SHARING OF D-DIMENSIONAL QUANTUM STATES

2012 ◽  
Vol 10 (02) ◽  
pp. 1250003 ◽  
Author(s):  
OMAR JIMÉNEZ ◽  
CARLOS MUÑOZ ◽  
ANDREI B. KLIMOV ◽  
ALDO DELGADO
Keyword(s):  
Quantum State ◽  
Success Probability ◽  
Quantum States ◽  
Quantum State Sharing ◽  
Quantum Channels ◽  
Quantum State Discrimination ◽  
State Discrimination ◽  
Ideal Quantum

We propose a scheme for the deterministic sharing arbitrary qudit states among three distant parties and characterize the set of ideal quantum channels. We also show that the use of non-ideal quantum channels for quantum state sharing can be related to the problem of quantum state discrimination. This allows us to formulate a protocol which leads to perfect quantum state sharing with a finite success probability.

scholarly journals Support Vector Machines with Quantum State Discrimination

2021 ◽  
Vol 3 (3) ◽  
pp. 482-499
Author(s):  
Roberto Leporini ◽  
Davide Pastorello
Keyword(s):  
Support Vector Machines ◽  
Quantum State ◽  
Quantum States ◽  
Support Vector ◽  
Classification Algorithms ◽  
Quantum State Discrimination ◽  
Classification Problems ◽  
Density Operators ◽  
State Discrimination ◽  
Vector Machines

We analyze possible connections between quantum-inspired classifications and support vector machines. Quantum state discrimination and optimal quantum measurement are useful tools for classification problems. In order to use these tools, feature vectors have to be encoded in quantum states represented by density operators. Classification algorithms inspired by quantum state discrimination and implemented on classic computers have been recently proposed. We focus on the implementation of a known quantum-inspired classifier based on Helstrom state discrimination showing its connection with support vector machines and how to make the classification more efficient in terms of space and time acting on quantum encoding. In some cases, traditional methods provide better results. Moreover, we discuss the quantum-inspired nearest mean classification.

scholarly journals PT -symmetric quantum state discrimination

2013 ◽  
Vol 371 (1989) ◽  
pp. 20120160 ◽  
Author(s):  
Carl M. Bender ◽  
Dorje C. Brody ◽  
João Caldeira ◽  
Uwe Günther ◽  
Bernhard K. Meister ◽  
...  
Keyword(s):  
Quantum Mechanics ◽  
Quantum State ◽  
Success Probability ◽  
Inner Product ◽  
Perfect State ◽  
Quantum State Discrimination ◽  
Single Measurement ◽  
State Discrimination ◽  
Symmetric Quantum ◽  
Ordinary Quantum

The objective of this paper is to explain and elucidate the formalism of quantum mechanics by applying it to a well-known problem in conventional Hermitian quantum mechanics, namely the problem of state discrimination. Suppose that a system is known to be in one of two quantum states, | ψ 1 〉 or | ψ 2 〉. If these states are not orthogonal, then the requirement of unitarity forbids the possibility of discriminating between these two states with one measurement; that is, determining with one measurement what state the system is in. In conventional quantum mechanics, there is a strategy in which successful state discrimination can be achieved with a single measurement but only with a success probability p that is less than unity. In this paper, the state-discrimination problem is examined in the context of quantum mechanics and the approach is based on the fact that a non-Hermitian -symmetric Hamiltonian determines the inner product that is appropriate for the Hilbert space of physical states. It is shown that it is always possible to choose this inner product so that the two states | ψ 1 〉 and | ψ 2 〉 are orthogonal. Using quantum mechanics, one cannot achieve a better state discrimination than in ordinary quantum mechanics, but one can instead perform a simulated quantum state discrimination, in which with a single measurement a perfect state discrimination is realized with probability  p .

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.

scholarly journals Protocol for unambiguous quantum state discrimination using quantum coherence

2021 ◽  
Vol 21 (11-12) ◽  
pp. 931-944
Author(s):  
Sunho Kim ◽  
Longsuo Li ◽  
Asutosh Kumar ◽  
Chunhe Xiong ◽  
Sreetama Das ◽  
...  
Keyword(s):  
Quantum Entanglement ◽  
Quantum State ◽  
Optimal Strategy ◽  
Quantum Coherence ◽  
Quantum States ◽  
Quantum State Discrimination ◽  
State Discrimination

Roa et al. showed that quantum state discrimination between two nonorthogonal quantum states does not require quantum entanglement but quantum dissonance only. We find that quantum coherence can also be utilized for unambiguous quantum state discrimination. We present a protocol and quantify the required coherence for this task. We discuss the optimal unambiguous quantum state discrimination strategy in some cases. In particular, our work illustrates an avenue to find the optimal strategy for discriminating two nonorthogonal quantum states by measuring quantum coherence.

scholarly journals Understanding of Various Type of Unambiguous Discrimination in View of Coherence Distribution

Entropy ◽  
2020 ◽  
Vol 22 (12) ◽  
pp. 1422
Author(s):  
Min Namkung ◽  
Younghun Kwon
Keyword(s):  
Quantum Information ◽  
Quantum State ◽  
Quantum Key Distribution ◽  
Key Distribution ◽  
Quantum States ◽  
Quantum State Discrimination ◽  
Mixed States ◽  
Generalized Measurement ◽  
Unambiguous Discrimination ◽  
State Discrimination

Unambiguous quantum state discrimination is a strategy where the conclusive result can always be trusted. This strategy is very important, since it can be used for various quantum information protocols, including quantum key distribution. However, in the view of quantumness, it is not clear what is going on in performing unambiguous quantum state discrimination. To answer the question, we investigate coherence distribution when unambiguous discrimination is performed by generalized measurement. Specially, we study coherence distribution in three cases, which consist of unambiguous quantum state discrimination, sequential quantum state discrimination, and assisted optimal discrimination, which are considered to be a family of unambiguous quantum state discrimination. In this investigation, we show that the structure of generalized measurements performing various types of unambiguous quantum state discrimination can be understood in terms of coherence distribution. Our result is not limited to the discrimination of two pure quantum states, but it is extended to the discrimination of two mixed states.

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.

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