglement breaking and to evaluate entanglement breaking rank, based on an analysis of multiplicative domains determined by comple…
Entanglement distribution in quantum networks via swapping of partially entangled pure states
研究通过交换协议在不同拓扑结构的量子网络中分发纠缠，探讨初始部分纠缠纯态在协议下的纠缠演变及生成最大纠缠态的成功概率。
Entanglement concentration of high-dimensional unknown partially entangled state
本文提出一种通用方案，通过交叉凯尔非线性、X-四频谐振子测量和单体投影测量，在鲍勃侧实现高维广义贝尔态的非本地纠缠浓缩，同时保留部分纠缠qubit态作为资源。
We introduce and study the entanglement breaking rank of an entanglement breaking channel. We show that the entanglement breaking rank of the channel $\mathfrak Z: M_d \to M_d$ defined by \begin{align*} \mathfrak Z(X) = \frac{1}{d+1}(X+\text{Tr}(X)\mathbb I_d) \end{align*} is $d^2$ if and only if there exists a symmetric informationally-complete POVM in dimension $d$.
Entanglement generation from degeneracy breaking of superradiant Liouvillian steady states by local operations
该研究利用简并非厄米微扰理论，通过引入非相干局域操作打破超辐射Liouvillian稳态简并性，在辐射体间产生并展现出鲁棒的纠缠，揭示了局域操作与纠缠产生的关联。
Instantaneous nonlocal quantum computation (INQC) evades apparent quantum and relativistic constraints and allows to attack generic quantum position verification (QPV) protocols (aiming at securely certifying the location of a distant prover) at an exponential entanglement cost. We consider adversaries sharing maximally entangled pairs of qudits and find low-dimensional INQC attacks against the simple practical family of QPV protocols based on single photons polarized at an angle $θ$. We find exact attacks against some rational angles, including some sitting outside of the Clifford hierarchy (…
We show that inseparability of quantum states can be partially broadcasted (copied, cloned) with the help of local operations, i.e. distant parties sharing an entangled pair of spin 1/2 states can generate two pairs of partially nonlocally entangled states using only local operations. This procedure can be viewed as an inversion of quantum purification procedures.
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