Unambiguous discrimination of two nonorthogonal multipartite states using local measurements and classical communication (Invited Paper)

2005 ◽  
Author(s):  
Jihane Mimih ◽  
Mark Hillery
Keyword(s):  
Classical Communication ◽  
Unambiguous Discrimination ◽  
Local Measurements ◽  
Multipartite States

A combinatorial approach for studying local operations and classical communication transformations of multipartite states

2005 ◽  
Vol 46 (12) ◽  
pp. 122105 ◽  
Author(s):  
Sudhir Kumar Singh ◽  
Sudebkumar Prasant Pal ◽  
Somesh Kumar ◽  
R. Srikanth
Keyword(s):  
Combinatorial Approach ◽  
Classical Communication ◽  
Multipartite States

scholarly journals QUANTUM SECURE CONDITIONAL DIRECT COMMUNICATION VIA EPR PAIRS

2005 ◽  
Vol 16 (08) ◽  
pp. 1293-1301 ◽  
Author(s):  
TING GAO ◽  
FENGLI YAN ◽  
ZHIXI WANG
Keyword(s):  
Secure Communication ◽  
Secret Message ◽  
Quantum Channels ◽  
Classical Communication ◽  
Direct Communication ◽  
Classical Information ◽  
Epr Pairs ◽  
Unitary Transformations ◽  
Local Measurements ◽  
The Common

Two schemes for quantum secure conditional direct communication are proposed, where a set of EPR pairs of maximally entangled particles in Bell states, initially made by the supervisor Charlie, but shared by the sender Alice and the receiver Bob, functions as quantum information channels for faithful transmission. After insuring the security of the quantum channel and obtaining the permission of Charlie (i.e., Charlie is trustworthy and cooperative, which means the "conditional" in the two schemes), Alice and Bob begin their private communication under the control of Charlie. In the first scheme, Alice transmits secret message to Bob in a deterministic manner with the help of Charlie by means of Alice's local unitary transformations, both Alice and Bob's local measurements, and both of Alice and Charlie's public classical communication. In the second scheme, the secure communication between Alice and Bob can be achieved via public classical communication of Charlie and Alice, and the local measurements of both Alice and Bob. The common feature of these protocols is that the communications between two communication parties Alice and Bob depend on the agreement of the third side Charlie. Moreover, transmitting one bit secret message, the sender Alice only needs to apply a local operation on her one qubit and send one bit classical information. We also show that the two schemes are completely secure if quantum channels are perfect.

scholarly journals Locally restricted measurements on a multipartite quantum system: data hiding is generic

2015 ◽  
pp. 513-540
Author(s):  
Guillaume Aubrun ◽  
Cecilia Lancien
Keyword(s):  
Quantum System ◽  
Data Hiding ◽  
Quantum Measurements ◽  
Quantum States ◽  
Classical Communication ◽  
Substantial Loss ◽  
Local Measurements ◽  
System Data

We study the distinguishability norms associated to families of locally restricted POVMs on multipartite systems. These norms (introduced by Matthews, Wehner and Winter) quantify how quantum measurements, subject to locality constraints, perform in the task of discriminating two multipartite quantum states. We mainly address the following question regarding the behaviour of these distinguishability norms in the highdimensional regime: On a bipartite space, what are the relative strengths of standard classes of locally restricted measurements? We show that the class of PPT measurements typically performs almost as well as the class of all measurements whereas restricting to local measurements and classical communication, or even just to separable measurements, implies a substantial loss. We also provide examples of state pairs which can be perfectly distinguished by local measurements if (one-way) classical communication is allowed between the parties, but very poorly without it. Finally, we study how many POVMs are needed to distinguish almost perfectly any pair of states on C^d, showing that the answer is exp(Θ(d^2 )).

scholarly journals Local transformations of multiple multipartite states

2021 ◽  
Vol 11 (2) ◽  
Author(s):  
Antoine Neven ◽  
David Kenworthy Gunn ◽  
Martin Hebenstreit ◽  
Barbara Kraus
Keyword(s):  
Single Copy ◽  
Partial Ordering ◽  
Multipartite Entanglement ◽  
Entanglement Measure ◽  
Classical Communication ◽  
Wide Range ◽  
Pure States ◽  
Multipartite States ◽  
The Individual ◽  
Probabilistic Protocols

Understanding multipartite entanglement is vital, as it underpins a wide range of phenomena across physics. The study of transformations of states via Local Operations assisted by Classical Communication (LOCC) allows one to quantitatively analyse entanglement, as it induces a partial order in the Hilbert space. However, it has been shown that, for systems with fixed local dimensions, this order is generically trivial, which prevents relating multipartite states to each other with respect to any entanglement measure. In order to obtain a non-trivial partial ordering, we study a physically motivated extension of LOCC: multi-state LOCC. Here, one considers simultaneous LOCC transformations acting on a finite number of entangled pure states. We study both multipartite and bipartite multi-state transformations. In the multipartite case, we demonstrate that one can change the stochastic LOCC (SLOCC) class of the individual initial states by only applying Local Unitaries (LUs). We show that, by transferring entanglement from one state to the other, one can perform state conversions not possible in the single copy case; provide examples of multipartite entanglement catalysis; and demonstrate improved probabilistic protocols. In the bipartite case, we identify numerous non-trivial LU transformations and show that the source entanglement is not additive. These results demonstrate that multi-state LOCC has a much richer landscape than single-state LOCC.

scholarly journals Quantum nonlocality without entanglement depending on nonzero prior probabilities in optimal unambiguous discrimination

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Donghoon Ha ◽  
Jeong San Kim
Keyword(s):  
Quantum State ◽  
Quantum States ◽  
Quantum Nonlocality ◽  
Quantum State Discrimination ◽  
Classical Communication ◽  
Minimum Error ◽  
Prior Probabilities ◽  
Separable States ◽  
Unambiguous Discrimination ◽  
State Discrimination

AbstractNonlocality without entanglement(NLWE) is a nonlocal phenomenon that occurs in quantum state discrimination of multipartite separable states. In the discrimination of orthogonal separable states, the term NLWE is used when the quantum states cannot be discriminated perfectly by local operations and classical communication. In this case, the occurrence of NLWE is independent of nonzero prior probabilities of quantum states being prepared. Recently, it has been found that the occurrence of NLWE can depend on nonzero prior probabilities in minimum-error discrimination of nonorthogonal separable states. Here, we show that even in optimal unambiguous discrimination, the occurrence of NLWE can depend on nonzero prior probabilities. We further show that NLWE can occur regardless of nonzero prior probabilities, even if only one state can be locally discriminated without error. Our results provide new insights into classifying sets of multipartite quantum states in terms of quantum state discrimination.

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