scholarly journals Strong NP-hardness of the quantum separability problem

2010 ◽  
Vol 10 (3&4) ◽  
pp. 343-360 ◽  
Author(s):  
S. Gharibian
Keyword(s):  
Lower Bound ◽  
Density Matrix ◽  
Quantum State ◽  
Quantum States ◽  
Entangled State ◽  
Completely Positive ◽  
Linear Map ◽  
Separability Problem ◽  
Np Hardness ◽  
Simple Combination

Given the density matrix $\rho$ of a bipartite quantum state, the quantum separability problem asks whether $\rho$ is entangled or separable. In 2003, Gurvits showed that this problem is NP-hard if $\rho$ is located within an inverse exponential (with respect to dimension) distance from the border of the set of separable quantum states. In this paper, we extend this NP-hardness to an inverse polynomial distance from the separable set. The result follows from a simple combination of works by Gurvits, Ioannou, and Liu. We apply our result to show (1) an immediate lower bound on the maximum distance between a bound entangled state and the separable set (assuming $\rm{P}\neq\rm{ NP}$), and (2) NP-hardness for the problem of determining whether a completely positive trace-preserving linear map is entanglement-breaking.

MULTIPARTY REMOTELY PREPARING MULTIPARTITE EQUATORIAL ENTANGLED STATES IN HIGH DIMENSIONS

2011 ◽  
Vol 09 (06) ◽  
pp. 1437-1448
Author(s):  
YI-BAO LI ◽  
KUI HOU ◽  
SHOU-HUA SHI
Keyword(s):  
Quantum State ◽  
Quantum Channel ◽  
Success Probability ◽  
Quantum States ◽  
Remote State Preparation ◽  
Entangled States ◽  
Entangled State ◽  
High Dimensions ◽  
Original State ◽  
State Preparation

We propose two kinds of schemes for multiparty remote state preparation (MRSP) of the multiparticle d-dimensional equatorial quantum states by using partial entangled state as the quantum channel. Unlike more remote state preparation scheme which only one sender knows the original state to be remotely prepared, the quantum state is shared by two-party or multiparty in this scheme. We show that if and only if all the senders agree to collaborate with each other, the receiver can recover the original state with certain probability. It is found that the total success probability of MRSP is only by means of the smaller coefficients of the quantum channel and the dimension d.

Experimental realization of quantum controlled teleportation of arbitrary two-qubit state via a five-qubit entangled state

2021 ◽  
Author(s):  
Xiao-Fang Liu ◽  
Dong-Fen Li ◽  
Yun-Dan Zheng ◽  
Xiao-Long Yang ◽  
Jie Zhou ◽  
...  
Keyword(s):  
Density Matrix ◽  
Quantum State ◽  
Bell State ◽  
Third Party ◽  
Controlled Teleportation ◽  
Entangled State ◽  
Entanglement Measure ◽  
Experimental Realization ◽  
Operation Process ◽  
Photonic States

Abstract Quantum controlled teleportation is the transmission of the quantum state under the supervision of a third party. This paper presents a theoretical and experimental combination of an arbitrary two-qubit quantum controlled teleportation scheme. In the scheme, the sender Alice only needs to perform two Bell state measurements, and the receiver Bob can perform the appropriate unitary operation to reconstruct arbitrary two-qubit states under the control of the supervisor Charlie. We verified the operation process of the scheme on the IBM Quantum Experience platform and further checked the accuracy of the transmitted quantum state by performing quantum state tomography. Meanwhile, good fidelity is obtained by calculating the theoretical density matrix and the experimental density matrix. We also introduced a sequence of photonic states to analyze the possible intercept-replace-resend, intercept-measure-resend, and entanglement-measure-resend attacks on this scheme. The results proved that our scheme is highly secure.

scholarly journals Experimental creation of multi-photon high-dimensional layered quantum states

2020 ◽  
Vol 6 (1) ◽  
Author(s):  
Xiao-Min Hu ◽  
Wen-Bo Xing ◽  
Chao Zhang ◽  
Bi-Heng Liu ◽  
Matej Pivoluska ◽  
...  
Keyword(s):  
Quantum Information ◽  
Quantum Entanglement ◽  
Quantum State ◽  
Quantum States ◽  
High Dimensional ◽  
Entangled States ◽  
Entangled State ◽  
Quantum Network ◽  
Quantum Networks ◽  
Qubit States

Abstract Quantum entanglement is one of the most important resources in quantum information. In recent years, the research of quantum entanglement mainly focused on the increase in the number of entangled qubits or the high-dimensional entanglement of two particles. Compared with qubit states, multipartite high-dimensional entangled states have beneficial properties and are powerful for constructing quantum networks. However, there are few studies on multipartite high-dimensional quantum entanglement due to the difficulty of creating such states. In this paper, we experimentally prepared a multipartite high-dimensional state $$\left|{\Psi }_{442}\right\rangle =\frac{1}{2}(\left|000\right\rangle +\left|110\right\rangle +\left|221\right\rangle +\left|331\right\rangle )$$ Ψ 442 = 1 2 ( 000 + 110 + 221 + 331 ) by using the path mode of photons. We obtain the fidelity F = 0.854 ± 0.007 of the quantum state, which proves a real multipartite high-dimensional entangled state. Finally, we use this quantum state to demonstrate a layered quantum network in principle. Our work highlights another route toward complex quantum networks.

scholarly journals A SUFFICIENT AND NECESSARY CONDITION FOR SUPERDENSE CODING OF QUANTUM STATES

2008 ◽  
Vol 06 (05) ◽  
pp. 1115-1125 ◽  
Author(s):  
DAOWEN QIU
Keyword(s):  
Lower Bound ◽  
Success Probability ◽  
Quantum States ◽  
Entangled States ◽  
Necessary Condition ◽  
Entangled State ◽  
Maximally Entangled State ◽  
High Success Probability ◽  
Sufficient And Necessary Condition ◽  
Arbitrary Quantum

Recently, Harrow et al. [Phys. Rev. Lett.92 (2004) 187901] gave a method for preparing an arbitrary quantum state with high success probability by physically transmitting some qubits, and by consuming a maximally entangled state, together with exhausting some shared random bits. In this paper, we discover that some states are impossible to be perfectly prepared by Alice and Bob initially sharing some entangled states. In particular, we present a sufficient and necessary condition for the states being enabled to be exactly prepared with probability equal to unity, in terms of the initial entangled states (maybe nonmaximally). In contrast, if the initially shared entanglement is maximal, then the probabilities for preparing these quantum states are smaller than unity. Furthermore, the lower bound on the probability for preparing some states are derived.

Assigning Values and States

2017 ◽  
Author(s):  
Richard Healey
Keyword(s):  
Quantum State ◽  
Density Operator ◽  
Entangled State ◽  
Physical Situation ◽  
Born Rule ◽  
Correct Assignment ◽  
Significant Magnitude ◽  
Good Advice ◽  
Empirical Significance ◽  
Important Idea

If a quantum state is prescriptive then what state should an agent assign, what expectations does this justify, and what are the grounds for those expectations? I address these questions and introduce a third important idea—decoherence. A subsystem of a system assigned an entangled state may be assigned a mixed state represented by a density operator. Quantum state assignment is an objective matter, but the correct assignment must be relativized to the physical situation of an actual or hypothetical agent for whom its prescription offers good advice, since differently situated agents have access to different information. However this situation is described, it is true, empirically significant magnitude claims that make the description correct, while others provide the objective grounds for the agent’s expectations. Quantum models of environmental decoherence certify the empirical significance of these magnitude claims while also licensing application of the Born rule to others without mentioning measurement.

Entanglement

2017 ◽  
Author(s):  
Richard Healey
Keyword(s):  
Quantum Theory ◽  
Quantum State ◽  
Physical Condition ◽  
Physical System ◽  
Polarization State ◽  
Quantum Systems ◽  
Ghz State ◽  
Mathematical Representation ◽  
Entangled State ◽  
Physical Relation

Often a pair of quantum systems may be represented mathematically (by a vector) in a way each system alone cannot: the mathematical representation of the pair is said to be non-separable: Schrödinger called this feature of quantum theory entanglement. It would reflect a physical relation between a pair of systems only if a system’s mathematical representation were to describe its physical condition. Einstein and colleagues used an entangled state to argue that its quantum state does not completely describe the physical condition of a system to which it is assigned. A single physical system may be assigned a non-separable quantum state, as may a large number of systems, including electrons, photons, and ions. The GHZ state is an example of an entangled polarization state that may be assigned to three photons.

Time fractional evolution of a single quantum state and entangled state

2021 ◽  
Vol 147 ◽  
pp. 110930
Author(s):  
Chuanjin Zu ◽  
Yanming Gao ◽  
Xiangyang Yu
Keyword(s):  
Quantum State ◽  
Entangled State ◽  
Single Quantum

scholarly journals Gaussian quantum states can be disentangled using symplectic rotations

2021 ◽  
Vol 111 (3) ◽  
Author(s):  
Maurice A. de Gosson
Keyword(s):  
Quantum State ◽  
Covariance Matrices ◽  
Quantum States ◽  
Weyl Quantization ◽  
Symplectic Transformation ◽  
Metaplectic Operator

AbstractWe show that every Gaussian mixed quantum state can be disentangled by conjugation with a passive symplectic transformation, that is a metaplectic operator associated with a symplectic rotation. The main tools we use are the Werner–Wolf condition on covariance matrices and the symplectic covariance of Weyl quantization. Our result therefore complements a recent study by Lami, Serafini, and Adesso.

scholarly journals Purification and redistribution of entanglement via single local filtering

2014 ◽  
Vol 12 (01) ◽  
pp. 1450004 ◽  
Author(s):  
K. O. Yashodamma ◽  
P. J. Geetha ◽  
Sudha
Keyword(s):  
Quantum State ◽  
The State ◽  
Quantum States ◽  
Local Action ◽  
Entanglement Transfer ◽  
Local Filtering

The effect of filtering operation with respect to purification and concentration of entanglement in quantum states are discussed in this paper. It is shown, through examples, that the local action of the filtering operator on a part of the composite quantum state allows for purification of the remaining part of the state. The redistribution of entanglement in the subsystems of a noise affected state is shown to be due to the action of local filtering on the non-decohering part of the system. The varying effects of the filtering parameter, on the entanglement transfer between the subsystems, depending on the choice of the initial quantum state is illustrated.

Sign in / Sign up

Export Citation Format

Share Document