Entanglement of Assistance is not an entanglement monotone

The entanglement of assistance quantifies the entanglement that can be generated between two parties, Alice and Bob, given assistance from a third party, Charlie, when the three share a tripartite state and where the assistance consists of Charlie initially performing a measurement on his share and communicating the result to Alice and Bob through a one-way classical channel. We argue that if this quantity is to be considered an operational measure of entanglement, then it must be understood to be a tripartite rather than a bipartite measure. We compare it with a distinct tripartite measure that quantifies the entanglement that can be generated between Alice and Bob when they are allowed to make use of a two-way classical channel with Charlie. We show that the latter quantity, which we call the entanglement of collaboration, can be greater than the entanglement of assistance. This demonstrates that the entanglement of assistance (considered as a tripartite measure of entanglement), and its multipartite generalizations such as the localizable entanglement, are not entanglement monotones, thereby undermining their operational significance.The entanglement of assistance quantifies the entanglement that can be generated between two parties, Alice and Bob, given assistance from a third party, Charlie, when the three share a tripartite state and where the assistance consists of Charlie initially performing a measurement on his share and communicating the result to Alice and Bob through a one-way classical channel. We argue that if this quantity is to be considered an operational measure of entanglement, then it must be understood to be a tripartite rather than a bipartite measure. We compare it with a distinct tripartite measure that quantifies the entanglement that can be generated between Alice and Bob when they are allowed to make use of a two-way classical channel with Charlie. We show that the latter quantity, which we call the entanglement of collaboration, can be greater than the entanglement of assistance. This demonstrates that the entanglement of assistance (considered as a tripartite measure of entanglement), and its multipartite generalizations such as the localizable entanglement, are not entanglement monotones, thereby undermining their operational significance.

arXiv:quant-ph/0512139Physical Review AJun 26, 200644 citations

Entanglement of collaboration

Gilad Gour

The entanglement of collaboration (EOC) quantifies the maximum amount of entanglement that can be generated between two parties, $A$ and $B$ , given collaboration with $N\ensuremath{-}2$ other parties, when the $N$ parties share a multipartite (possibly mixed) state and where the collaboration consists of local operations and classical communication by all parties. The localizable entanglement (LE) is defined similarly except that $A$ and $B$ do not participate in the effort to generate bipartite entanglement. We compare between these two operational definitions and find sufficient conditions for which the EOC is equal to the LE. In particular, we find that the two are equal whenever they are measured by the concurrence or by one of its generalizations called the G-concurrence. We also find a simple expression for the LE in terms of the Jamiolkowski isomorphism and prove that it is convex.The entanglement of collaboration (EOC) quantifies the maximum amount of entanglement that can be generated between two parties, $A$ and $B$, given collaboration with $N\ensuremath{-}2$ other parties, when the $N$ parties share a multipartite (possibly mixed) state and where the collaboration consists of local operations and classical communication by all parties. The localizable entanglement (LE) is defined similarly except that $A$ and $B$ do not participate in the effort to generate bipartite entanglement. We compare between these two operational definitions and find sufficient conditions for which the EOC is equal to the LE. In particular, we find that the two are equal whenever they are measured by the concurrence or by one of its generalizations called the G-concurrence. We also find a simple expression for the LE in terms of the Jamiolkowski isomorphism and prove that it is convex.

arXiv:quant-ph/0610132Physical Review ANov 6, 200616 citations

Weaker entanglement between two parties guarantees stronger entanglement with a third party

Masahito Hayashi, Lin Chen

The monogamy of entanglement is one of the basic quantum mechanical features, which says that when two partners Alice and Bob are more entangled then either of them has to be less entangled with the third party. Here we qualitatively present the converse monogamy of entanglement: given a tripartite pure system and when Alice and Bob are weakly entangled, then either of them is generally strongly entangled with the third party. Our result leads to the classification of tripartite pure states based on bipartite reduced density operators, which is an effective way to this longstanding problem compared to the means by stochastic local operations and classical communications. We also systematically indicate the structure of the classified states and generate them.The monogamy of entanglement is one of the basic quantum mechanical features, which says that when two partners Alice and Bob are more entangled then either of them has to be less entangled with the third party. Here we qualitatively present the converse monogamy of entanglement: given a tripartite pure system and when Alice and Bob are weakly entangled, then either of them is generally strongly entangled with the third party. Our result leads to the classification of tripartite pure states based on bipartite reduced density operators, which is an effective way to this longstanding problem compared to the means by stochastic local operations and classical communications. We also systematically indicate the structure of the classified states and generate them.

arXiv:1102.0439Physical Review AJul 21, 201135 citations

Multiparty Zero-Error Classical Channel Coding With Entanglement

Teresa Piovesan, Giannicola Scarpa, Christian Schaffner

We study the effects of quantum entanglement on the performance of two classical zero-error communication tasks among multiple parties. Both tasks are generalizations of the two-party zero-error channel-coding problem, where a sender and a receiver want to perfectly communicate messages through a one-way classical noisy channel. If the two parties are allowed to share entanglement, there are several positive results that show the existence of channels for which they can communicate strictly more than what they could do with classical resources. In the first task, one sender wants to communicate a common message to multiple receivers. We show that if the number of receivers is greater than a certain threshold then entanglement does not allow for an improvement in the communication for any finite number of uses of the channel. On the other hand, when the number of receivers is fixed, we exhibit a class of channels for which entanglement gives an advantage. The second problem we consider features multiple collaborating senders and one receiver. Classically, cooperation among the senders might allow them to communicate on average more messages than the sum of their individual possibilities. We show that whenever a channel allows single-sender entanglement-assisted advantage, then the gain extends also to the multisender case. Furthermore, we show that entanglement allows for a peculiar amplification of information which cannot happen classically, for a fixed number of uses of the channels.We study the effects of quantum entanglement on the performance of two classical zero-error communication tasks among multiple parties. Both tasks are generalizations of the two-party zero-error channel-coding problem, where a sender and a receiver want to perfectly communicate messages through a one-way classical noisy channel. If the two parties are allowed to share entanglement, there are several positive results that show the existence of channels for which they can communicate strictly more than what they could do with classical resources. In the first task, one sender wants to communicate a common message to multiple receivers. We show that if the number of receivers is greater than a certain threshold then entanglement does not allow for an improvement in the communication for any finite number of uses of the channel. On the other hand, when the number of receivers is fixed, we exhibit a class of channels for which entanglement gives an advantage. The second problem we consider features multiple collaborating senders and one receiver. Classically, cooperation among the senders might allow them to communicate on average more messages than the sum of their individual possibilities. We show that whenever a channel allows single-sender entanglement-assisted advantage, then the gain extends also to the multisender case. Furthermore, we show that entanglement allows for a peculiar amplification of information which cannot happen classically, for a fixed number of uses of the channels.

arXiv:1403.5003IEEE Transactions on Information TheoryDec 10, 20144 citations

Deterministic entanglement of assistance and monogamy constraints

Gilad Gour, DAVID A. MEYER, Barry C. Sanders

Certain quantum-information tasks require entanglement of assistance, namely, a reduction of a tripartite entangled state to a bipartite entangled state via local measurements. We establish that concurrence of assistance (COA) identifies capabilities of and limitations to producing pure bipartite entangled states from pure tripartite entangled states and prove that COA is an entanglement monotone for $(2\ifmmode\times\else\texttimes\fi{}2\ifmmode\times\else\texttimes\fi{}n)$-dimensional pure states. Moreover, if the COA for the pure tripartite state is at least as large as the concurrence of the desired pure bipartite state, then the former may be transformed to the latter via local operations and classical communication, and we calculate the maximum probability for this transformation when this condition is not met.Certain quantum-information tasks require entanglement of assistance, namely, a reduction of a tripartite entangled state to a bipartite entangled state via local measurements. We establish that concurrence of assistance (COA) identifies capabilities of and limitations to producing pure bipartite entangled states from pure tripartite entangled states and prove that COA is an entanglement monotone for $(2\ifmmode\times\else\texttimes\fi{}2\ifmmode\times\else\texttimes\fi{}n)$-dimensional pure states. Moreover, if the COA for the pure tripartite state is at least as large as the concurrence of the desired pure bipartite state, then the former may be transformed to the latter via local operations and classical communication, and we calculate the maximum probability for this transformation when this condition is not met.

arXiv:quant-ph/0505091Physical Review AOct 26, 2005108 citations

Quantum secure direct communication with line-based quantum walks and decoy photons

Si-si Liu, Yanyan Feng, Jie Li +3 more

Quantum secure direct communication (QSDC) enables direct private message transmission over quantum channels without pre-shared keys. This paper proposes a QSDC protocol based on two-step line-based quantum walks (QWs), which involves sender Alice, receiver Bob and an untrusted third party Charlie, and three stages consisting of preparing, checking quantum channel and communicating secret messages. In the first stage, Bob generates entangled states as the desired quantum channel via one-step QW and prepares decoy photons for the subsequent security checking of the quantum channel; In the second stage, Bob first sends a sequence comprising the photons from the entangled states and Bob’s decoy photons to Alice, who forwards Bob’s decoy photons along with her own decoy photons to Charlie for measurement, with Alice and Bob verifying security by comparing the measurement outcomes; In the third stage, Alice prepares a sequence of photons as coin state for encoding messages to be communicated, which along with the prepared entangled states form a quantum teleportation system, which completes the transmission of the messages under the dominance of another-step QW. Security analyses show the suggested protocol can resist against intercept-and-resend and measure-and-resend attacks, promoting the QSDC’s practicality via QW-based entanglement generation, simplified measurement operations and security checking under the assistance of the third party Charlie.Quantum secure direct communication (QSDC) enables direct private message transmission over quantum channels without pre-shared keys. This paper proposes a QSDC protocol based on two-step line-based quantum walks (QWs), which involves sender Alice, receiver Bob and an untrusted third party Charlie, and three stages consisting of preparing, checking quantum channel and communicating secret messages. In the first stage, Bob generates entangled states as the desired quantum channel via one-step QW and prepares decoy photons for the subsequent security checking of the quantum channel; In the second stage, Bob first sends a sequence comprising the photons from the entangled states and Bob’s decoy photons to Alice, who forwards Bob’s decoy photons along with her own decoy photons to Charlie for measurement, with Alice and Bob verifying security by comparing the measurement outcomes; In the third stage, Alice prepares a sequence of photons as coin state for encoding messages to be communicated, which along with the prepared entangled states form a quantum teleportation system, which completes the transmission of the messages under the dominance of another-step QW. Security analyses show the suggested protocol can resist against intercept-and-resend and measure-and-resend attacks, promoting the QSDC’s practicality via QW-based entanglement generation, simplified measurement operations and security checking under the assistance of the third party Charlie.

International Conference on Computing, Communication, Perception and Quantum Technology (CCPQT)Oct 24, 20250 citations

The entanglement of collaboration (EOC) quantifies the maximum amount of entanglement that can be generated between two parties,

A

and

B

, given collaboration with $N\ensuremath{-}2$ other parties, when the

N

parties share a multipartite (possibly mixed) state and where the collaboration consists of local operations and classical communication by all parties. The localizable entanglement (LE) is defined similarly except that

A

and

B

do not participate in the effort to generate bipartite entanglement. We compare between these two operational definitions and find sufficient conditions for which the EOC is equal to the LE. In particular, we find that the two are equal whenever they are measured by the concurrence or by one of its generalizations called the G-concurrence. We also find a simple expression for the LE in terms of the Jamiolkowski isomorphism and prove that it is convex.